optimal treatment policies for pelvic organ prolapse in women · 2019/9/4 · author: optimal...

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Optimal Treatment Policies for Pelvic OrganProlapse in Women

Yueran Zhuo, Senay SolakIsenberg School of Management, University of Massachusetts Amherst

[email protected], [email protected]

Oz HarmanliDepartment of Obstetrics, Gynecology, and Reproductive Sciences, Yale School of Medicine

[email protected]

Keisha A. JonesDepartment of Obstetrics and Gynecology, Tufts University School of Medicine Baystate Medical Center

[email protected]

Pelvic organ prolapse (POP) is a very common gynecological disorder greatly affecting the quality of life

(QoL) of females in the society. Studies have shown that approximately 40% of women in the U.S. have POP

that requires medical intervention. In clinical practice there are four treatment options for POP: watchful

waiting, conservative treatment, reconstructive surgery, and obliterative surgery. In this study, we utilize

practical data obtained through surveys and clinical literature, and develop a model to help physicians

and POP patients dynamically select treatment options in order to maximize a patient’s expected future

quality of life. Results from the model are presented in the form of optimal policy tables, which can be

used by physicians and patients by entering several attributes as inputs, such as the patient’s age, current

observed QoL defined by the severity of POP symptoms, preferences over preserving coital function, and

other potential restrictive conditions. The results show significant socio-economic incentives for potential

utilization of optimal treatment policies in POP treatment. We estimate based on QoL to dollar conversions

that the expected value of improved QoL for an individual POP patient is around $10 thousand. When

aggregated over the entire POP population seeking treatment, the total annual expected value for the society

is at least $675 million under medium level valuations of QoL. Moreover, the optimization based policies

imply an overall reduction of about $200 million in annual POP treatment costs, which corresponds to a

savings of about 5% in these costs.

Key words : healthcare, treatment selection, pelvic organ prolapse, quality of life, Markov decision process,

dynamic programming

1

Author: Optimal Treatment Policies for Pelvic Organ ProlapseArticle submitted to ; manuscript no. 1

1. Introduction

Pelvic organ prolapse (POP) is a common gynecological disorder impairing many women’s quality

of life (QoL). Prolapse results from weakening of the muscles and ligaments supporting the pelvic

organs. A POP patient suffers from symptoms such as constant pelvic pressures, low back pains,

bleeding, incontinence and constipation. As a chronic disease, POP affects a large population of

females in the world, especially senior women with childbirth experience. Studies have shown that

up to 76% of women in the U.S. have shown some levels of POP symptoms, and up to 19% require

some kind of medical intervention (Barber 2016). Overall, approximately 200,000 inpatient surgical

procedures are performed every year in the U.S. to treat POP, incurring costs of over $1.5 billion

(Jones et al. 2010). Moreover, with the increasing life expectancy worldwide, the impact of POP

on quality of life has become even a bigger concern, as the condition is more common in elder

patients. The 2013 World Population Aging Report, released by the Department of Economic and

Social Affairs of United Nations, indicates that the number of people above age 60 will increase

rapidly in the next four decades to reach 21% of the entire population by the year 2050. This is

expected to result in a 45% increase in the demand for POP treatment (Jones and Harmanli 2010).

Given these observations, it is important to consider the various options available to treat POP

patients and identify practical guidelines for selecting treatment options for such patients, as there

is no such quantitative-based guidance available in the literature. In this paper, we study this

problem using a stochastic dynamic model that aims to maximize the expected future quality of

life in patients with POP, where the results are aimed to provide insights to physicians in making

clinical decisions when treating patients with POP.

1.1. Problem Description and Research Questions

A number of options has been developed and implemented in clinical practice when treating POP.

These options can be classified into four categories: watchful waiting, conservative treatments,

reconstructive surgery, and obliterative surgery. Watchful waiting involves no specific treatment

action other than observing the progress of POP symptoms. Conservative treatments include non-

surgical options for POP, such as the use of a pessary to support the pelvic organ, pelvic floor muscle

exercises, weight-loss, and other treatment that aims to relieve POP related discomfort. Recon-

structive and obliterative surgeries represent the surgical options for POP, but the two approaches

and subsequent consequences differ. Reconstructive surgeries restore pelvic organ’s anatomy and

provide resuspension of vaginal vault. Reconstructive procedures typically have longer operating

times and pose a higher risk of complications, but postoperative coital function is preserved. Oblit-

erative surgeries, on the other hand, permanently close the vagina. In comparison to reconstructive

Author: Optimal Treatment Policies for Pelvic Organ Prolapse2 Article submitted to ; manuscript no.

surgeries, obliterative procedures require shorter operating times and have a decreased risk of com-

plications. Overall, obliterative surgeries have success rates near 100% (Fitzgerald et al. 2006),

which is significantly higher than that of reconstructive surgeries, as it is estimated that 27% of

reconstructive surgeries might require follow-on operations (Harmanli 2009).

When discussing POP treatment options with patients, gynecologists consider factors such as the

patient’s age, expectations, health state, degree of bother, and desire to maintain coital function.

Based on such factors, a patient with lower POP stages may prefer more conservative treatment

options before considering a surgical intervention. For patients with higher stages of POP, as the

degree of discomfort is higher, a patient may be more amenable to some surgical intervention. On

the other hand, there are no general guidelines that a physician can use to recommend a specific

treatment option to a patient. Physicians make recommendations based on patient preferences and

clinical experience without referring to a specific quantitative analysis based guideline.

Our objectives in this paper are to identify optimization-based treatment policies to serve as

a reference for physicians, and also to assess the value of such optimization-based policies by

comparing these with the current policies used in practice. More specifically, we utilize both clinical

data and survey data, and try to answer the following research questions: (1) Given the available

data on treatment options and their effectiveness over time, what are optimization based treatment

policies that maximize a POP patient’s expected future quality of life? (2) How do the treatment

decisions in these policies differ from those currently used by physicians? (3) What value can

potentially be generated through the use of optimal policies as decisions aids by physicians? (4)

What is the cost impact of optimization based treatment policies when compared with the current

practice?

Our approach to answer these questions involves a Markov decision process (MDP) model that

captures the dynamics of the decision process in POP treatment by utilizing physician surveys and

available clinical data. The model is used to derive optimal policies under different settings, and

these policies are then compared with the current clinical policies as identified through survey data

collected from physicians.

1.2. Review of Relevant Literature

MDP-based approaches have been extensively used in studying a variety of medical decision-making

problems, especially for certain major life-threatening illnesses (Schaefer et al. 2004, Alagoz et al.

2010). Some of these applications include organ transfers (Ahn and Hornberger 1996, Alagoz et al.

2004, 2007a,b), cancer screening (Maillart et al. 2008, Chhatwal et al. 2010), treatment of diabetes

(Denton et al. 2009, Kurt et al. 2011, Mason et al. 2012, Kirkizlar et al. 2013), human immunode-

ficiency virus (HIV) infection (Shechter et al. 2008), and cardiovascular diseases (Hauskrecht and

Fraser 2000, Montgomery et al. 2003).


Of these papers, Alagoz et al. (2004) study the timing decisions for liver transplans under insuf-

ficient cadaveric organ supply, where the authors build an MDP model to maximize the expected

quality of life for patients. Similarly, Shechter et al. (2008) discuss the time to initiate HIV treat-

ments for patients in critical status. Another study of this type is by Denton et al. (2009), where

the optimal timing for statin therapy is determined to treat Type-II diabetes in order to minimize

cardiovascular risk according to a patient’s age, gender, and metabolic state. Similar to our paper,

all these studies utilize the concept of QoL as the measure to be optimized. On the other hand,

the medical decisions considered in the studies above are one-time treatment decisions rather than

consisting of multi-period treatment plans, as in the case of POP treatment which is prolonged

over the lifetime of a patient. One study that assumes a multi-period treatment plan is by Chhat-

wal et al. (2010), where a patient’s risk of breast cancer is evaluated in regular intervals, and the

decision of whether or not to perform a biopsy is made based on the patient’s observed condition.

Using a finite-horizon MDP model, the authors identify an optimal policy based on the patient’s

age and breast cancer risk level. Similarly, in our problem framework, the treatment decisions are

also made based on an annual examination of the POP patient, but the available actions involve

four different treatment options. The multi-period treatment plan and the availability of multiple

actions at each decision epoch add complexity to both the modeling and analysis in our problem

framework.

As a non-fatal disease, POP has been rarely studied in the field of operations management, and

moreover, MDP-based approaches have not been previously utilized in the gynecology area, despite

its successful applications in other medical fields. However, one cannot neglect the significance of

the disease and its growing social implications especially due to an aging population. To the best

of our knowledge, our work is the first study to address treatment planning for POP using an

optimization approach that provides patient-specific long-term treatment recommendations. Thus,

as a novel and data-based application of operation management methods in healthcare, our study

complements the existing MDP-based models on impactful disease treatment management.

With respect to the existing literature in the gynecology field on POP treatment, most studies

focus on the characteristics of POP and associated treatment options. Samuelsson et al. (1999),

Swift et al. (2005), and Jones et al. (2010) provide some general statistics about the population of

POP patients, while Barber et al. (2001) introduce two measures for POP’s impact on quality of

life. Ellerkmann et al. (2001), Nygaard et al. (2004), Handa et al. (2004), and Gutman et al. (2008)

study the natural progress of POP development, and evaluate how such progression impacts a

patient’s quality of life. These studies help characterize the model assumptions and input structure

in our research. Wheeler et al. (2005), Barber et al. (2006), Barber et al. (2007), Nguyen and

Burchette (2008), and Harmanli (2009) each study a specific POP treatment option, and report the


effectiveness of the corresponding treatment. In addition, another study relevant for our work is by

Jelovsek et al. (2015). In that study, the authors describe the characteristics and application scopes

for each of the POP treatment options, and then provide specific qualitative suggestions for POP

patients as to which surgical procedure to use at a given age for different levels of POP symptoms.

With some degree of consistency with our work, the conclusion of that paper can be seen as a

qualitative counterpart of our quantitative study, which can help physicians better interpret our

policy findings.

1.3. Contributions and Major Findings

Our study contributes both to the current state of research and clinical practice for POP by

providing insights for treatment. As part of the major findings of our research, we draw the following

general conclusions for optimal POP treatment policies: (1) For younger patients up to age 50,

watchful waiting is always recommended when the patient’s QoL level is above 7 based on a scale1

of 1 to 10 for QoL, with 10 being the healthiest case. This QoL threshold gradually decreases at a

rate of around 1 level per 16 years as the patient gets older; (2) Surgical options are recommended

for patients with QoL levels below 6 for all ages; (3) The age threshold to prefer obliterative surgery

over reconstructive surgery is 74; (4) Obliterative surgery should not be considered when the desire

to preserve coital function corresponds to more than 40% of a patient’s quality of life.

Comparing these policies with the current practice, we quantitatively conclude that: (1) The

proposed policies are expected to provide QoL improvements of between 9% and 18% over currently

utilized physician policies; (2)The expected annual socio-economic value of optimization based

policies can be at least $675 million when the treatment seeking POP population in the U.S. is

considered; (3) Optimal policies imply an estimated savings of around $200 million in annual POP

treatment costs while at the same time improving the QoL of patients.

The remainder of this paper is organized as follows. We develop the MDP model for selecting

treatment options for POP in Section 2. In Section 3.1, the MDP model is used to identify optimal

treatment policies based on available clinical data. In Section 3.2, we compare the optimal treatment

policies with the current physician policies, and quantify the potential value generated by our

proposed policies. In Section 4, we summarize the policy implications of our findings, and in Section

5 we conclude the paper by some final remarks.

1 We describe in Section 2.1 how this scale is developed and how the current QoL of a patient is measured based onthis scale.


2. Methods

In this section we modeling the Decision Process for POP Treatment Selection. Consider a patient

seeking treatment for POP symptoms. The decision process for treatment selection starts with the

evaluation of relevant patient data, which include the patient’s age and other measures defining

her quality of life, mainly as it relates to POP-related discomfort. After consideration of all rele-

vant inputs, a treatment option is recommended by the physician. Once the treatment option is

implemented, the effect of the treatment is then observed and the post-treatment quality of life is

evaluated. If necessary, further treatment options can be considered based on this evaluation. Such

decision cycle continues until the termination of a planning horizon, which usually happens when

the patient’s status remains stable or when an age limit is reached. In the following subsections we

describe in detail how the components of an MDP model can be developed in the POP treatment

context based on the decision process described above.

2.1. Decision Framework

POP is mostly common in middle to older aged women, especially among those with childbirth

experience. Most empirical studies on POP consider subject groups of ages between 45 to 85, as rare

cases of pelvic organ prolapse at younger ages are seldom symptomatic (Samuelsson et al. 1999).

Hence, we choose an age range of 45 to 85 years as the planning period for selecting treatment

options for POP. We further assume that a gynecological exam is performed annually to assess

a patient’s condition. Based on the assessment at each exam, a treatment option is selected and

implemented. This dynamic treatment decision process is illustrated in Figure 1, where an initial

treatment is followed by a period of observation of the resulting disease progression before another

treatment plan is decided at the next decision epoch. The process goes on repetitively until the

end of the treatment planning horizon.

2.1.1. Modeling Inputs for the Decision Process Based on interviews with physicians,

it can be noted that the treatment decisions for POP are mainly based on the patient’s age and

three other high level measures: the current quality of life of the patient, the surgical history of the

patient, and the patient’s preference over preserving coital function. We describe these measures

in detail in the following paragraphs.

Modeling Quality of Life. When appropriately devised, a measure of patient’s current quality

of life captures the severity of POP symptoms, as well as the impact of the resulting distress on

daily life. While quantification of quality of life in this context is somewhat of a challenge, the

gynecology literature contains some symptom-based quality of life measurements. Two of these

metrics have been widely adopted by physicians, namely the scores from the Pelvic Floor Distress


Inventory (PFDI) and the Pelvic Floor Impact Questionnaire (PFIQ), which are surveys completed

by POP patients before and after treatment to assess POP-related distress symptoms. These two

metrics evaluate the quality of life of a POP patient by assessing the degree of discomfort and other

problems caused by pelvic floor symptoms. Three major concerns due to POP are considered in

both measures: impacts on daily activities due to pressure in pelvic area, urinary incontinence, and

fecal incontinence. The PFDI score is a summation of the sub-scores for three sub-questionnaires

corresponding to the three areas of concern above, where each area is scored using a range of 0 to

100. Similarly, PFIQ also has three sub-scales on these concerns, each with a scale between 0 and

100. The summation of these three sub-scales presents a total PFDI or PFIQ score between 0 and

300 with higher scores being indicative of more severe levels of symptoms.

Barber et al. (2001) compare PFDI and PFIQ scores, and conclude that these two scoring systems

have significant internal consistency with a high degree of correlation. Hence, in our study we

use existing empirical studies on POP that utilize one or both of these measures. We do this by

converting the PFDI and PFIQ scores into a new scale ranging from 1 to 10, based on a rescaling

of the original PFDI and PFIQ scores reported in the POP related empirical studies.

Modeling Surgical History. The second important criterion in deciding on a treatment option

is the surgical history of the patient. This is relevant because some patients may end up going

through multiple reconstructive surgeries as part of their treatment process due to recurrence of

symptoms after surgery. On the other hand, due to the theoretical risk of complications associated

with multiple surgeries, the total number of reconstructive surgeries a patient can have is limited.

Olsen et al. (1997) report that only in extreme cases a patient should be going through more

than three reconstructive surgeries. Similarly, for a patient with a previous obliterative surgery, no

further surgical options are feasible due to the permanent closure of the vaginal opening. Hence,

the number of obliterative surgeries a patient can have during the treatment period cannot exceed

one. Based on these, we keep track of the number of surgeries for a patient in our model, and limit

the number to three for reconstructive surgery, and to one for obliterative surgery.

We also note that the surgical history is not the only factor constraining surgery choices of a

POP patient. The patient’s health condition, preparedness and personal preference on the available

types of treatment also play a role in choosing a surgical procedure. Therefore, the categories

used to distinguish surgical history can also be used to characterize these special conditions of a

patient. For example, a patient who is determined to preserve coital function would be considered

equivalent to a patient who had gone through obliterative surgery, as in both cases the obliterative

surgery option is not feasible. In Section 3.1 we perform analyses based on such considerations.


Modeling Patient’s Preference of Preserving Coital Function One particularly important issue

about treatment of POP is the impact of treatment options on the lifestyle of a patient. According

to Ratner et al. (2011), 30% of women between the ages of 55 and 75 remain sexually active.

This ratio is around 17% for women between the ages of 75 and 85 (Matthias et al. 1997). While

conservative treatments and reconstructive surgeries result in some temporary inconvenience in a

patient’s daily life, they do not have long-term impacts on coital function. On the other hand,

obliterative surgery closes the vaginal opening and inhibits any coital activity permanently. Despite

the prevalence of such concerns in treatment selection for POP, the issue has been seldom discussed

in the gynecology literature. Jelovsek et al. (2015) suggest that obliterative surgery should be

conducted on a patient only when the patient cannot tolerate more extensive surgeries, and/or

does not plan any further coital activity. However, the definitions of extensive surgery tolerance

as well as inclination for coital activity are somewhat vague, and typically are not considered in a

systematic way in practice. It is reported in a post-surgery survey that 9% of POP patients have

regrets after obliterative surgery (Wheeler et al. 2005).

In this study, we introduce a preference index Pn(t) to capture the desire of a t−year old POP

patient to preserve coital function. We then perform sensitivity analysis around this preference

index to determine the impact of a patient’s choice on this concern. We assume that before deciding

on a treatment option, a patient will be first asked about her desire for maintaining coital function

and its importance in her QoL, which will then be integrated into the decision making process. As

an example, if a 75-year-old patient believes that coital function accounts for 10% of her quality

of life, then the new QoL value achieved through the obliterative surgery option will be reduced

by 10% in model calculations.

Given that the initial Pn(to) value is valid for the current age to of the patient, the value of

the preference factor Pn(t) needs to be defined as a decreasing function of age t. According to

Matthias et al. (1997) and Pauls et al. (2007), the desirability for coital function over the general

population is estimated to decrease following a linear pattern at a rate of 1.9% per year, until

the value drops to zero. To this end, we express the preference factor as a function of time, such

that Pn(t) = max{Pn(to)− 0.019(t− to),0} for t ∈ [46,85], where Pn(to) is the current preference

factor value and t > to is the age of the patient. Through this structure, the impact of a patient’s

willingness in preserving coital function can be reflected on the calculation of the earliest age to

recommend obliterative surgery for that patient.

The three types of inputs defined above are used to select a treatment option for a given patient

by considering the potential impacts of these options on improving the QoL of the patient. This

can be achieved by a stochastic characterization of these impacts, which we describe as follows.


2.1.2. Modeling Treatment Options As noted earlier, there are four major categories of

treatment options for a given patient. These treatment categories consist of (1) watchful waiting,

which implies that no treatment action will be taken before the next annual exam; (2) conser-

vative treatments, which correspond to the non-surgical therapy options for POP treatment; (3)

reconstructive surgery, in which the vaginal vaults are supported by surgical procedures; and (4)

obliterative surgery, in which the vaginal opening is closed to prevent prolapse of pelvic organs.

The treatment options above have been studied extensively in the literature in terms of their

impact on a POP patient’s quality of life, where such impacts are assessed using the PFDI and

PFIQ scores. Hence, we utilize such scores in quantifying the transitions between different QoL

levels as a result of a treatment option selected. Clearly, such transitions are probabilistic, which

should be taken into consideration in determining a treatment plan. We use available information

in the clinical literature to characterize these probabilities.

Barber et al. (2006) study the effects of reconstructive surgery and conservative treatments by

comparing PFDI and PFIQ scores before and after these treatment options. The authors conclude

that reconstructive surgeries provide much more significant improvement in PFDI and PFIQ scores

when compared with the outcome after conservative treatments. Similar to that study, Barber et al.

(2007) evaluate and compare the effectiveness of reconstructive and obliterative surgeries using the

same measures and criteria. A noteworthy feature of reconstructive surgery is the role that patient

age plays in the level of QoL improvement after such surgery. To capture such age-dependency in

the transition probabilities, we utilize the findings of Nguyen and Burchette (2008), where patients

from different age groups are studied. As for the watchful waiting option, we refer to Handa et al.

(2004) where the authors provide information on the natural progression and regression rates of

POP over time.

Based on these findings, we characterize the changes in the QoL of a POP patient after each

treatment option according to a normal distribution, where each treatment option has a different

mean and standard deviation. We truncate and discretize these distributions to capture the bounds

and the discrete nature of the QoL levels, repsectively. The mean and standard deviation values for

the treatment options are shown in Table 1, along with the reference studies used in defining these

parameter values. Note that the mean change in QoL level for the reconstructive surgery option is

defined as a function of patient age t, where t varies between 46 and 85. Also, it is assumed that this

mean value is independent of the number of previous reconstructive surgeries and the time since

such a surgery, as each subsequent reconstructive surgery is aimed at restoring the pelvic usually

by fixing a different compartment than the one operated on in the previous surgical procedures

Price et al. (2008).


The goal of POP treatment planning is to maximize a patient’s expected future quality of life.

Therefore, the returns from choosing a treatment option are measured based on an aggregation of

the QoL levels over the planning horizon. For each year, we consider the QoL level at the beginning

and end of that year, and use the average level as the representative value for QoL in that year.

We also note that each surgical treatment option requires a certain recovery period before there

is an improvement in a patient’s QoL. Similarly, conservative treatments also require frequent office

visits and other treatment related discomfort. These inconveniences are quantified by a disutility

ratio dat which is proportional to the length of the recovery period. The QoL-adjusted reward due

to the improvement of the status of a patient for the year is then discounted by this disutility ratio.

Finally, considering the aging process, the World Health Organization suggests a general discount

factor of 3% when utilizing measures that involve quality of life metrics (Mathers et al. 2008).

Hence, we also utilize such discounting in our model and associated calculations. More specifics on

these measures and their role in the model are provided in Section 2.2 below.

2.2. Model Formulation

In this section we provide the specifics on the model components described in Section 2.1, and

present a complete formulation of an MDP model that can help determine treatment options for

POP patients. As part of our model development, we formally define the following notation:

Decision Epochs. We assume that decisions on treatment options will be made annually for

patients in the age group considered. This is consistent with the results of (Bibbins-Domingo et al.

2017), where the authors recommend an annual pelvic exam for gynecology patients. To this end,

we let t∈ T refer to each decision epoch where T = {46,47, ...,85}.

States. The state of a patient at age t∈ T is denoted by st =< lt, ht >∈ S for all t∈ T , where st is

a two-dimensional vector consisting of the QoL index lt and surgical history ht for the patient. The

domains for these state parameters are defined such that lt ∈ {1,2, ...,10} and ht ∈ {−1,0,1,2,3},

where −1 corresponds to the case of a previous obliterative surgery, while 0,1,2, and 3 correspond

to the number of previous reconstructive surgeries that a patient had.

Actions. The set of treatment options for a patient is defined by A= {Ww,Cs,Re,Ob}, where

Ww is watchful waiting, Cs is conservative treatment, Re is reconstructive surgery, and Ob is

obliterative surgery. The set of allowable actions at a given state st =< lt, ht > would depend on

the surgical history ht of the patient, and is denoted as Aht ⊆A. We provide a list of allowable

actions in each surgical history state ht in Table 3. We note that these allowable actions also apply

to patients with special conditions as discussed previously in Section 2.1, as such conditions may

result in the same surgical restrictions as the corresponding surgical history state.


Transition Probabilities. The transitions between stages are such that for st =< lt, ht > the next

state st+1 =< lt+1, ht+1 > is defined probabilistically as a function of the action at. More specifically,

lt+1 is dependent on a random outcome defined by the treatment option selected, while ht+1 = ht+1

if at =Re, ht+1 = ht for at ∈ {Ww,Cs} and ht+1 =−1 for at =Ob. Probability of transition from

state s to another state s′ under a given treatment a at age t is denoted as pt(st+1 = s′|st = s, at = a).

As discussed in Section 2.1, we utilize clinical data on QoL transitions to build transition prob-

ability matrices for different treatment options in each period. The transitions for each treatment

option a ∈ A are assumed to follow a truncated normal distribution with mean µat and standard

deviation σat where the lower and upper bounds for the distribution are set as 1 and 10, respectively.

We then discretize this truncated normal distribution and define discrete probability distributions

over the state and action space assuming only integer values for QoL levels. The specific numerical

values for these probability distributions are provided in Online Appendix A.

Rewards. The reward of transitioning from a given state s to another state s′ after a selected

treatment option a at age t is denoted by rt(st+1 = s′|st = s, at = a), and is calculated based

on the current QoL, the disutility measure for the option selected, and preference Pn(t) on the

preservation of coital function. Defining s′ =< l′, h′ > and s=< l,h >, we represent this value as

rt(st+1 = s′|st = s, at = a) = 12(l+ l′)(1− dat )(1−Pn(t)), where the QoL value is averaged over the

past and transitioned QoL levels, and discounted by a factor dat ∈ [0,1] representing the disutility

ratio of treatment option a for a patient of age t. The specific values for dat and the recovery period

lengths used for their calculations are shown in Table 2, which are identified through physician

surveys as functions of patient age. Recall regarding the preference over preserving coital function

that if a patient of age to provides her age-dependent preference parameter value as Pn(to), then

for t > to the preference parameter values are defined as Pn(t) = max{Pn(to)− 0.019(t− to),0}.

Based on these definitions, the optimality equations for the POP treatment selection problem

can be stated as follows:

V ∗t (lt, ht) = maxat∈Aht

{∑

<lt+1,ht+1>∈S

pt(lt+1, ht+1|lt, ht, at)1

2(lt + lt+1)(1− datt )(1−Pn(t)) + γE[V ∗t+1(lt+1, ht+1)]}

∀<lt,ht>∈S,t∈T \{T} (1)

where VT (lT , hT ) = 0 and γ is the discount factor based on aging as introduced earlier.

3. Results

3.1. Optimization Based Treatment Policies

In this section we implement our model using the data described in Section 2, and present our

findings on recommended POP treatment options for different patient types. The recommendations


are aimed at providing guidance to physicians and patients in the selection of a treatment option.

As noted earlier, the planning horizon for our implementation covers an age span between 46-years

and 85-years, and state definitions include 10 distinct QoL levels and 5 different surgical history

measures.

We present the analysis on the optimal POP treatment policies through four distinct cases,

defined by the surgical history and/or relevant restrictions of a patient. In terms of preference over

preserving coital function, the general analysis initially assumes a default Pn(to) value of zero for

a patient of age to. Sensitivity analysis is then performed to examine how the optimal policy is

affected by a patient’s concern for preserving coital function by considering different preference

parameter values.

3.1.1. Case I: All Treatment Options Available We first consider a situation where any

of the four treatment options can be selected for a given POP patient. From a surgical history

perspective, this case corresponds to the history of no more than two reconstructive surgeries

previously performed on a POP patient. In Figure 9a, we present the optimal treatment policy

under this case, where the recommended action for an observed QoL level is shown for each age and

for 0, 1, or 2 previous reconstructive surgeries - as the treatment structure for POP patients with

0, 1 and 2 previous reconstructive surgeries is the same. This similarity in optimal policies under

different surgical history cases is also supported by clinical observations. Price et al. (2008) conduct

an 11-year retrospective study and conclude that most repeat procedures in follow-up reconstructive

surgeries do not involve repairing the same pelvic compartment that was treated in the original

surgery. As a matter of fact, any follow-up reconstructive surgeries actually improve the QoL of

a patient mostly independent of the surgeries conducted earlier. Therefore, such independency

in the effectiveness of surgeries results in the selection of treatment options being insensitive to

reconstructive surgical history of a patient. Also note that the results presented in Figure 9a assume

no preference towards the preservation of coital function, but later in this section we describe how

such preferences impact the optimal policy.

We observe in Figure 9a that for patients with relatively high QoL levels, i.e. at or above 9,

watchful waiting is recommended at all ages. This threshold reduces to 8 between the ages of

68 and 80, and to 7 after age 80. Surgical treatment options are recommended only for patients

with QoL levels below 6 or 7. In general, patients younger than 53 years old should consider

reconstructive surgery if their QoL levels are below 7. Conservative treatment options act mostly

as a transition zone between the surgical options and the watchful waiting option. Between ages

46 and 80, patients of QoL levels 7 or 8 are generally recommended to go through conservative

treatment. Such conservative treatment options are also recommended for patients of very high

age, e.g. 83-85 years old, at even lower QoL levels, as the disutility of going through a surgery

increases significantly at such high ages.


Impact of Preference over Preservation of Coital Function. While the representation in Figure

9a assumes a default Pn(to) value of zero, it is worthwhile to consider the situation when a Pn(to)

value of 0.3 is assumed for the patient. In Figure 9b we present the optimal treatment policy

when preference factor Pn(to) takes value of 0.3. It is observed that conservative treatment is

recommended for patients of a wider range of QoL levels from 6 to 9, specifically between ages

48 and 80. This is expected, because as obliterative surgery becomes undesirable, conservative

treatments create more utility.

The earliest age to recommend obliterative surgery is also affected by the preference over pre-

serving coital function. In Figure 5a, we show the earliest age to recommend obliterative surgery

under different preference parameter Pn(t) values for Case I. The horizontal and vertical axes in

Figure 5a represent a patient’s age t and her preference factor Pn(t) at that age, respectively.

As suggested by the optimal policy under Case I, the earliest age for recommending obliterative

surgery is 74 and thus the results in Figure 5 are displayed for age 74 and onwards only. The QoL

levels in each region in Figure 5a imply that obliterative surgery is recommended for a patient at or

below that QoL level. As observed in Figure 5b, the earliest age to recommend obliterative surgery

generally increases as a patient’s preference over preserving coital function increases but only for

levels above 20%. This increase is almost linear with respect to the preference factor value Pn(t)

when Pn(t) is less than 30%, and then slowly converges at higher Pn(t) levels. Based on this, a

general rule can be concluded as never to recommend obliterative surgery at any age if a patient’s

preference factor for preserving coital function is around 40% or higher. In such situations, other

treatment options should be selected instead.

3.1.2. Case II: No Reconstructive Surgery Option Available The next case we study

is when a patient is unable or unwilling to go through reconstructive surgery. Following the obser-

vation that a maximum of three reconstructive surgeries are allowed for a POP patient, such a

case might also imply that a patient has had three previous reconstructive surgeries in her sur-

gical history. In addition, a POP patient may be unwilling to have reconstructive surgery due to

the associated discomfort or other physical restrictions. Obliterative surgery remains an option in

this case, as it has a high success rate and results in fewer complications and less post-surgery

discomfort.

Since reconstructive surgery is omitted from the potential treatment options, obliterative surgery

becomes the only surgical option to treat a patient. Note that it is rare for a POP patient to

undergo multiple reconstructive surgeries at relative young age, and such a restrictive situation

where a patient is forced to select obliterative surgery at a young age is very unlikely. Hence, the

optimal policies derived under this case are of more value to elder patients. In our analysis, we


display the results over the full age span from age 46 to 85 but note that the youngest patients going

through obliterative surgery are around age 60 (Fitzgerald et al. 2006). Given these observations,

the optimal policy structure under Case II is shown in Figure 2a, where the blank region corresponds

to impractical ages for obliterative surgery. While the optimal policy might indicate the use of

obliterative surgery at these ages when Pn(t) values of zero are assumed, conservative treatments

are practical in these situations.

As it can be observed in Figure 2a for Pn(to) = 0, obliterative surgery is recommended for

patients with QoL levels below 6 at almost all ages. Similar to the treatment policy illustrated in

Figure 9a for Case I, watchful waiting is recommended for patients with higher QoL levels, while

for conservative treatments there is an increased preference at QoL level 7 for younger patients.

For patients older than 74, the optimal treatment policy stays the same as in Case I.

Impact of Preference over Preservation of Coital Function Preference over preserving coital

function serves as a key factor when recommending an obliterative surgery in Case II. It can be

observed in Figure 2b for Pn(to) = 0.3 that conservative treatments take over obliterative surgery

as the main recommendation for a majority of the patients below QoL level 8, while the earliest

age for recommending obliterative surgery moves to age 81.

The overall impact of the value of the preference factor Pn(t) under Case II is presented in

Figure 3. We display the results starting from age 60 as obliterative surgeries are rarely performed

below such age, which we noted earlier. Compared with the results in Figure 5a, the earliest age

for recommending obliterative surgery is lower for the same Pn(t) values in Figure 3a, due to

the fact that obliterative surgery is the only effective surgical option under Case II. It is also

observed that for patients above the age of 83, the highest QoL level for recommending obliterative

surgery decreases. This is due to the planning horizon terminating at age 85, and for patients

with medium QoL levels the improvement in QoL after obliterative surgery is not sufficient to

counter the discomfort due to the surgery. The earliest age to recommend obliterative surgery also

increases with Pn(t) values as shown in Figure 3b, and converges to age 83 when Pn(t) exceeds

40%. Considering that such a threshold is not significantly different from that of Case I, we again

conclude that the obliterative surgery should not be performed under any case when coital function

accounts for higher than 40% of the QoL for a patient.

3.1.3. Case III: No Obliterative Surgery Option Available A third case we consider is

when only reconstructive surgery is available as a surgical option for the patient. This situation

may be observed in clinical practice due to some patients having reservations about the obliterative

surgery option. Such a case can be interpreted as being equivalent to a case where the preference

on preservation of coital function has a relatively large value, such as 40% or higher.


In Figure 6, we observe just like in the previous case that watchful waiting option is recommended

for patients with high QoL levels, where the threshold of switching to conservative treatment

decreases from QoL level 9 to level 8 at age 64, and further decreases to level 7 at age 80. Recon-

structive surgery is recommended for patients with lower QoL levels at around level 5 between

ages 46 and 79. After age 79, the QoL threshold for switching to conservative treatment gradually

decreases as the effectiveness of reconstructive surgery gets lower and the inconvenience due to the

surgery increases.

To some extent, the optimal treatment plan in Case III resembles Cases I and II. In all these

three cases, watchful waiting, conservative treatment and the surgery options form a three-layer

structure. In this structure, watchful waiting is always the top layer as it is recommended for

patients with high QoL levels, while surgical options form the bottom layer to treat low QoL level

patients. Conservative treatment would serve as the transition zone between watchful waiting and

surgical options for patients with medium QoL levels. However, this transition zone for conservative

treatment in Figure 6 is wider than those in Figures 9a and 2a. The reason is that reconstructive

surgery, as the only surgical option under Case III, has larger disutility and a decreasing effective-

ness as a patient gets older. As a result, conservative treatment is more appropriate for patients

with QoL level 6, and thus it replaces the reconstructive surgery recommendation at that QoL

level.

Note that the preference over preserving coital function is irrelevant under Case III, as oblit-

erative surgery is assumed to be ruled out. Hence, no sensitivity analysis over Pn(t) values is

performed for this case.

3.1.4. Case IV: No Surgical Options Available We also study the case where no surgical

procedures can be considered for a given patient. This case might refer to a surgical history involving

one previous obliterative surgery after which no surgical treatment options can be performed.

Another real life scenario fitting into this case is where a patient can not endure reconstructive

surgery, but also declines to have an obliterative surgery due to the preference of preserving coital

function or for other reasons. In such a situation, the only treatment options available are watchful

waiting and conservative treatments. Similar to the recommended treatment policy structure in

Cases I, II and III, watchful waiting is recommended for patients with higher QoL levels, while the

previous surgery recommendations are now replaced by the conservative treatment option. The

split of these two treatment options in the optimal policy is shown in Figure 4. Starting at age

46, watchful waiting is recommended for POP patients with QoL levels at or above 9, and this

QoL threshold is further reduced to 8 at age 57, and then to 7 at age 80. For all other situations,

conservative treatment options are recommended.


As a summary for all four cases, in Table 5 we display some key cut-off values for the available

treatment options in terms of patient age and QoL. The cut-off age between watchful waiting and

conservative treatment gradually decreases through Case I to Case IV, from 67 to 56 for QoL level

9, and slightly from 80 to 79 for QoL level 8. As for reconstructive surgery, the recommended cut-off

QoL levels are more gradual for Case III than for Case I. Obliterative surgery cut-off ages and QoL

levels turn out to be the same for Case I and Case II, which apply to patients at very high ages.

The table serves as a general reference summarizing some key points of the optimal policy results

in a simpler format.

3.2. Physician Based Treatment Policies and Value Comparisons

The optimal policies derived in Section 3.1 are based on clinical data that describe the effectiveness

of treatment options for different types of patients. Given this, a relevant question is how well these

policies match the treatment choices currently being recommended by physicians. This is clearly

a challenging question, as such recommendations are based on a physician’s personal views and

experiences which could vary significantly from one physician to the other. In trying to answer that

question, we performed a written survey of obstetricians and gynecologists that are members of the

New England Urogynecologic Society. The survey was aimed towards identifying general insights on

the treatment policies used by gynecologists when treating POP patients of certain ages, QoL level,

and surgical history. The survey questions addressed all four of the cases described in Section 3.1,

capturing the differences in availability of the treatment options. 32 questions were presented, and

in each of the questions physicians were provided with key patient information, which included the

patient’s age, surgical history, and QoL level on a scale of 1 to 10. The respondent was then asked

to choose the treatment option that they would use among the available options for that patient.

The survey received responses from 17 physicians, which were then analyzed to develop a stochastic

representation of physician-based treatment policies used in current practice. The analysis of the

survey data was done as follows. Under each of the four cases, we identified the probability that

the ‘optimal’ treatment option will be selected by physicians, which was based on the distribution

of physician responses to the survey questions related to that case. This allowed us to develop a

probabilistic representation of physician decisions for any given patient. In other words, one can

identify the optimization based treatment policy for a patient, and then probabilistically estimate

the treatment option to be selected for that patient by a physician. These probability distributions

are summarized for each treatment option under each case in Table 4.

With regard to value comparisons, it is easy to calculate the optimization based expected QoL for

a patient of age t and state st =< lt, ht > using the MDP model and the corresponding optimization

results. These simply correspond to V ∗t (st) which are calculated as part of the backward induction


algorithm used to identify the optimal treatment selection decisions. To calculate the expected QoL

under physician based policies for the same patient, we first assume that the selected treatment

option for the patient will be based on the probability distributions shown in Table 4. This structure

implies a randomized Markovian policy, which can be evaluated using a policy evaluation algorithm.

We let qρ(at|st, a∗t ) denote the probability of selecting treatment option at under a physician based

policy, and define uρt (st) as the expected future QoL for a patient of age t in state st. Note that

qρ(at|st, a∗t ) is defined as a function of the optimal action a∗t for the given state st as discussed

in the description of Table 4. We then calculate uρt (st) for all t ∈ T \{T} and st ∈ S through the

following recursion:

uρt (st) =∑at∈A

qρ(at|st, a∗t ){∑

st+1∈S

pt(st+1|st, at)1

2(lt + lt+1)(1− datt )(1−Pn(t)) + γE[uρt+1(st+1)]} (2)

Moreover, we have uρT (sT ) = 0 for all sT ∈ S.

Based on this representation of the physician based policies, we can perform QoL and cost

based analyses on the two types of policies and quantify the value and costs of optimization based

treatment policies over those that are currently being utilized in practice.

A first key question involves as to whether the optimization based policies can help create some

additional value over current policies used by physicians. We answer this question by comparing the

expected QoL levels for patients of different cases under the two policies and calculating the percent

differences in expected QoL when the distribution characteristics of POP patients in the population

are considered. These differences are calculated asV ∗t (st)−u

ρt (st)

uρt (st)

×100% for a given state vector st ∈ S.

For analysis purposes, we first assume that the patients are indifferent towards the preservation

of their coital function when selecting a treatment option, implying the assumption of Pn(to) = 0.

This assumption is later relaxed by showing the results over different Pn(to) values. Moreover, we

also develop in Section 3.2.3 an estimate of the dollar value due to any QoL improvements that

can be achieved by utilizing our optimization results as decision aids.

3.2.1. Value of Optimization Based Treatment Policies for Individuals We first

present in Table 6 the specific values of the percent differences between the optimization and

physician based policies for a given individual patient. For the sake of compactness, in Table 6 we

indicate the improvements in terms of age groups, but more detailed age-specific tables are included

in Online Appendix B. Based on these estimates, we study below the value of optimization over

different initial QoL levels, different patient ages and different coital function preference values.

Value of Optimization over Initial QoL The expected improvements in patients due to opti-

mization based policies for different initial QoL levels are summarized in the bottom rows of the

subtables in Table 6, and visually depicted in Figure 7a. For Cases I, II and III in general, results

suggest that the most significant improvements occur for patients with very high QoL levels. These


patients typically suffer from lighter discomfort and are easier to treat, and can have their QoL

improved by as much as 20% to 30% by following the optimal treatment policies. The majority of

patients with QoL levels below 8 are also shown to have relatively high QoL improvements ranging

from 10% - 20%. In contrast, for Case IV patients, the expected improvements tend to decrease

over higher initial QoL levels from as high as 40% down to 0%, implying probably the currently

insufficient implementation of conservative treatment options for low QoL patients.

Value of Optimization over Patient Ages For the expected improvements as a function of patient

age, we demonstrate the variations in Figure 7b. It can be observed that Cases I, II, and III show

an increasing improvement trend until around age 65, and then starts dropping afterwards. These

trends suggest that medium aged patients between 55 and 65 years of age are likely to benefit

most from the optimization based policies as a group, and a physician can be more motivated to

refer to the optimization based policies when such a patient is considered. Case IV, on the other

hand, presents a quite different trend when compared with the other cases, where the expected

QoL improvement is relatively low around 8% before age 65 and then increases up to around 18%

at age 80, implying larger potential benefits of implementing the optimization based policies for

elder Case IV patients. The sharp drop at age 85 for Case IV patients is a boundary effect due to

the termination of the planning horizon.

Value of Optimization over Preference Factor Pn(to) As the last set of analysis in this subsection,

we test the physician based treatment policies under different preference factor levels Pn(to) and

compare the expected QoL improvement that can be achieved under different preference situations.

As part of the analysis, we consider Pn(to) values of 0.1, 0.2, 0.3, and 0.4. Since Cases III and IV do

not involve any decisions on obliterative treatment, the comparative analysis is performed for Cases

I and II only. As shown in Figure 8, as a patient’s preference level for preserving coital function

increases, the optimization based treatment policies provide larger improvements in QoL. A likely

reason is that physician based policies may not be placing sufficient emphasis on the preference

over coital function when suggesting obliterative surgeries, thus a larger Pn(to) value would result

in a greater gap between the values yielded by optimization based and physician based policies.

Hence, it can be concluded that the case of no preference, i.e. Pn(to) = 0, which is the assumption

for several of the analyses conducted in this section, implies a lower bound for the expected QoL

improvement due to optimization based policies.

3.2.2. Value of Optimization Based Treatment Policies for the Society While the

expected QoL improvement by utilizing the optimal treatment plan can be estimated for a specific

patient, we are also interested in estimating the overall impact at the societal level within the

U.S. An overall expected QoL improvement value can be calculated by taking into account the


distribution of POP prevalence in the population, for which we adopt the statistical data provided

by Hove et al. (2009) and Wu et al. (2014) on age and severity distributions of POP in the U.S.

The data in these studies suggest the estimates shown in Table 7 for each age group and severity

level. Each entry in the QoL columns in the table corresponds to the estimated percentage of

POP patients in that category for the given age range. A more detailed version of the table with

estimates for specific ages is provided in Online Appendix C.

Given the expected QoL improvements according to the patient’s initial QoL and age as described

earlier in this section, the weighted averages of QoL improvements under each case are then calcu-

lated using the above distribution of POP patients as weights. As shown in Table 6, the expected

QoL improvement in the society due to potential utilization of optimization based policies for the

four different cases are about 18%, 13%, 16%, and 9%, respectively. While the overall expected QoL

improvement in the society based on different case scenarios are quite different from each other,

we realize that the distribution of the four cases among POP patients are not even. Therefore, a

simple average over the four case scenarios will not be representative of the overall improvement

on a societal level. Despite the difficulty of coming up with the exact breakdown of patient pop-

ulations over the four cases due to lack of any such data in the gynecology literature, estimates

were obtained through interviews of gynecologists at a partner hospital. Based on these estimates,

5% of the POP patients belong to Case IV where a patient can not tolerate any of the surgical

options. About 10% of POP patients consider themselves open to all four treatment options includ-

ing obliterative surgery, which corresponds to Case I. Case II, where a patient cannot tolerate

reconstructive surgery but is able to go through obliterative surgery, is somewhat rare in practice,

to the extent that it can be considered negligible at a population scale. Therefore, the remaining

85% of the POP population can be estimated to be Case III patients. Taking into consideration

of the population distribution among the four cases, the overall expected QoL improvement in the

society due to potential utilization of our proposed optimization based policies is estimated to be

15.4%.

3.2.3. Monetary Value Estimates of Improved QoL Given the abstractness of QoL

measures, a natural question involves as to what these percent improvements represent in more

concrete terms. To provide an answer to this question, we express the QoL based improvements

in economic terms, as there exist several studies that develop estimates for quantifying the value

of QoL in dollars. Most mainstream models use a willingness-to-pay structure to measure the

economic value of a quality-adjusted life year. In the case of POP treatment, such quantification is

especially important for the evaluation of social welfare related to the large group of affected female

patients. To this end, based on the aggregated QoL improvements and the overall population of


POP patients in the U.S., we can compute the expected monetary value of QoL improvements

resulting from potential utilization of optimization based treatment policies for POP.

A list of commonly used QoL value estimates based on willingness-to-pay models is summarized

in the detailed survey paper by Hirth et al. (2000). We consider three major models, and study how

the dollar value of potential QoL improvements can be defined based on the proposed estimates

by each of these models. The three QoL value models we consider are referred to as the human

capital model of Rice and Cooper (1967), revealed preference-safety model of Ghosh et al. (1975),

and contingent valuation model of Jones-Lee et al. (1985). These three models provide different

estimates for the value of a quality-adjusted life year (QALY) under distinct settings. QALY is

a measure of disease burden that considers both the quality and length of life lived by a person.

Each unit of QALY equals one year of living under a perfect health condition. Given the differences

in assumptions and calculation methods, the three models produce different monetary values for

QALY. Hirth et al. (2000) conducts a thorough review of 42 previous studies from the health

economic literature and concludes the median monetary value of a QALY by each of the three

models respectively are $24,777 for the human capital model, $93,402 for the revealed preference-

safety model, and $161,305 for the contingent valuation model. We refer to these three values in

our analyses as low, medium, and high estimates of QALY, and identify financial values under each

estimate level separately.

Similar to the analysis in Section 4.1, we first consider the expected monetary value of optimiza-

tion for an individual patient, and then use these findings to estimate an overall social value in

dollars. To this end, in Table 8 we display the expected dollar value for an individual patient due to

optimization based policies for patients of different age groups and initial QoL levels under medium

QALY estimates. While the entries in the tables are based on medium QALY estimates, the bottom

rows of the subtables contain dollar value estimates under low and high QALY assumptions as well.

We note that of the three QALY assumptions, the low estimates consider the social impact from

the angle of people’s working efficiency, so the corresponding financial value provides an estimate

of improved productivity in the society. The medium estimate relates to a patient’s income, so

the financial impact can be seen to represent the overall monetary value of enhanced welfare. The

high estimate is related to the situation where a patient is considering to have POP symptoms

treated by paying for the medical expenses, and hence the corresponding financial impact provides

an estimate of saved medical costs at a societal level.

As it can be seen in Table 8, the value of potential QoL improvements due to optimal policies

for a given individual patient can be estimated to be around 10 thousand dollars for patients of

Cases I-III. As expected, this value is lower for Case IV patients, i.e. around 3 thousand dollars

based on medium level estimates of QALY. In addition, patients with higher initial QoL levels


appear to have higher expected returns from optimization based policies for all but the last case

of patients. The monetary values can serve as a further motivation for patients and physicians

to adopt optimization based treatment policies, as they provide a more concrete measure of the

potential improvements due to such policies.

In addition to these individual value estimates, we can also obtain the monetary value of opti-

mization on a societal level by considering the population breakdown among the distinct cases as

described in Section 3.2.2. Using this distribution and the national population projections for 2014

by the U.S. Census Bureau, the societal monetary value of optimization based POP treatment

policies over the entire POP population for the three QALY estimate levels are $7.2 billion, $27

billion, and $45 billion, respectively. A lower bound for the annual impact of this value can be

calculated by assuming that the value for each patient will be realized over a 40-year period, i.e.

the planning window considered in this study. In reality, the value realization for most patients

will happen over a shorter period. This implies a potential annual societal value of at least $675

million (based on medium QALY estimates) due to optimization based treatment policies.

3.3. Impact of Optimization Based Treatment Policies on Treatment Costs

While our analysis indicates that there is a significant socio-economic value that can be gained

through optimization based treatment policies for POP, another issue involves as to whether such

policies imply increased costs in POP treatment. More specifically, we investigate whether opti-

mization based policies prefer more costly treatment alternatives when compared with policies that

represent physician recommendations in current practice. This has significance from a trade-off

perspective, but could also be a relevant concern for healthcare providers and insurance companies.

Barber and Maher (2013) estimate the annual cost of treatment for POP related symptoms in 2013

to be around $1.4 billion in the U.S., and forecast a 4% increase in these costs each year. In this

section, we quantify how this overall cost value can change if optimization based policies were to

be followed in treatment selection for POP.

As part of our analysis, we first consider the frequency of the usage of different treatment options

by optimization based and physician based policies. Given that our representation of the physician

based policies is in the form of randomized policies, we estimate the frequency of the usage of

different treatment options by comparing the expected number of times that each treatment action

is performed over the entire population of POP patients, utilizing the age and QoL distribution of

POP patients as weights. These frequencies under each of the four different cases we consider are

shown in Table 9. The third column under each case in the table contains the percent change in the

implementation frequency of each treatment option due to optimization based policies. As it can be

observed, comparing to physician based treatment policies, optimization based treatment policies


appear to suggest a lower frequency of usage of watchful waiting and conservative treatments for

Cases I, III, and IV. This implies a higher utilization of surgical treatments, with potentially higher

overall treatment costs for the society, as the costs for non-surgical treatments are minimal with

respect to the costs for surgical options. An exception to this is Case III, implying a cost reduction

due to a more frequent usage of watchful waiting under this case.

While the differences in implementation rates can be estimated as such, the cost of a typical

reconstructive or obliterative surgery is somewhat difficult to evaluate. A given surgery can involve

one or more procedures to address POP related symptoms, such as vaginal hysterectomy, abdominal

hysterectomy, cystocele/rectocele repair, vault suspension, and vaginal vault obliteration. In this

study, we utilize the average cost values for reconstructive surgeries as calculated by Calvo et al.

(2017), where the average cost for a reconstructive surgery is estimated to be $5,986. For obliterative

surgery costs, we adopt the costs listed in the Current Procedural Terminology document of the

American Medical Association. The average cost for an obliterative surgery is reported in that

document as being $3,895. The cost estimation for conservative treatments is discussed by Hullfish

et al. (2011) at a level of $1,300, while the cost for watchful waiting is assumed to be zero as such

cost is mostly negligible compared to the other treatment options.

With the frequencies of usage of different treatment methods shown in Table 9, we can develop

estimates for the actual numbers of treatment instances based on the fact that around 200,000

surgeries are performed to treat POP in the U.S annually (Jones et al. 2010). Using this information

in a proportional way, we further show the overall differences in annual treatment costs due to

the implementation of optimization based policies over the entire POP patient population. These

differences are shown in Table 10 for Cases I, III, and IV, as Case II was noted to be seldom

observed in practice. We note that with the increased recommendations for surgical options under

Case I, the overall costs spent on the estimated 10% of the POP patient population is increased by

$19.9 million. Similarly, optimal policies for Case IV use conservative treatments more frequently

than watchful waiting, which results in a slight cost increase of $11.5 million over 5% of the

POP patient population. However, Case III, which corresponds to approximately 85% of the POP

patient population has a reduced frequency of the surgical treatment options under the optimal

policies, resulting in a savings of $223.5 million. In summary, we estimate that the implementation

of optimization based treatment policies can reduce annual treatment costs for POP by around $200

million in the U.S. Hence, optimal policies are expected to result in significant QoL improvements

while at the same time reducing treatment costs.

4. Discussion

As for policy implications, the results and findings of this paper can potentially improve the cur-

rent practice of POP treatments by achieving higher QoL levels for POP patients. To utilize the


optimization based treatment policies, an evaluation of the patient’s QoL is needed by complet-

ing the PFDI and PFIQ questionnaire. Also, a patient would be surveyed about her preference

for preserving coital function to determine its relative importance in quality of life. Based on

these implementations, some policy implications of optimization based treatment policies can be

described as follows.

First, watchful waiting should be the recommended action for most patients with QoL levels

above 7, while surgical treatments should be recommended mostly to patients with QoL levels below

6. However, these cutoff values are not rigid. To that end, conservative treatment methods serve as

a potential option in the transition zone involving QoL levels 5 to 8. In general, for patients with

same QoL levels in this range, the younger patients are better off by utilizing surgical treatments

and more senior patients would benefit from conservative treatments or watchful waiting. As shown

in Table 5, the specifics of these cut-off values vary according to the case considered.

We also demonstrate that there exists a distinct age threshold for choosing obliterative surgery

over reconstructive surgery for a given patient. This cut-off age, specifically when the patient does

not have any preference over preserving coital function, is around 74. In general, a patient younger

than this cut-off age should not go through obliterative surgery. In addition, we show how the

preference of preserving coital function by a patient impacts this cutoff age for choosing obliterative

surgery. In both Case I and II, where obliterative surgery is a potential treatment option, having

some degree of preference for preserving coital function would always move the threshold age up

significantly from 74. A quick reference is that if a patient considers the preservation of coital

function as representing more than 40% of her quality of life, then obliterative surgery should never

be considered as part of the treatment plan.

Through comparison of optimization based and physician based policies we also conclude that

while all POP patients can potentially benefit from using the optimization based treatment policies,

the room for improvement is particularly large for patients younger than 65 years old and with very

low or high initial QoL levels. Our results also indicate that although for some surgical restriction

cases the cost of treatment is slightly increased under optimization based policies, overall at a

societal level the treatment costs are reduced while at the same time improving the expected quality

of life of the patients.

5. Conclusions

With an aging population, POP is becoming an increasingly important disease greatly affecting

the quality of life of females in the society. Therefore, proper treatment planning for POP is of

increasing concern. In this paper, we propose an MDP based model to identify optimal treatment

policies for POP patients in order to maximize their expected future quality of life. We utilize the


best available data to provide findings which can help physicians to potentially treat POP patients

better in practice.

Our optimization based treatment policies are presented in the form of optimal policy tables,

which can be used by physicians and patients by taking into account several attributes, such as the

patient’s age, QoL according to POP symptoms, preferences over preserving coital function, and

other potential restrictive conditions. While many factors play a role in the selection of a treatment

option, our model aggregates all key factors and provides some general guidelines to serve as aids or

references in making treatment selection decisions. The value of optimization is shown by comparing

optimal treatment polices with practical policies, where the latter are identified through physician

surveys. The results also show significant economic incentives for implementation of the optimal

treatment policies in POP treatment practice, as they were demonstrated to be cost-saving.

As future work on this study, implementation of recommended options as part of actual physician

decisions on a given set of patients can be performed. While this requires a long and significant

clinical effort, any conclusions from such a study can be used to validate the findings or help adjust

model assumptions to reflect any other potentially relevant factors.

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Supporting Information

Additional supporting information may be found in the online version of this article:

Appendix A. Transition Probabilities Used in the MDP Model

Appendix B. Expected Percent Improvement in QoL Values over Physician Based Polices by

Implementing Optimization Based Policies

Appendix C. Estimated Distribution of POP Patients in the U.S. by Age Group and QoL

Author: Optimal Treatment Policies for Pelvic Organ ProlapseArticle submitted to ; manuscript no.

Figures

Figure 1 Dynamic treatment decision process for POP.

Prescribe treatment plan Prescribe treatment plan

Observe POP progression


Figure 2 Optimal POP treatment policy when reconstructive surgery option is not available (Case II).

(a) Pn(to) = 0.

Age

10

9

8

7

6

5

4

3

2

1

46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

QoLLevel

Conservative treatments

Watchful waiting

Obliterative surgery

(b) Pn(to) = 0.3.

10

9

8

7

6

5

4

3

2

146 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

Age

QoLLevel


Watchful waiting

Ob


Figure 3 Sensitivity analysis around the preference factor Pn(t) under Case II.

(a) Age and QoL level to recommend oblit-

erative surgery based on preference over the

preservation of coital function.

Age

42

41

40

39

38

37

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

QoL 1

QoL 2

QoL 4

QoL 5

QoL 6

QoL 3

Perform obliterative

surgery if QoL at or

below shown level

Do not recommend

obliterative surgery

Pre

fere

nce facto

r P

n(t

)at tim

e o

f surg

ery

(%

)

(b) Earliest age to recommend obliterative

surgery as a function of preference over the


Preference factor Pn(t) at time of surgery (%) E

arl

iest age t

o r

ecom

mend o

blit

era

tive s

urg

ery

40

45

50

55

60

65

70

75

80

85

0 10 20 30 40 50 60


Figure 4 Optimal POP treatment policy when no surgical option is available (Case IV).

Age

10

9

8

7

6

5

4

3

2

1

46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

Qo

LL

evel


Watchful waiting


Figure 5 Sensitivity analysis around the preference factor Pn(t) under Case I.

(a) Age and QoL level to recommend oblit-

erative surgery based on preference over the


Pre

fere

nce

fa

cto

r P

n(t

) a

t tim

e o

f su

rge

ry (

%)

Age

38

37

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

74 75 76 77 78 79 80 81 82 83 84 85

QoL 1

QoL 2

QoL 3

QoL 4

QoL 5

QoL 6

QoL3

QoL4

Perform obliterative

surgery if QoL at or

below shown level

Do not recommend

obliterative surgery

(b) Earliest age to recommend obliterative

surgery as a function of preference over the


Ea

rlie

st a

ge

to

re

co

mm

en

d o

blit

era

tive

su

rge

ry

Preference factor Pn(t) at time of surgery (%)

72

74

76

78

80

82

84

86

88

0 10 20 30 40 50 60


Figure 6 Optimal POP treatment policy when obliterative surgery option is not available (Case III).

Age

10

9

8

7

6

5

4

3

2

1

46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

Qo

LL

evel

Reconstructive surgery


Watchful waiting


Figure 7 Expected percent improvement in QoL for different cases.

(a) Expected percent improvement in QoL as a

function of initial QoL.

1086420

40%

30%

20%

10%

0%

Initial QoL Level

Expect

ed Qo

L Imp

rovem

ent

Case ICase IICase IIICase IV

(b) Expected percent improvement in QoL as a

function of patient age.

858075706560555045

20%

18%

15%

13%

10%

8%

5%

Age

Expect

ed Qo

L Imp

rovem

ent

Case ICase IICase IIICase IV


Figure 8 Expected percent improvement in QoL as a function of the initial preference factor level for Cases I and

II.

0%

5%

10%

15%

20%

25%

30%

35%

Case I Case III

Exp

ecte

d Q

oL

Imp

rove

me

nt

Pn = 0

Pn = 0.1

Pn = 0.2

Pn = 0.3

Pn = 0.4

Changing Pn_improvementsQoL

Pn(to)=0

Pn(to)=0.1

Pn(to)=0.2

Pn(to)=0.3

Pn(to)=0.4


Figure 9 Optimal POP treatment policy when all treatment options are available (Case I).

(a) Pn(to) = 0

10

9

8

7

6

5

4

3

2

1

46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

Qo

LL

evel



Watchful waiting

Obliterative surgery

Age

(b) Pn(to) = 0.3

Age

Qo

LL

evel

10

9

8

7

6

5

4

3

2

1

46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85


Watchful waiting


Ob


Tables

Table 1 The mean and standard deviation of change in the QoL of a patient after each treatment option based

on a normal distribution.

Mean Standard Deviation Reference

Watchful waiting -0.046 0.025 Handa et al. [2004]

Conservative treatment 0.052 0.447 Barber et al. [2006]

Reconstructive surgery 0.286-0.001t 0.371 Barber et al. [2007], Nguyen and Burchette [2008]

Obliterative surgery 0.238 0.540 Barber et al. [2007]


Table 2 Disutility of treatment options.

Disutility Factor dat Recovery Period

Watchful waiting (Ww) 0 0Conservative (Cs) 0.020 ∼1 weekReconstructive (Re) 0.0026t− 0.0256 4-10 weeksObliterative (Ob) 0.0009t− 0.0085 1-3 weeks


Table 3 Potential treatment options for each surgical history state ht.

Surgical History Indicator ht Potential Treatment Options Aht

ht =−1 A−1 ={Ww,Cs}ht = 0 A0 ={Ww,Cs,Re,Ob}ht = 1 A1 ={Ww,Cs,Re,Ob}ht = 2 A2 ={Ww,Cs,Re,Ob}ht = 3 A3 ={Ww,Cs,Ob}


Table 4 Probabilistic representation of the physician based treatment policies as a function of the optimization

based treatment decisions for each case (Ww: Watchful waiting, Cs: Conservative treatment, Re: Reconstructive

surgery, Ob: Obliterative surgery).

(a) Case I: All Treatment Options are Available.

Case I

Probability thatthe physician basedpolicy decision is

Ww Cs Re Ob

When theoptimization basedpolicy decision is

Ww 0.434 0.433 0.133 -Cs 0.675 0.225 0.100 -Re 0.036 0.238 0.655 0.071Ob - 0.347 0.236 0.417

(b) Case II: No Reconstructive Surgery Option.

Case II

Probability thatthe physician basedpolicy decision isWw Cs Ob


Ww 0.500 0.500 -Cs 0.583 - 0.417Ob - 0.833 0.167

(c) Case III: No Obliterative Surgery Option.

Case III

Probability thatthe physician basedpolicy decision isWw Cs Re


Ww 0.616 0.267 0.117Cs - 0.667 0.333Re - 0.259 0.741

(d) Case IV: No Surgical Options.

Case IV

Probability thatthe physician basedpolicy decision isWw Cs


Ww 1 0.5Cs 0.5 0.5


Table 5 Summary table showing key cut-off values of patient age and QoL for all four cases considered at

Pn(to) = 0.

Watchful waiting: Apply ifQoL greater than or equal to

Reconstructive Surgery: Applyif QoL less than or equal to

Obliterative Surgery: Applyif QoL less than or equal to

Level 9 Level 8 Level 7 L7 L6 L5 L4 L3 L2 L1 Level 6 Level 5 Level 4

Apply treatmentoption if patientyounger than

Case I 67 80 85 53 73 - - - - 74 83 84 85Case II 66 80 85 - - - - - - - 83 84 85Case III 63 79 85 - 47 79 81 82 83 84 - - -Case IV 56 79 85 - - - - - - - - - -


Table 6 Expected percent improvement in QoL due to optimization based policies by age group and symptom

level for different surgical restriction cases.

(a) Case I: All treatment options available.

Age Group QoL 1 QoL 2 QoL 3 QoL 4 QoL 5 QoL 6 QoL 7 QoL 8 QoL 9 QoL 10 Total

46-50 14.1% 14.0% 14.0% 13.9% 13.9% 13.9% 16.4% 15.8% 22.2% 28.7% 16.7%51-55 14.6% 14.5% 14.4% 14.4% 14.4% 14.3% 17.3% 16.1% 23.3% 30.2% 18.2%56-60 15.6% 15.4% 15.3% 15.2% 15.1% 15.1% 17.6% 16.4% 24.6% 31.8% 19.1%61-65 16.6% 16.4% 16.2% 16.1% 16.0% 15.9% 17.2% 16.3% 25.6% 33.1% 19.5%66-70 16.8% 16.5% 16.2% 15.9% 15.7% 15.4% 16.3% 16.3% 25.6% 33.2% 19.4%71-75 14.9% 14.0% 13.2% 12.7% 12.3% 11.8% 13.2% 15.3% 24.1% 30.9% 15.2%76-80 13.2% 11.9% 10.7% 9.6% 8.6% 7.6% 9.0% 13.7% 20.7% 25.8% 11.2%80+ 18.1% 13.8% 11.5% 8.5% 6.8% 4.7% 6.1% 9.9% 13.4% 15.8% 9.4%

Total 16.0% 13.8% 12.8% 12.6% 13.4% 13.5% 15.2% 15.5% 24.1% 31.7% AVG: 17.6%

(b) Case II: No reconstructive surgery option available.


46-50 12.6% 12.3% 12.2% 12.0% 11.9% 11.4% 13.6% 13.2% 19.9% 26.4% 14.4%51-55 12.9% 12.6% 12.5% 12.2% 12.1% 11.6% 14.5% 13.6% 21.0% 27.8% 15.7%56-60 13.9% 13.6% 13.3% 13.1% 12.9% 12.4% 15.0% 14.1% 22.5% 29.4% 16.8%61-65 15.2% 14.8% 14.5% 14.1% 13.9% 13.9% 14.6% 14.5% 23.9% 31.1% 17.5%66-70 15.2% 14.0% 13.3% 12.5% 11.8% 11.2% 12.5% 14.6% 23.1% 29.5% 14.8%76-80 13.6% 12.2% 11.0% 9.6% 8.6% 7.5% 8.5% 13.2% 19.8% 24.9% 11.2%80+ 18.3% 14.5% 11.2% 8.5% 6.5% 4.6% 5.7% 9.6% 12.6% 15.6% 9.4%

Total 25.2% 20.4% 17.0% 14.4% 13.3% 13.4% 12.8% 13.0% 19.4% 25.4% AVG: 13.2%

(c) Case III: No obliterative surgery option available.


46-50 12.6% 12.1% 11.6% 11.1% 10.6% 8.8% 8.0% 7.6% 17.5% 23.7% 10.9%51-55 13.0% 12.5% 11.9% 11.3% 10.8% 8.6% 7.8% 7.3% 18.4% 24.6% 11.9%56-60 14.1% 13.4% 12.7% 12.1% 11.5% 9.4% 7.9% 7.4% 19.6% 26.1% 12.9%61-65 15.5% 14.8% 14.0% 13.2% 12.4% 11.8% 8.1% 8.1% 21.0% 27.5% 14.0%66-70 16.7% 15.7% 14.6% 13.8% 12.8% 11.9% 8.3% 12.5% 21.5% 27.8% 15.5%71-75 17.6% 16.0% 14.6% 13.3% 11.9% 10.8% 7.9% 12.5% 20.1% 25.6% 14.2%76-80 20.2% 17.4% 14.6% 12.2% 10.0% 7.9% 5.8% 10.4% 15.9% 20.0% 13.4%80+ 30.4% 21.3% 14.6% 9.8% 6.6% 3.9% 3.1% 6.1% 8.8% 10.6% 12.5%

Total 16.1% 13.8% 12.2% 11.6% 11.9% 11.7% 13.2% 13.8% 22.4% 29.6% AVG: 15.8%

(d) Case IV: No surgical options available.


46-50 19.9% 17.6% 15.2% 13.2% 11.2% 9.3% 7.5% 5.2% 0.3% 0.0% 7.2%51-55 20.8% 18.4% 15.8% 13.5% 11.2% 9.3% 7.1% 3.6% 0.1% 0.0% 6.4%56-60 22.9% 19.7% 17.0% 14.5% 11.9% 9.6% 7.1% 0.7% 0.1% 0.0% 6.4%61-65 25.8% 21.8% 18.5% 15.4% 12.4% 10.0% 7.2% 0.6% 0.0% 0.0% 7.0%66-70 28.9% 24.7% 20.2% 16.3% 12.9% 10.0% 6.9% 0.4% 0.0% 0.0% 8.6%71-75 33.9% 27.8% 21.7% 16.8% 12.7% 9.2% 5.6% 0.2% 0.0% 0.0% 13.2%76-80 41.4% 31.2% 22.0% 15.9% 10.7% 6.3% 1.6% 0.0% 0.0% 0.0% 18.2%80+ 42.8% 27.3% 16.7% 10.1% 5.5% 2.1% 0.0% 0.0% 0.0% 0.0% 14.0%

Total 38.7% 27.0% 18.8% 14.2% 11.4% 9.0% 6.1% 1.8% 0.1% 0% AVG: 8.6%


Table 7 Estimated distribution of POP patients in the U.S. by age group and QoL.

Age Group QoL 1 QoL 2 QoL 3 QoL 4 QoL 5 QoL 6 QoL 7 QoL 8 QoL 9 QoL 10

46-50 0 % 1.2% 3.1% 6.8% 12.4% 17.2% 21.0% 19.5% 12.7% 6.1%51-55 0 % 1.4% 3.4% 6.8% 11.6% 15.5% 18.3% 17.9% 14.4% 10.7%55-60 0 % 1.5% 4.4% 7.9% 12.1% 15.0% 16.6% 16.3% 14.2% 12.0%61-65 0.5 % 2.1% 4.3% 7.8% 12.6% 15.5% 16.5% 15.8% 13.6% 11.3%66-70 4.7 % 4.3% 4.0% 6.8% 12.8% 15.1% 13.8% 13.0% 12.8% 12.7%71-75 10.2% 9.8% 9.5% 10.0% 11.3% 12.1% 12.4% 11.1% 8.3% 5.3%76-80 15.4% 15.1% 14.9% 13.0% 9.5% 8.7% 10.7% 8.9% 3.5% 0.3%80+ 19.1% 18.9% 18.6% 14.9% 7.5% 5.5% 8.7% 6.6% 0.2% 0%

Total 6.2 % 6.8% 7.8% 9.2% 11.2% 13.1% 14.8% 13.6% 10.0% 7.3%


Table 8 Estimates of the monetary value (in thousands of U.S dollars) due to optimization based policies for an

individual POP patient.

(a) Case I: All treatment options available.


46-50 0 2.62 3.92 5.23 6.54 7.75 10.74 11.77 18.68 26.9051-55 0 2.71 4.02 5.42 6.72 8.03 11.21 12.05 19.61 28.2156-60 0 2.90 4.30 5.70 7.10 8.50 11.49 12.24 20.64 29.6161-65 1.59 3.08 4.58 5.98 7.47 8.87 11.21 12.14 21.58 30.9266-70 1.59 3.08 4.48 5.98 7.38 8.59 10.65 12.14 21.48 31.0171-75 1.40 2.52 3.64 4.67 5.79 6.63 8.59 11.49 20.36 29.1476-80 1.21 2.24 2.99 3.55 4.11 4.30 5.98 10.27 17.84 26.6280+ 1.77 2.71 3.27 3.08 3.08 2.43 3.83 7.01 14.10 0

Low Estimate: $3,029 MEDIUM ESTIMATE: $11,420 High Estimate: $19,722

(b) Case II: No reconstructive surgery option available.


46-50 0 12.61 12.33 11.96 11.58 11.96 12.14 12.33 16.72 21.7651-55 0 12.89 12.52 12.14 11.77 12.70 12.33 12.70 17.28 22.5156-60 0 13.64 13.17 12.61 12.24 12.98 12.80 13.08 18.31 23.4461-65 15.69 14.38 13.73 13.17 12.70 13.08 13.17 12.98 19.24 24.7566-70 16.53 15.69 14.94 14.20 13.54 13.73 13.54 12.52 19.52 25.4171-75 17.65 16.53 15.41 14.38 13.45 12.89 12.80 12.14 18.59 23.1676-80 19.61 17.75 15.88 14.20 12.52 10.74 9.71 10.18 15.32 20.9280+ 33.72 25.22 19.24 14.01 10.46 7.66 4.30 6.44 11.68 0


(c) Case III: No obliterative surgery option available.


46-50 0 11.58 11.40 11.21 11.11 10.65 12.70 12.33 18.59 24.6651-55 0 11.77 11.68 11.40 11.30 10.83 13.54 12.70 19.61 25.9756-60 0 12.70 12.52 12.33 12.05 11.58 14.01 13.17 20.92 27.4661-65 14.57 13.92 13.45 13.17 12.98 12.98 13.64 13.54 22.42 29.1466-70 14.85 14.38 13.92 13.54 13.17 12.80 13.92 14.10 22.88 29.3371-75 14.10 12.98 12.14 11.58 11.02 10.65 11.68 13.64 21.67 27.8376-80 12.70 11.40 10.18 8.97 8.03 7.10 8.03 12.33 19.05 25.5980+ 18.12 14.10 10.55 7.75 5.79 4.11 5.14 8.59 14.20 0


(d) Case IV: No surgical options available.


46-50 0 16.44 14.20 12.33 10.46 8.69 7.01 4.86 0.28 051-55 0 17.19 14.76 12.61 10.46 8.69 6.63 3.36 0.09 056-60 0 18.49 15.88 13.54 11.11 8.97 6.63 0.65 0.09 061-65 25.03 20.36 17.19 14.29 11.58 9.34 6.72 0.56 0 066-70 27.37 23.44 19.05 15.22 12.05 9.34 6.44 0.37 0 071-75 31.94 26.06 20.27 15.69 11.86 8.59 5.23 0.19 0 076-80 38.95 29.23 20.46 14.76 9.99 5.98 1.59 0 0 080+ 39.23 24.00 14.48 8.31 4.48 1.59 0 0 0 0

Low Estimate: $899 MEDIUM ESTIMATE: $3,389 High Estimate: $5,853


Table 9 Frequency of usage of different treatment options in physician based and optimization based policies.

TreatmentsCase I Case II Case III Case IV

OPT PHY DIFF OPT PHY DIFF OPT PHY DIFF OPT PHY DIFF

Ww 24.2% 30.5% -6.3% 24.5% 33.5% -9.0% 26.0% 16.0% 10.0% 31.1% 65.6% -34.5%Cs 27.6% 29.3% -1.7% 36.3% 44.9% -8.6% 41.0% 42.9% -1.9% 68.9% 34.4% 34.5%Re 38.0% 33.3% 4.7% - - - 33.0% 41.1% -8.1% - - -Ob 10.2% 6.9% 3.3% 39.2% 21.6% 17.4% - - - - - -


Table 10 Estimated total annual cost differences (in millions of U.S dollars) of the treatment options in

physician based and optimization based policies under Cases I, III, and IV.

TreatmentCase I Case III Case IV

OPT PHY DIFF OPT PHY DIFF OPT PHY DIFF

Ww - - - - - - - - -Cs 18.4 19.5 -1.1 232.9 242.9 -10.0 23.0 11.5 11.5Re 116.8 102.2 14.6 860.2 1073.7 -213.5 - - -Ob 20.3 13.9 6.4 - - - - - -

Change in cost +$19.9 mil -$223.5 mil +$11.5 mil

Overall difference: -$192.1 mil


Appendix A. Transition Probabilities Used in the MDP Model

Table A.1 pt(lt+1 = l′|lt = l, at = Ww).HH

HHHll′

1 2 3 4 5 6 7 8 9 10

1 0.967 0.033 0 0 0 0 0 0 0 0

2 0.015 0.953 0.033 0 0 0 0 0 0 0

3 0 0.015 0.953 0.033 0 0 0 0 0 0

4 0 0 0.015 0.953 0.033 0 0 0 0 0

5 0 0 0 0.015 0.953 0.033 0 0 0 0

6 0 0 0 0 0.015 0.953 0.033 0 0 0

7 0 0 0 0 0 0.015 0.953 0.033 0 0

8 0 0 0 0 0 0 0.015 0.953 0.033 0

9 0 0 0 0 0 0 0 0.015 0.953 0.033

10 0 0 0 0 0 0 0 0 0.015 0.985

Table A.2 pt(lt+1 = l′|lt = l, at = Cs).HH

HHHll′

1 2 3 4 5 6 7 8 9 10

1 0.144 0.148 0.144 0.134 0.118 0.099 0.079 0.060 0.044 0.030

2 0.121 0.130 0.134 0.131 0.121 0.107 0.090 0.072 0.055 0.040

3 0.100 0.113 0.122 0.125 0.122 0.114 0.100 0.084 0.067 0.051

4 0.081 0.097 0.110 0.118 0.121 0.118 0.110 0.097 0.082 0.065

5 0.065 0.081 0.097 0.110 0.118 0.121 0.119 0.110 0.097 0.082

6 0.051 0.067 0.084 0.100 0.113 0.122 0.126 0.123 0.114 0.101

7 0.039 0.054 0.072 0.090 0.107 0.121 0.131 0.134 0.131 0.122

8 0.030 0.043 0.060 0.079 0.099 0.118 0.134 0.144 0.148 0.145

9 0.022 0.034 0.050 0.069 0.090 0.113 0.135 0.153 0.165 0.169

10 0.016 0.026 0.040 0.059 0.081 0.107 0.134 0.160 0.181 0.195

Table A.3 pt(lt+1 = l′|lt = l, at = Re). As the transition probabilities are a function of age t, a sample matrix for

t = 60 is included.HHHHHl

l′1 2 3 4 5 6 7 8 9 10

1 0.104 0.113 0.118 0.119 0.116 0.109 0.099 0.087 0.074 0.061

2 0.090 0.101 0.109 0.114 0.115 0.112 0.106 0.096 0.084 0.072

3 0.078 0.090 0.101 0.109 0.113 0.114 0.111 0.105 0.095 0.084

4 0.066 0.079 0.092 0.102 0.111 0.116 0.117 0.114 0.107 0.097

5 0.056 0.069 0.083 0.096 0.107 0.116 0.121 0.122 0.119 0.112

6 0.047 0.060 0.074 0.089 0.103 0.115 0.124 0.130 0.131 0.128

7 0.039 0.051 0.066 0.082 0.098 0.113 0.127 0.137 0.143 0.144

8 0.032 0.044 0.058 0.074 0.092 0.111 0.128 0.144 0.155 0.162

9 0.026 0.037 0.051 0.067 0.087 0.107 0.129 0.149 0.167 0.180

10 0.021 0.031 0.044 0.061 0.081 0.103 0.128 0.154 0.178 0.199


Table A.4 pt(lt+1 = l′|lt = l, at = Ob).HHHHHl

l′1 2 3 4 5 6 7 8 9 10

1 0.103 0.111 0.117 0.118 0.116 0.109 0.100 0.088 0.075 0.062

2 0.089 0.100 0.108 0.113 0.115 0.112 0.106 0.097 0.086 0.073

3 0.076 0.089 0.099 0.108 0.113 0.114 0.112 0.106 0.097 0.086

4 0.065 0.078 0.091 0.102 0.110 0.116 0.117 0.115 0.108 0.099

5 0.055 0.068 0.082 0.095 0.107 0.116 0.121 0.123 0.120 0.114

6 0.046 0.059 0.073 0.088 0.102 0.115 0.125 0.131 0.132 0.129

7 0.038 0.051 0.065 0.081 0.097 0.113 0.127 0.138 0.144 0.146

8 0.031 0.043 0.057 0.074 0.092 0.110 0.128 0.144 0.156 0.164

9 0.026 0.036 0.050 0.067 0.086 0.107 0.129 0.149 0.168 0.182

10 0.021 0.031 0.044 0.060 0.080 0.103 0.128 0.154 0.179 0.201


Appendix B. Expected Percent Improvement in QoL Values over PhysicianBased Polices by Implementing Optimization Based Policies

Table B.1 Expected percent improvement in QoL - Case I.

Case I QoL 1 QoL 2 QoL 3 QoL 4 QoL 5 QoL 6 QoL 7 QoL 8 QoL 9 QoL 10

Age 46 14.0% 14.1% 13.9% 13.8% 13.9% 13.9% 14.7% 15.6% 21.8% 28.2%Age 47 13.9% 14.0% 13.9% 13.8% 13.8% 13.8% 16.6% 15.7% 22.0% 28.4%Age 48 14.0% 13.9% 13.9% 13.9% 14.0% 13.9% 16.7% 15.8% 22.2% 28.7%Age 49 14.2% 14.1% 14.1% 14.0% 13.9% 13.8% 16.9% 15.8% 22.3% 28.9%Age 50 14.2% 14.1% 14.1% 14.2% 14.1% 13.9% 17.0% 15.9% 22.6% 29.2%Age 51 14.3% 14.2% 14.1% 14.2% 14.2% 14.0% 17.1% 16.0% 22.8% 29.6%Age 52 14.4% 14.3% 14.3% 14.3% 14.4% 14.2% 17.2% 16.1% 23.0% 29.8%Age 53 14.7% 14.5% 14.4% 14.3% 14.4% 14.1% 17.2% 16.2% 23.3% 30.2%Age 54 14.7% 14.5% 14.5% 14.5% 14.4% 14.4% 17.3% 16.2% 23.6% 30.4%Age 55 14.9% 14.7% 14.7% 14.8% 14.6% 14.6% 17.5% 16.3% 23.8% 30.8%Age 56 15.1% 15.1% 15.0% 14.9% 14.6% 14.8% 17.5% 16.3% 24.1% 31.2%Age 57 15.3% 15.2% 15.1% 15.1% 15.0% 14.9% 17.6% 16.4% 24.4% 31.4%Age 58 15.6% 15.3% 15.3% 15.3% 15.0% 15.0% 17.6% 16.4% 24.5% 31.8%Age 59 15.8% 15.7% 15.6% 15.3% 15.3% 15.3% 17.6% 16.5% 24.8% 32.1%Age 60 16.0% 15.8% 15.8% 15.6% 15.4% 15.5% 17.6% 16.5% 25.0% 32.3%Age 61 16.2% 16.1% 15.9% 15.7% 15.6% 15.5% 17.4% 16.5% 25.3% 32.8%Age 62 16.4% 16.0% 16.0% 15.8% 15.7% 16.0% 17.3% 16.5% 25.5% 32.9%Age 63 16.7% 16.5% 16.3% 16.1% 16.1% 15.8% 17.1% 16.4% 25.8% 33.2%Age 64 17.0% 16.9% 16.7% 16.5% 16.5% 16.1% 16.6% 16.2% 25.9% 33.3%Age 65 16.9% 16.8% 16.3% 16.3% 16.2% 15.8% 17.4% 16.1% 25.8% 33.3%Age 66 16.9% 16.6% 16.5% 16.2% 15.9% 15.6% 17.1% 16.1% 25.8% 33.5%Age 67 16.9% 16.6% 16.5% 16.1% 16.0% 15.7% 16.8% 16.2% 25.8% 33.4%Age 68 16.7% 16.6% 16.3% 16.0% 15.7% 15.4% 16.4% 16.5% 25.7% 33.2%Age 69 16.7% 16.5% 16.1% 15.8% 15.5% 15.2% 15.9% 16.5% 25.5% 33.1%Age 70 16.5% 16.2% 15.8% 15.5% 15.3% 15.0% 15.3% 16.3% 25.2% 32.7%Age 71 16.3% 15.9% 15.4% 15.2% 14.9% 14.5% 14.6% 16.0% 24.8% 32.1%Age 72 15.8% 15.4% 14.8% 14.2% 14.1% 13.7% 13.9% 15.6% 24.5% 31.5%Age 73 14.9% 13.9% 13.3% 12.9% 12.5% 12.3% 13.1% 15.2% 24.2% 30.9%Age 74 14.3% 12.4% 11.4% 10.8% 10.1% 9.4% 12.4% 15.1% 23.6% 30.4%Age 75 13.4% 12.4% 11.3% 10.6% 9.9% 9.0% 11.7% 14.8% 23.2% 29.7%Age 76 13.1% 12.1% 10.9% 10.3% 9.5% 8.6% 10.9% 14.5% 22.5% 28.5%Age 77 13.1% 11.9% 10.7% 9.9% 9.1% 8.2% 10.0% 14.2% 21.8% 27.3%Age 78 13.0% 11.9% 10.6% 9.6% 8.6% 7.7% 9.0% 13.8% 20.7% 25.8%Age 79 13.1% 11.9% 10.5% 9.3% 8.3% 7.1% 8.0% 13.3% 19.9% 24.7%Age 80 13.9% 11.9% 10.7% 9.1% 7.6% 6.5% 7.0% 12.6% 18.7% 22.6%Age 81 14.6% 12.5% 11.1% 8.7% 7.3% 5.8% 6.6% 11.8% 16.8% 19.7%Age 82 16.9% 14.1% 11.3% 8.9% 7.0% 5.0% 6.4% 10.3% 14.2% 16.4%Age 83 21.5% 16.2% 13.3% 9.3% 6.9% 3.7% 5.9% 8.5% 10.6% 12.5%Age 84 23.6% 14.4% 10.9% 6.6% 5.0% 2.4% 4.6% 6.1% 6.9% 7.8%


Table B.2 Expected percent improvement in QoL - Case II.

Case II QoL 1 QoL 2 QoL 3 QoL 4 QoL 5 QoL 6 QoL 7 QoL 8 QoL 9 QoL 10



Table B.3 Expected percent improvement in QoL - Case III.

Case III QoL 1 QoL 2 QoL 3 QoL 4 QoL 5 QoL 6 QoL 7 QoL 8 QoL 9 QoL 10



Table B.4 Expected percent improvement in QoL - Case IV.

Case IV QoL 1 QoL 2 QoL 3 QoL 4 QoL 5 QoL 6 QoL 7 QoL 8 QoL 9 QoL 10



Appendix C. Estimated Distribution of POP Patients in the U.S. by AgeGroup and QoL

Table C.1 Estimated distribution of POP patients in the U.S. by age group and QoL.

QoL 1 QoL 2 QoL 3 QoL 4 QoL 5 QoL 6 QoL 7 QoL 8 QoL 9 QoL 10

Age 46 0% 1% 2.9% 7% 13.2% 18.2% 21.7% 19.6% 12% 4.4%Age 47 0% 1.1% 3% 6.9% 12.8% 17.7% 21.3% 19.6% 12.4% 5.2%Age 48 0% 1.2% 3.1% 6.8% 12.4% 17.3% 21% 19.5% 12.7% 6%Age 49 0% 1.4% 3.2% 6.8% 12% 16.6% 20.7% 19.5% 13.1% 6.7%Age 50 0% 1.5% 3.3% 6.7% 11.6% 16.2% 20.3% 19.4% 13.5% 7.5%Age 51 0% 1.6% 3.4% 6.6% 11.2% 15.7% 20% 19.4% 13.8% 8.3Age 52 0% 1.5% 3.4% 6.7% 11.4% 15.7% 19.1% 18.6% 14.1% 9.5%Age 53 0% 1.4% 3.4% 6.8% 11.6% 15.4% 18.3% 17.9% 14.4% 10.8%Age 54 0% 1.3% 3.4% 6.9% 11.8% 15.3% 17.5% 17.2% 14.6% 12%Age 55 0% 1.2% 3.3% 6.9% 12% 15.3% 16.7% 16.5% 14.9% 13.2%Age 56 0% 1.1% 3.3% 7% 12.2% 15.1% 15.9% 15.9% 15.1% 14.4%Age 57 0% 1.3% 3.9% 7.5% 12.1% 15% 16.2% 16.1% 14.7% 13.2%Age 58 0% 1.5% 4.4% 7.9% 12.1% 15% 16.6% 16.3% 14.2% 12%Age 59 0% 1.6% 4.9% 8.4% 12% 15% 17% 16.6% 13.7% 10.8Age 60 0% 1.8% 5.4% 8.8% 12% 14.9% 17.4% 16.8% 13.2% 9.7%Age 61 0% 2% 6% 9.3% 11.9% 14.7% 17.7% 17.1% 12.8% 8.5%Age 62 0% 2% 5.1% 8.6% 12.3% 15.3% 17.1% 16.5% 13.2% 9.9%Age 63 0% 2.1% 4.3% 7.8% 12.7% 15.5% 16.6% 15.9% 13.7% 11.4%Age 64 0.8% 2.1% 3.5% 7.1% 12.9% 15.8% 15.8% 15.2% 14% 12.8%Age 65 1.7% 2.2% 2.6% 6.3% 13.2% 16% 15.1% 14.5% 14.3% 14.1%Age 66 2.6% 2.2% 1.8% 5.5% 13.4% 16.3% 14.4% 13.8% 14.6% 15.4%Age 67 3.6% 3.3% 2.9% 6.2% 13.1% 15.7% 14.1% 13.4% 13.7% 14%Age 68 4.7% 4.3% 4% 6.8% 12.8% 15.2% 13.8% 13% 12.8% 12.6%Age 69 5.8% 5.4% 5.1% 7.4% 12.5% 14.5% 13.5% 12.7% 11.9% 11.2%Age 70 6.9% 6.5% 6.2% 8.1% 12.2% 13.9% 13.2% 12.3% 11% 9.7%Age 71 8% 7.6% 7.3% 8.7% 11.9% 13.2% 13% 11.9% 10.1% 8.3%Age 72 9.1% 8.7% 8.4% 9.3% 11.6% 12.6% 12.7% 11.5% 9.2% 6.9%Age 73 10.2% 9.8% 9.5% 10% 11.3% 12% 12.4% 11.1% 8.3% 5.4%Age 74 11.3% 11% 10.6% 10.6% 11% 11.4% 12.1% 10.7% 7.3% 4%Age 75 12.4% 12.1% 11.8% 11.3% 10.6% 10.8% 11.8% 10.3% 6.4% 2.5%Age 76 13.5% 13.2% 12.9% 11.9% 10.3% 10.3% 11.5% 9.9% 5.5% 1%Age 77 14.6% 14.3% 14% 12.5% 10% 9.5% 11.1% 9.5% 4.5% 0%Age 78 15.5% 15.2% 14.9% 13% 9.5% 8.8% 10.7% 8.9% 3.5% 0%Age 79 16.3% 16.1% 15.8% 13.5% 9.1% 8% 10.2% 8.4% 2.6% 0%Age 80 17.2% 16.9% 16.7% 13.9% 8.6% 7.4% 9.8% 7.9% 1.6% 0%Age 81 18% 17.8% 17.6% 14.4% 8.2% 6.5% 9.4% 7.4% 0.7% 0%Age 82 18.8% 18.6% 18.4% 14.8% 7.8% 5.8% 8.9% 6.9% 0% 0%Age 83 19.4% 19.2% 19% 15% 7.3% 5.2% 8.5% 6.4% 0% 0%Age 84 20% 19.8% 19.6% 15.3% 6.9% 4.5% 8% 5.9% 0% 0%

optimal treatment policies for pelvic organ prolapse in women · 2019/9/4 · author: optimal...

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