comparing strategies to prevent stroke and ischemic heart...

Research ArticleComparing Strategies to Prevent Stroke and Ischemic HeartDisease in the Tunisian Population Markov Modeling ApproachUsing a Comprehensive Sensitivity Analysis Algorithm

Olfa Saidi 1MartinOrsquoFlaherty2 Nada Zoghlami1 DhaferMalouche13 SimonCapewell2

Julia A Critchley4 Piotr Bandosz2 Habiba Ben Romdhane1 and Maria Guzman Castillo2

1Cardiovascular Epidemiology and Prevention Research Laboratory Faculty of Medicine of Tunis University Tunis El ManarTunis Tunisia2Department of Public Health and Policy University of Liverpool Liverpool UK3National Institute of Statistics and Data Analysis Tunis Tunis Tunisia4Population Health Research Institute St Georgersquos University of London London UK

Correspondence should be addressed to Olfa Saidi olfasaidiyahoofr

Received 25 September 2018 Revised 27 November 2018 Accepted 18 December 2018 Published 29 January 2019

Guest Editor Giedrius Vanagas

Copyright copy 2019 Olfa Saidi et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Background Mathematical models offer the potential to analyze and compare the effectiveness of very different interventions toprevent future cardiovascular diseaseWe developed a comprehensiveMarkovmodel to assess the impact of three interventions toreduce ischemic heart diseases (IHD) and stroke deaths (i) improvedmedical treatments in acute phase (ii) secondary preventionby increasing the uptake of statins (iii) primary prevention using health promotion to reduce dietary salt consumptionMethodsWe developed and validated a Markov model for the Tunisian population aged 35ndash94 years old over a 20-year time horizon Wecompared the impact of specific treatments for stroke lifestyle and primary prevention on both IHD and stroke deaths We thenundertook extensive sensitivity analyses using both a probabilistic multivariate approach and simple linear regression (meta-modeling) Results +e model forecast a dramatic mortality rise with 111134 IHD and stroke deaths (95 CI 106567 to 115048)predicted in 2025 in Tunisia +e salt reduction offered the potentially most powerful preventive intervention that might reduceIHD and stroke deaths by 27 (minus30240 [minus30580 to minus29900]) compared with 1 for medical strategies and 3 for secondaryprevention +e metamodeling highlighted that the initial development of a minor stroke substantially increased the subsequentprobability of a fatal stroke or IHD death Conclusions +e primary prevention of cardiovascular disease via a reduction in dietarysalt consumption appearedmuchmore effective than secondary or tertiary prevention approaches Our simple but comprehensivemodel offers a potentially attractive methodological approach that might now be extended and replicated in other contextsand populations

1 Background

Cardiovascular diseases (CVDs) cause nearly one-third of alldeaths worldwide 80 of these deaths occur in low-incomeand middle-income countries Ischemic heart diseases(IHD) and stroke account for the greatest proportion ofCVDs [1ndash3]

+e burden of IHD and stroke is considerable and theyare the first and second leading causes of death respectively

worldwide [4 5] +ey accounted for 152 million deaths(150 million to 156 million) in 2015 [4] According to theWorld Health Organization (WHO) there are 15 millionpeople worldwide who suffer from stroke each year amongthem 5 million die and another 5 million are left perma-nently disabled causing a heavy burden for the family andcommunity

+e burden of stroke will increase significantly over thenext 20 years particularly in developing countries [6] +us

HindawiComputational and Mathematical Methods in MedicineVolume 2019 Article ID 2123079 11 pageshttpsdoiorg10115520192123079

the analysis of the effectiveness of health promotion in-terventions is urgently required for appropriate planning toreduce this burden [7]

Traditional epidemiological study designs cannot ad-dress these issues even clinical trials are usually restricted byinclusion and exclusion criteria and not necessarily gener-alizable to the entire population [8]

Mathematical modeling overcomes many of these lim-itations It plays a crucial role in helping to guide the mosteffective and cost-effective ways to achieve the goals of healthpromotion designed and validated to guide health policiesand development strategies at several levels [9 10]

Briefly a model is a simplification of a real situation andcan encompass a simple descriptive tool up to systems ofmathematical equations [11]

+e application of mathematical models in medicine hasproved useful and has become more frequent especially forcardiovascular diseases (CVDs) [12ndash16] and assessing po-tential impacts of policies or interventions designed to alterdisease trajectories in Tunisia [17 18]

A commonly used technique is Markov modeling an ap-proach that models groups of individuals transitioning acrossspecified pathways informed by transition probabilities [18ndash20]

Due to the frequent uncertainty of the Markov modelrsquosinputs sensitivity analyses to assess the robustness of themodel results are strongly recommended by modelingguidelines Such uncertainty analyses assess confidence in achosen course of action and ascertain the value of collectingadditional information to better inform the decision [21]

Our study aims (i) to describe a comprehensive Markovmodel based on both a probabilistic multivariate approachand simple linear regressionmetamodeling and (ii) using themodel to evaluate the effects of increases in uptake of stroketreatments lifestyle changes and primary prevention amongthe Tunisian population aged 35ndash94 years old in 2025 Weexamined three interventions (a) improved medical treat-ments in the acute phase (b) secondary prevention of strokeby increasing the prescribing of statins and (c) primaryprevention aiming to reduce salt intake

2 Methods

In this study we describe the development of a Markov IHDand stroke model

21 Definition of Markov Model Markov models are a typemathematical model based on matrix algebra which de-scribes the transitions a cohort of patients make among anumber of mutually exclusive and exhaustive health statesduring a series of short intervals or cycles In this model apatient is always in one of the finite number of health statesevents are modeled as transitions from one state to anotherand contribution of utility to overall prognosis depend onlength of time spent in health states [19] +e components ofa Markov model are shown below (Figure 1)

(i) States the set of distinct health states under con-sideration in the model together with the possibletransitions between them

(ii) Cycle length the length of time represented by asingle stage (or cycle) in a Markov process Markovmodels are developed to simulate both short-cycleand long-term processes (eg cardiovasculardiseases)

(iii) Transition probabilities the matrix of probabilitiesof moving between health states from one stage tothe next

22 Process of Mathematical Modeling Based on MarkovApproach Before starting the data collection and the cal-culation we first defined our model by specifying the dif-ferent states that can be included based on the literature andexpert opinions

S S1 S2 S31113864 1113865 set of states in the process (1)

Having specified the structure of the model in terms ofthe possible transitions between states we defined thetransition probabilities based on available data

+e transition probability (TPij) is defined as a condi-tional probability (Pt(sjsi)) of making a transition (mov-ing) from state i to state j during a single cycle (t)Additionally transition probabilities are stratified by sex andage groups ag isin c1 c2 cg1113966 1113967 where c1 c2 cg repre-sents a set of age groups [19 22]

One of the goals of the Markov model is to study thepotential effects of some health promotion interventionsWe modeled first a baseline scenario and then the in-tervention scenarios

For the baseline scenario we assumed no change willhappen during the period ldquoTrdquo of study (20 years) in eitherthe present uptake rates of medical therapies or populationlevel uptakes of specific nutrients

Based on the model structure in Figure 1 we assume thatwe will apply three interventions to study their impact onmortality in the future (over the 20 years from t year 1 toyear 20)

We define a policy Π (I0 I1 I2 I3) as a set of thehealth promotion interventions

I0 refers the baseline scenario we assumed no changewill happen during 20 yearsI1 scenario aimed to improve medical treatments inacute phase

Healthypopulation

Dead

SickTP11

TP12

TP13 TP23

TP22

Figure 1 Markov diagram states and transition probabilities (eachcircle represents a Markov state and arrows indicate transitionprobabilities)

2 Computational and Mathematical Methods in Medicine

I2 scenario for secondary preventionI3 scenario for primary prevention

Starting by the baseline scenario the process of theMarkov model is based on the two first steps below

Step I Calculate probabilistic transition probabilitiesProbabilistic sensitivity analysis aims to fully evaluate the

combination of uncertainty in all model inputs (includingtransition probabilities) simultaneously on the robustness ofmodel results

+e point estimates in the model can be replaced withprobability distributions where the mean of the distributionreflects the best estimate of the parameter

In this step each input parameter (TPij) is assigned anappropriate statistical distribution and a Monte Carlosimulation is run multiple times (eg 1000) +e iteration isstopped when the difference of the outcomes is sufficientlysmall

We assume for example that TPs follow the distributiondefined by beta (α β) where α probability distributions aredefined on the interval [0 1] parameterized by two positiveshape parameters denoted by α and β that appear as ex-ponents of the random variable and control the shape of thedistribution [23]

Step II Calculate the number of people in each state for thebaseline scenario

+e next step is to define the number of people in eachstate based on the TPs between states and the number ofpeople in the starting state ldquohealthy peoplerdquo

In this stage we define the number of people in each statefor the baseline scenario (healthy people (NHP) sick (NS)and deaths (ND)) for all gender and age groups from t year1 to yearT given by the following equations

NHPt NHPtminus1 times 1minus 1113944TPij1113872 1113873

NSt NStminus1 + NHPtminus1 times TP121113872 1113873

NDt NDtminus1 + NHPtminus1 times TP131113872 1113873 + NStminus1 times TP231113872 1113873

(2)

Another indicator can be calculated based on this modelthat is life years gained (LY) defined by the followingequation

LYt NHPt minusNDt (3)

+e model is then run several times (eg 1000 simu-lations) For each simulation model parameter values arerandomly drawn from each of the distributions and theexpected model outcome is recorded +e 1000 simulationsresult in a distribution of expected model outcomes(eg deaths) which reflects the overall parameter un-certainty in the mode [24]

At the end of the simulation the mean as well as thelower bound (LB) and upper bound (UB) of 95 confidenceinterval of the inputs and outputs will be calculated whichcorrespond to Steps I and II presented in Algorithm 1

Step III Calculate the number of people in each state for theinterventions scenarios

For the interventions scenarios the model required abase estimate of risk reduction in deaths and the age effect tocalculate policy effectiveness (ΠIi

e ) of each intervention+e policy effectiveness is defined by the following

formula

1113945

Ii

e

1minus RRi times ae( 1113857 (4)

where RRi is the risk reduction associated with the in-tervention Ii(i13) obtained from previous randomizedcontrolled trials and meta-analyses to estimate the re-duction in age-specific deaths and ae represents the ageeffects for each intervention risk reduction valueΠIi

e is thenused to scale the transition probabilities connected to deathstates

In this stage after recalculating the TPs we define thenumber of people in each state (healthy people (NHPIi) sick(NSIi) and deaths (NDIi) for all sex and age groups fromt year 1 to yearT for the interventions scenarios Ii givenby the following equations

NHPlit NHPli

tminus1 times 1minusTP12 minusTP13 times 1113945

Ii

e

⎛⎝ ⎞⎠

NSlit NSli

tminus1 + NHPlitminus1 times TP121113872 1113873

NDlit NDli

tminus1 + NHPlitminus1 times TP131113872 1113873 + NSli

tminus1 times TP23 times 1113945Ii

e

⎛⎝ ⎞⎠

LYlit NHPli

t minusNDlit

(5)

Step IV Calculate the final outputs (DPPs and LY)Finally we calculate the total number of CVD deaths

(ischemic stroke and IHD deaths) that could be prevented orpostponed (DPPs) and the life years gained (LY) under eachspecific scenario (equations (6) and (7)) compared to thebaseline scenario for all sex and age groups from t year 1 toyearT for the interventions scenarios Ii

DPPlist

NDlit minusND

l0t (6)

LYligt

LYlit minus LY

l0t (7)

Step V Linear regression metamodelingMost current modeling studies are limited to the first

four stages and ignore this important step of metamodelingto analyze which model inputs are most influential in af-fecting the results +e goal of metamodeling was thus toincrease the transparency of decision-making analyticmodels and better communicate their results

+is step is based on the application of a simple linearregression metamodel (LRM) for the optimalpolicy (Figure 2) [25]

Computational and Mathematical Methods in Medicine 3

+e original motivation for metamodeling was to definea simpler mathematical relationship between model outputsand inputs than the actual model

+e LRM is defined by the following formulaND β0 + βijTPij + ε (8)

where ND is the number of deaths (output of the model) β0(the intercept) is the expected outcomewhen all parameters areset to zero TPij the transition probabilities (inputs) βij the

other coefficients are interpreted relative to a 1-unit change ineach parameter on the original scales and ε is the residual term

Furthermore the absolute value of the coefficients of theparameters ldquoβijrdquo can be used to rank parameters by theirimportance the higher the coefficient is the more thevariable is important and relevant

+e algorithm below summarizes the process with threestates that could be generalized to n states depending on thecontext to study (Algorithm 1)

Step I Calculate probabilistic transition probabilitiesfor all k isin 1Male 2 Female dofor all age groups ag isin c1 c2 cg1113966 1113967 dofor t 1T do

TPij⟵ beta(αij βij)

end forend for

end forStep II Calculate the number of people in each state NHP NS and ND (Baseline scenario)for all k isin 1Male 2 Female dofor all age groups ag isin c1 c2 cg1113966 1113967 dofor t 1T doNHPt NHPtminus1 times (1minus 1113936TPij)

NSt NStminus1 + (NHPtminus1 times TP12)

NDt NDtminus1 + (NHPtminus1 times TP13) + (NStminus1 times TP23)

LYt NHPt + NDt

end forend for

end forStep III Calculate the number of people in each state for the interventions scenariosfor all k isin 1Male 2 Female dofor all age groups ag isin c1 c2 cg1113966 1113967 do

for all intervention Ii isin Π (I1 I3) doΠIi

e 1minus (RRi times ae) where RRIiis the intervention risk reduction value and ae its age effects

for t 1 T

NHPlit NHPli

tminus1 times (1minusTP12 minusTP13 timesΠIie )

NSlit NSli

tminus1 + (NHPlitminus1 times TP12)

NDlit NDli

tminus1 + (NHPlitminus1 times TP13) + (NSli

tminus1 times TP23 times ΠIie )

LYlit NHPli

t minusNDlit

end forend forend for

end forStep IV Calculate the final outputs (DPPs and LY)for all k isin 1Male 2 Female dofor all age groups ag isin c1 c2 cg1113966 1113967 dofor all intervention Ii isin Π (I1 I3) doDPPli

st 1113936

T1 ND

lit minusND

l0t

LYligt

1113936T1 LY

lit minus LY

l0t end for

end forend for

end forStep V Linear regression metamodelingCalculate the βij coefficients of the parametersfor all k isin 1Male 2 Female dofor all age groups ag isin c1 c2 cg1113966 1113967 doSolve the equation ND β0 + βijTPij + ε

end forend for

ALGORITHM 1 Comprehensive algorithm of the Markov model and of sensitivity analysis


23 Case Study +e algorithm introduced above has beenimplemented using R (Version R320) software and ap-plied on Tunisian data +e source codes are available fromthe authors upon request

Our model predicts both IHD and stroke deaths in 2025among the Tunisian population aged 35ndash94 years old bothmen and women and compares the impact of specifictreatments for stroke lifestyle changes and primaryprevention

24 Model Structure Data were integrated and analyzedusing a closed cohort model based on a Markov approachwith transition probabilities starting from population free ofischemic stroke and moving to health states reflecting thenatural history of ischemic stroke [26 27] +erefore thestarting states are defined by the size of the population andthe number of strokes occurring within this population +enumber of persons moving from the starting states to thestroke and death states is estimated by the transitionprobabilities (Table 9 in the appendix in the supplementarymaterials)

+ere are two absorbing states IHD and stroke deathsand non-IHD and stroke deaths as competing risks formortality IHD and stroke have several risk factors incommon increased salt intake is associated with hyper-tension which is one of the major risk factors for both strokeand IHD +erefore any policy aimed at decreasing pop-ulation levelrsquos intake of salt will reduce the risk of bothdiseases [28]

Potential overlaps between the healthy minor majorstroke and deaths are managed by calculating the condi-tional probabilities of membership A key element of themodel is the calculation of the transition probabilities (TPs)particularly those related to stroke and IHD mortality(Figure 3) +e TP calculations are detailed in Table 10 in theAppendix in the supplementary materials

25 Baseline Scenario In the baseline scenario we assumedthere would be no change over the 20-year model period inthe present uptake rates of acute phase medical treatments(thrombolysis aspirin and stroke unit) or treatments forsecondary prevention following stroke (aspirin statin an-ticoagulants blood pressure control and smoking cessation)or treatment and policies for primary prevention (blood

pressure control glucose control lipid lowering salt uptakeand smoking cessation)

26 Prevention Scenarios In this paper we evaluated thefollowing three scenarios

(1) I1 the first scenario aimed to improve medicaltreatments in the acute phase increasing throm-bolysis prescribing from 0 to 50 and hospitali-zation in stroke units from 10 to 100 in Tunisia

(2) I2 the second scenario aimed to act on medicaltreatments after a stroke increasing the prescribingof statins from 11 to 100 (secondary prevention)

(3) I3 the third scenario aimed to reduce the con-sumption of salt by 30 from 14 grams to 9 gramsper day (primary prevention)

Total policy refers to the combined effects of all the threeprevious strategies acute treatment + secondary pre-vention + primary prevention

27 Modeling Policy Effectiveness and Its Impact in Mortality+e model applies the relative risk reduction (RRR) asmentioned in the algorithm above quantified for each in-tervention scenario in previous randomized controlled trialsand meta-analyses based on international studies (data aredetailed in the Appendix in the supplementary materials(Table 8))

28 Data Sources Published and unpublished data wereidentified by extensive searches complemented with specif-ically designed surveys Data items included (i) number ofstroke patients (minor and major) (ii) uptake of specificmedical and surgical treatments (iii) population data in theinitial study year (2005) and (iv) mortality data (after one year(data in 2006) and after 5 years (data in 2010)) Data sourcesare detailed in Appendixin the supplementary materials

29 Model Outputs +e outputs of this model are theprediction of stroke and IHD deaths prevented or postponed(DPPs) and the life years gained (LY) among the Tunisianpopulation aged 35ndash94 years old starting from 2005 over atwenty-year time period(to 2025) with and without possibleinterventions to reduce this mortality

We modeled all the intervention scenarios to calculatethe total number of CVD deaths (ischemic stroke andIHD deaths) that may be prevented or postponed and theLY for each specific scenario compared to the baselinescenario

3 Results

31 Baseline Scenario In the baseline scenario the modelforecast 111140 [95 CI 106570 to 115050] IHD and is-chemic stroke deaths for people aged 35ndash94 years between2005 and 2025 including 68890 [95 CI 65730 to 72350]among men and 42250 [95 CI 38840 to 44600] amongwomen

Real life Outputs (egdeaths (ND))

Inputs (TPij)

LRMND = β0 + βij TPij + ε

Figure 2 Simple linear regression metamodel (LRM) to sum-marize the relationship between model inputs and outputs


+emodel estimated that the acute stroke treatment andsecondary prevention following stroke would respectivelyprevent 230 [95 CI 200 to 260] deaths due to stroke andIHD and 1920 [95 CI 1830 to 2000] in 2025 whilst primaryprevention could prevent 20330 [95 CI 20050 to 20610]cumulative deaths due to stroke and IHD in 2025

In terms of life years 150 [95 CI 130 to 180] and 2390[95 CI 2300 to 2490] would be gained in 2025 by acutestroke treatment and secondary prevention respectivelywhereas for primary prevention (blood pressure controlglucose control lipid lowering and smoking cessation)14590 [95 CI 14350 to 14820] life years would be gained in2025 (Table 1)

32 Scenario Projections

321 Improvement on Acute Stroke Treatment If we adopt astrategy to increase thrombolysis uptake from 0 to 50and stroke units use from 10 to 100 600 [95 CI 550 to650] fewer deaths could be achieved by 2025 (Table 2)

In terms of life years 370 [95 CI 330 to 410] would begained in 2025 by increasing thrombolysis uptake (Figure 4)

322 Improvement on Secondary Prevention If the uptakeof statins for secondary prevention following stroke could beincreased from 11 to 100 3300 [95 CI 3190 to 3410]fewer deaths could be avoided by 2025 (Table 2)

In terms of life years 4120 [95 CI 4000 to 4250] wouldbe gained in 2025 (Figure 4)

323 Food Policies If the Tunisian government imple-mented a strategy recommended by the WHO to reduce thedaily consumption of salt by 30 (from 14 gday to 9 gday)30240 [95 CI 29900 to 30580] deaths could be avoided bythis scenario in 2025 (Table 2) +is results in 20630 [95 CI20350 to 20910] life year gain by 2025 (Figure 4)

33 Linear Regression Metamodeling of the Optimal Policy+e table below shows the results of linear regressing pa-rameters on the stroke and IHD deaths prevented or

postponed (DPPs) by the salt reduction intervention +e R2

is 08999 suggesting that 89 99 of the variance in themodel outcomes is explained by our model (Table 3)

Figure 5 shows the five first important parameters basedon the absolute value of the coefficients of the parameters Inour case study the uncertainty of the probability of minorstroke in the first year has the greatest impact on the strokeand IHD deaths estimates associated with salt reductionfollowed by the probability of the stroke-free population todie from stroke and IHD causes in the year 1 and theprobability of recurrent stroke in ischemic stroke patientsafter one year Although the main objective of the meta-regression is to identify the most important parameters ofthe model it could also serve to give a rough idea of the sizeof the effect of each parameter We know that for each unitincrease in the independent variable our outcome shouldincrease by 1113954I

2 units For example the probability for thestroke-free population to have first stroke in the year 1 hasan absolute coefficient of 64635 this means that for each10 risk increase in this probability strokes and IHD willincrease by 65 IHD and stroke deaths However this shouldbe interpreted with caution since the meta-analysis re-gression model assumes a linear relationship betweenoutcomes and inputs which is not the case in a Markovmodel (Figure 5)

4 Discussion

In this study we have developed a simple but comprehensiveMarkov model and used it to identify key factors that predictmortality from stroke and IHD in Tunisia in the future aswell as the potential impacts of some medical and healthpolicies

Different mathematical models have been highly used inmedical decision making [19 29ndash32] but the technique ofmetamodeling is less developed inmedicine It has been usedto identify the importance of variables that can justify thebest medical decisions among pregnant women with deepvein thrombosis [33] Additionally linear regression met-amodels have also been used in some epidemiologicalstudies [25 34]

TP44

TP24

TP11 TP12

TP15

TP16TP16

TP13

TP33

TP25

TP23TP26 TP35

TP36

TP46

TP45

Minorstroke and

TIAMinor

stroke andTIA

Stroke-freepopulation

Majorstroke

Nonstrokeand IHD

deaths

Stroke andIHD

deaths

Figure 3 Stroke model structure TIA transient ischemic attack IHD ischemic heart diseases


+is analysis is the first modeling study of stroke andIHD mortality in Tunisia based on a rigorous and com-prehensive modeling approach consisting of three stages

(i) Apply the Markov model in medical and strategicdecision making

(ii) Provide a probabilistic sensitivity analysis(iii) Use a linear regression metamodeling for the op-

timal policy

+is model has several strengths First it requires mul-tiple epidemiological national data on ischemic stroke anddemographics In general the data used in the model were ofgood quality However some assumptions were necessary tofill gaps in the missing information We made transparent

assumptions with clear justification (see Appendix in thesupplementary materials)

Another advantage characterizing our approach anddifferentiating it from the univariate traditional method ofdeterministic sensitivity analysis is that it allows varying allthe parameters of the model simultaneously and thus ex-ploring the whole parameter space +e use of only one-waysensitivity analyses is limited compared with multiwayanalyses [35]

Furthermore to increase the transparency of decision-making analytic models we have used metamodeling in thisstudy by applying a simpler mathematical relationship be-tween model outputs and inputs to analyze which are themost influential inputs on the output

Our metamodeling approach summarizes the results ofthe model studied in a transparent way and reveals itsimportant characteristics

+e intercept of the regression result is the expectedoutcome when all parameters are set to zero +e othercoefficients are interpreted relative to a 1-unit change in eachparameter on the original scales For example in our casechanging the risk of the first minor stroke in the first yearfrom the actual value to 1 increases the number of stroke andIHD deaths by 646 deaths In addition the regression co-efficients describe the relative importance of the uncertaintyin each parameter And the use of the linear metamodelingregression method can overcome the limitations of othertraditional statistical methods [36]

In addition models often ignore the interaction effectbetween the input parameters of a model when defining theresults However in our study the use of conditionalprobabilities allows us to take into account interactions inour algorithm

We also analyzed in parallel of the deaths prevented orpostponed (DPPs) the life years gained according to thedifferent scenarios +us our approach allows interpretingtwo key indicators in epidemiology via a rigorous andcomprehensive mathematical algorithm

Nevertheless this modeling approach has also somelimitations in fact a major limitation of our work is that the

Table 1 Life years and deaths due to stroke and IHD estimations in 2025 keeping the same practices of 2005 by gender

Life years [95 CI] Stroke and IHD deaths [95 CI]MenAcute stroke treatment 80 [70 to 100] minus140 [minus170 to minus120]Secondary prevention following stroke 1500 [1420 to 1580] minus1170 [minus1240 to minus1110]Primary prevention 12180 [11960 to 12400] minus16760 [minus17020 to minus16510]Policy totallowast 6830 [6700 to 6990] minus8530 [minus8710 to minus8340]WomenAcute stroke treatment 60 [50 to 80] minus80 [minus100 to minus70]Secondary prevention following stroke 860 [800 to 920] minus720 [minus770 to minus670]Primary prevention 2410 [2310 to 2510] minus3570 [minus3690 to minus3450]Policy totallowast 3730 [3610 to 3850] minus4860 [minus5000 to minus4720]BothAcute stroke treatment 150 [130 to 1804] minus230 [minus260 to minus200]Secondary prevention following stroke 2390 [2300 to 2490] minus1920 [minus2000 to minus1830]Primary prevention 14590 [14350 to 14820] minus20330 [minus20610 to minus20050]Policy totallowast 10560 [10360 to 10770] minus13380 [minus13610 to minus13160]lowastTotal policy refers to the combined effects of all the three previous strategies acute treatment + secondary prevention + primary prevention

Table 2 Life years and deaths due to stroke and IHD by in-corporating strategies in 2025 by gender

Stroke and IHD deaths [95CI]

MenAcute stroke treatment minus350 [minus390 to minus310]Secondary prevention followingstroke minus2060 [minus2150 to minus1970]

Primary prevention minus24500 [minus24810 to minus24200]Policy total minus23940 [minus24240 to minus23640]WomenAcute stroke treatment minus220 [minus250 to minus190]Secondary prevention followingstroke minus1240 [minus1310 to minus1170]

Primary prevention minus10630 [minus10830 to minus10430]Policy total minus17050 [minus17300 to minus16800]BothAcute stroke treatment minus600 [minus650 to minus550]Secondary prevention followingstroke minus3300 [minus3410 to minus3190]

Primary prevention minus30240 [minus30580 to minus29900]Policy totallowast minus40990 [minus41390 to minus40600]lowastTotal policy refers to the combined effects of all the three previousstrategies acute treatment + secondary prevention + primary prevention


model is a closed cohort and demographic changes were notconsidered

Linear regression is the metamodeling approach mostwidely used bymany researchers for its simplicity and ease ofuse +us our linear approximation of all input parameterscan be considered as a limit as state-transition models arenonlinear in general In all metamodeling approaches theloss of some information is always inevitable [25]

Another limitation of our study is not to consider in themodel the costs of the strategies

In terms of public health the present modeling studyfocuses on the future impact of ischemic stroke treatmentscenarios and population-level policy interventions onischemic stroke and IHD deaths and life years gained inTunisia +e model forecast a dramatic rise in the totalcumulative number of IHD and Stroke deaths by 2025

WomenMenBoth

15000

10000

5000

0

Life

yea

rs

Acute stroketreatment

Secondary preventionfollowing stroke

Primaryprevention

Policy total

Strategies

Figure 4 Life years estimations by incorporating strategies by gender in 2025

Table 3 Regression coefficients from metamodeling on the stroke and IHD deaths by the salt reduction intervention

Parameters Dependent variable (Y) stroke and IHD deathsIntercept 133786TP12 probability for the stroke-free population tohave first stroke in the year 1 64635

TP13 probability for the stroke-free population tohave first major stroke in the year 1 618

TP16 probability for the stroke-free population to diefrom stroke and IHD causes in the year 1 3849

TP11 probability for population free of stroke 245TP23 probability of recurrent stroke in ischemicstroke patients after 1 year 1305

TP26 probability for the minor stroke patients to diefrom stroke and IHD causes in the year 1 667

TP24 probability for first minor stroke (1st year) tominor stroke subsequent years 045

TP33 probability of recurrent stroke in ischemicstroke patients after 5 years minus649

TP46 probability for the stroke patients to die fromstroke and IHD deaths causes 1 year after firstadmission

minus172

TP44 probability for minor stroke subsequent years minus296TP36 probability for the major stroke patients to diefrom stroke and IHD causes minus010

Observations 1000R2 08999


this number was estimated to reach more than 100000deaths

Secondly the model shows that the rise of thrombolytictreatment and hospitalization in intensive care units ofstroke increased statin use for secondary prevention pale incomparison with the salt reduction impact on future deaths(1 3 vs 27 deaths prevented by 2025)

+e benefits of thrombolytic treatment among patientswith acute ischemic stroke are still matter of debatethrombolytic treatment increases short-term mortality andsymptomatic or fatal intracranial haemorrhage but decreaseslonger term death or dependence [25] Many studies provedthat stroke units have significant benefit to patient outcomesin terms of reducing mortality morbidity and improvingfunctional independence Stroke unit care was also costeffective [37ndash39]

+e substantial effect of salt reduction interventionfound in our study is consistent with the literature [40 41]High salt intake is associated with significantly increasedrisks of stroke and total cardiovascular disease ranging froma 14 to 51 increase depending on salt intake and pop-ulations [42ndash44]

Furthermore our results are consistent with a modelingstudy in Tunisia using a different approach Differentstrategies for salt reduction were associated with substantiallowering of CVD mortality and were cost saving apart fromhealth promotion [45] and consistent with the Rose hy-pothesis that the population level strategies are more ap-propriate in terms of less medicalization [46]

5 Conclusions

+e approach presented here is attractive since it is based ona simple comprehensive algorithm to present the results ofsensitivity analysis from the Markov model using linearregression metamodeling +is approach can reveal im-portant characteristics of Markov decision process includingthe base-case results relative parameter importance in-teraction and sensitivity analyses

+us we recommend using this algorithm for Markovdecision process it can be the object of creation of acomplete modeling package in R software and can be ex-tended to other contexts and populations

In terms of public health we forecast that absolutenumbers of IHD and stroke deaths will increase dramatically

in Tunisia over 2005ndash2025 +is Large increase in stroke andIHD mortality in Tunisia needs many actions not only inacute stroke treatment such as implementing more basic andorganized stroke units but also in population level primaryprevention such as salt reduction in order to manage andtreat acute strokes and to alleviate the global burden of thesediseases

Our study highlights the powerful impact of salt re-duction on deaths from stroke and IHD Furthermore thereducing dietary salt intake across the population appears aneffective way of reducing heart disease events and savingsubstantial costs +is result matches with that of themathematical model Indeed our metamodeling highlightsthat the probability of the first minor stroke among thehealthy population has the greatest impact on the stroke andIHD death estimations which confirms the importance ofprimary prevention Prevention is thus the best strategy tofight against stroke and IHD deaths

Data Availability

Data used are presented in Appendix in the supplementarymaterials

Disclosure

+e results of the manuscript were presented in the 62ndAnnual Scientific Meeting Society for Social MedicineUniversity of Strathclyde Glasgow on the 5th and 7th ofSeptember 2018 +e funders had no role in study designdata collection and analysis decision to publish or prepa-ration of the manuscript +e MedCHAMPS team had ac-cess to all data sources and has the responsibility for thecontents of the report On behalf of EC FP7 fundedMedCHAMPS project (MEDiterranean studies of Cardio-vascular Disease and Hyperglycaemia Analytical Modelingof Population Socio-economic transitions)

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Authorsrsquo Contributions

MOF OS SC and JC conceived the idea of the study OSDM and MOF led the project supervised by HBR JC andSC OS MG NZ and PB assembled the datasets extractedthe data and populated the models with input OS NZ DMMG and MOF wrote the first draft of the paper and OSHBR MOF SC and JC finalized the manuscript All authorscontributed to the analysis intellectual content criticalrevisions to the drafts of the paper and approved the finalversion HBR is the guarantor

Acknowledgments

We thank the MedCHAMPS and RESCAPMED advisorygroup for comments on study design and emerging findingsParticular thanks go to Pat Barker for managing the overallproject We thank also the Tunisian team especially Dr Afef

700600500400300200100

0TP12 TP16

38

646St

roke

and

IHD

dea

ths

13 7 6

TP23Transition probabilities

TP26 TP33

Figure 5 Five first important parameters in the model


Skhiri and Dr Olfa Lassoued who participated in data col-lection and Professor Faycel Hentati for his opinions andcomments on the work We thank Professor K Bennett forher comments on this paper +is study was funded by theEuropean Communityrsquos Seventh Framework Program (FP720072013) under grant agreement n223075 the Med-CHAMPS project MOF was also partially supported by theUK MRC JC and SC are supported by the UK HigherEducation Funding Council

Supplementary Materials

+e supplementary materials submitted contain sources ofdata and all data used in the model (SupplementaryMaterials)

References

[1] N D Wong ldquoEpidemiological studies of CHD and theevolution of preventive cardiologyrdquo Nature Reviews Cardi-ology vol 11 no 5 pp 276ndash289 2014

[2] S Ebrahim and G D Smith ldquoExporting failure Coronaryheart disease and stroke in developing countriesrdquo In-ternational Journal of Epidemiology vol 30 no 2 pp 201ndash52001

[3] T A Gaziano A Bitton S Anand et al ldquoGrowing epidemicof coronary heart disease in low- and middle-income coun-triesrdquo Current Problems in Cardiology vol 35 no 2pp 72ndash115 2010

[4] GBD 2015 Mortality and Causes of Death CollaboratorsldquoGlobal regional and national life expectancy all-causemortality and cause-specific mortality for 249 causes ofdeath 1980ndash2015 a systematic analysis for the Global Burdenof Disease Study 2015rdquo Ae Lancet vol 388 no 10053pp 1459ndash1544 2016

[5] G J Hankey ldquo+e global and regional burden of strokerdquoAeLancet Global Health vol 1 no 5 pp e239ndashe240 2013

[6] WHO ldquoGlobal burden of strokerdquo 2015 httpwwwwhointcardiovascular_diseasesencvd_atlas_15_burden_strokepdfua1

[7] World Health Organization ldquoHealth promotionrdquo 2018httpwwwwhointtopicshealth_promotionen

[8] P J Easterbrook M C Doherty J H Perrie J L Barcaroloand G O Hirnschall ldquo+e role of mathematical modelling inthe development of recommendations in the 2013 WHOconsolidated antiretroviral therapy guidelinesrdquo AIDS vol 28pp S85ndashS92 2014

[9] C J E Metcalf W J Edmunds and J Lessler ldquoSix challengesin modelling for public health policyrdquo Epidemics vol 10p 9396 2015

[10] M C Weinstein P G Coxson L W Williams T M PassW B Stason and L Goldman ldquoForecasting coronary heartdisease incidence mortality and cost the Coronary HeartDisease Policy Modelrdquo American Journal of Public Healthvol 77 no 11 pp 1417ndash1426 1987

[11] J Critchley and S Capewell ldquoWhy model coronary heartdiseaserdquo European Heart Journal vol 23 no 2 pp 110ndash1162002

[12] G R P Garnett S Cousens T B Hallett R Steketee andN Walker ldquoMathematical models in the evaluation of healthprogrammesrdquo Ae Lancet vol 378 no 9790 pp 515ndash5252011

[13] M Ortegon S Lim D Chisholm and S Mendis ldquoCost ef-fectiveness of strategies to combat cardiovascular diseasediabetes and tobacco use in sub-Saharan Africa and SouthEast Asia mathematical modelling studyrdquo BMJ vol 344no 1 p e607 2012

[14] L C Leea G S Kassabb and J M Guccionec ldquoMathematicalmodeling of cardiac growth and remodelingrdquo Wiley In-terdisciplinary Reviews Systems Biology and Medicine vol 8no 3 pp 211ndash226 2017

[15] G Elena ldquoComputational and mathematical methods incardiovascular diseasesrdquo Computational and MathematicalMethods in Medicine vol 2017 Article ID 4205735 2 pages2017

[16] S Basu David Stuckler S Vellakkal and E Shah ldquoDietary saltreduction and cardiovascular disease rates in India amathematical modelrdquo PLoS One vol 7 no 9 2012

[17] O Saidi N Ben Mansour M OrsquoFlaherty S CapewellJ A Critchley and H B Romdhane ldquoAnalyzing recentcoronary heart disease mortality trends in Tunisia between1997 and 2009rdquo PLoS One vol 8 no 5 Article ID e632022013

[18] O Saidi M OrsquoFlaherty N Ben Mansour et al ldquoForecastingTunisian type 2 diabetes prevalence to 2027 validation of asimple modelrdquo BMC Public Health vol 15 no 1 p 104 2015

[19] F A Sonnenberg and J R Beck ldquoMarkov models in medicaldecision makingrdquo Medical Decision Making vol 13 no 4pp 322ndash338 2016

[20] K Szmen B Unal S Capewell J Critchley andM OrsquoFlaherty ldquoEstimating diabetes prevalence in Turkey in2025 with and without possible interventions to reduceobesity and smoking prevalence using a modeling approachrdquoInternational Journal of Public Health vol 60 no 1 pp 13ndash212015

[21] A H Briggs M C Weinstein E A L Fenwick J KarnonM J Sculpher and A D Paltiel ldquoModel parameter estimationand uncertainty a report of the ISPOR-SMDM modelinggood research practices task force-6rdquo Value in Health vol 15no 6 pp 835ndash842 2012

[22] M L Puterman Markov Decision Processes Discrete Sto-chastic Dynamic Programming Wiley New York NY USA2005

[23] A Mahanta ldquoBeta distribution Kaliabor collegerdquo httpwwwkaliaborcollegeorgpdfMathematical_Excursion_to_Beta_Distributionpdf

[24] K Kuntz F Sainfort M Butler et al ldquoDecision and simu-lation modeling in systematic reviewsrdquo Methods ResearchReport 11(13)-EHC037-EF AHRQ Publication RockvilleMA USA 2013

[25] H Jalal D Bryan F Sainfort M Karen and Kuntz ldquoLinearregression metamodeling asa tool to summarize and presentsimulation model resultsrdquo Medical Decision Making vol 33no 7 pp 880ndash890 2013

[26] V Kapetanakis F E Matthews and A van den Hout ldquoAsemi-Markov model for stroke with piecewise-constanthazards in the presence of left right and interval censor-ingrdquo Statistics in Medicine vol 32 no 4 pp 697ndash713 2012

[27] C Eulenburg S Mahner L Woelber and KWegscheider ldquoAsystematic model specification procedure for an illness-deathmodel without recoveryrdquo PLoS One vol 10 no 4 Article IDe0123489 2015

[28] F J He and G A MacGregor ldquoRole of salt intake in pre-vention of cardiovascular disease controversies and chal-lengesrdquoNature Reviews Cardiology vol 15 no 6 pp 371ndash3772018


[29] J F Moxnes and Y V Sandbakk ldquoMathematical modelling ofthe oxygen uptake kinetics during whole-body enduranceexercise and recoveryrdquo Mathematical and Computer Mod-elling of Dynamical Systems vol 24 no 1 pp 76ndash86 2018

[30] R B Chambers ldquo+e role of mathematical modeling inmedical research research without patientsrdquo OchsnerJournal vol 2 no 4 pp 218ndash223 2000

[31] F Achana J Alex D K Sutton et al ldquoA decision analyticmodel to investigate the cost-effectiveness of poisoningprevention practices in households with young childrenrdquoBMC Public Health vol 16 no 1 p 705 2016

[32] O Alagoz H Hsu A J Schaefer and M S Roberts ldquoMarkovdecision processes a tool for sequential decision makingunder uncertaintyrdquo Medical Decision Making vol 30 no 4pp 474ndash483 2010

[33] J F Merz and M J Small ldquoMeasuring decision sensitivity acombined monte carlo-logistic regression approachrdquoMedicalDecision Making vol 12 no 3 pp 189ndash196 1992

[34] P M Reis dos Santos and M Isabel Reis dos Santos ldquoUsingsubsystem linear regression metamodels in stochastic simu-lationrdquo European Journal of Operational Research vol 196no 3 pp 1031ndash1040 2008

[35] A Moran D Gu D Zhao et al ldquoFuture cardiovasculardisease in China Markov model and risk factor scenarioprojections from the Coronary Heart Disease Policy Model-Chinardquo Circulation Cardiovascular Quality and Outcomesvol 3 no 3 pp 243ndash252 2010

[36] D Coyle M J Buxton and B J OBrien ldquoMeasures of im-portance for economic analysis based on decision modelingrdquoJournal of Clinical Epidemiology vol 56 no 10 pp 989ndash9972003

[37] K Meisel and B Silver ldquo+e importance of stroke unitsrdquoMedicine and Health Rhode Island vol 94 no 12pp 376-377 2011

[38] P Langhorne ldquoCollaborative systematic review of the rand-omised trials of organised inpatient (stroke unit) care afterstrokerdquo BMJ vol 314 no 7088 pp 1151ndash1159 1997

[39] B J T Ao P M Brown V L Feigin and C S AndersonldquoAre stroke units cost effective Evidence from a New Zealandstroke incidence and population-based studyrdquo InternationalJournal of Stroke vol 7 no 8 pp 623ndash630 2011

[40] N Bruce Ae Effectiveness and Costs of Population In-terventions to Reduce Salt Consumption WHO LibraryCataloguing-in-Publication Data Geneva Switzerland 2006httpwwwwhointdietphysicalactivityNeal_saltpaper_2006pdf

[41] N Wilson N Nghiem H Eyles et al ldquoModeling health gainsand cost savings for ten dietary salt reduction targetsrdquo Nu-trition Journal vol 15 no 1 p 44 2016

[42] D Klaus J Hoyer and M Middeke ldquoSalt restriction for theprevention of cardiovascular diseaserdquo Deutsches AerzteblattOnline vol 107 no 26 pp 457ndash462 2010

[43] J Tuomilehto P Jousilahti D Rastenvte et al ldquoUrinarysodium excretion and cardiovascular mortality in Finland aprospective studyrdquo Ae Lancet vol 357 no 9259 pp 848ndash851 2001

[44] WHO ldquoReducing salt intakerdquo 21-10-2011rdquo 2016 httpwwweurowhointenhealth-topicsdisease-preventionnutritionnewsnews201110reducing-salt-intake

[45] H Mason A Shoaibi R Ghandour et al ldquoA cost effectivenessanalysis of salt reduction policies to reduce coronary heartdisease in four eastern mediterranean countriesrdquo PLoS Onevol 9 no 1 Article ID e84445 2014

[46] G Rose ldquoStrategy of prevention lessons from cardiovasculardiseaserdquo BMJ vol 282 no 6279 pp 1847ndash1851 1981


Stem Cells International

Hindawiwwwhindawicom Volume 2018


MEDIATORSINFLAMMATION

of

EndocrinologyInternational Journal of



Disease Markers


BioMed Research International

OncologyJournal of



Oxidative Medicine and Cellular Longevity


PPAR Research

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Immunology ResearchHindawiwwwhindawicom Volume 2018

Journal of

ObesityJournal of



Computational and Mathematical Methods in Medicine


Behavioural Neurology

OphthalmologyJournal of


Diabetes ResearchJournal of



Research and TreatmentAIDS


Gastroenterology Research and Practice


Parkinsonrsquos Disease

Evidence-Based Complementary andAlternative Medicine

Volume 2018Hindawiwwwhindawicom

Submit your manuscripts atwwwhindawicom

the analysis of the effectiveness of health promotion in-terventions is urgently required for appropriate planning toreduce this burden [7]

Traditional epidemiological study designs cannot ad-dress these issues even clinical trials are usually restricted byinclusion and exclusion criteria and not necessarily gener-alizable to the entire population [8]

Mathematical modeling overcomes many of these lim-itations It plays a crucial role in helping to guide the mosteffective and cost-effective ways to achieve the goals of healthpromotion designed and validated to guide health policiesand development strategies at several levels [9 10]

Briefly a model is a simplification of a real situation andcan encompass a simple descriptive tool up to systems ofmathematical equations [11]

+e application of mathematical models in medicine hasproved useful and has become more frequent especially forcardiovascular diseases (CVDs) [12ndash16] and assessing po-tential impacts of policies or interventions designed to alterdisease trajectories in Tunisia [17 18]

A commonly used technique is Markov modeling an ap-proach that models groups of individuals transitioning acrossspecified pathways informed by transition probabilities [18ndash20]

Due to the frequent uncertainty of the Markov modelrsquosinputs sensitivity analyses to assess the robustness of themodel results are strongly recommended by modelingguidelines Such uncertainty analyses assess confidence in achosen course of action and ascertain the value of collectingadditional information to better inform the decision [21]

Our study aims (i) to describe a comprehensive Markovmodel based on both a probabilistic multivariate approachand simple linear regressionmetamodeling and (ii) using themodel to evaluate the effects of increases in uptake of stroketreatments lifestyle changes and primary prevention amongthe Tunisian population aged 35ndash94 years old in 2025 Weexamined three interventions (a) improved medical treat-ments in the acute phase (b) secondary prevention of strokeby increasing the prescribing of statins and (c) primaryprevention aiming to reduce salt intake

2 Methods

In this study we describe the development of a Markov IHDand stroke model

21 Definition of Markov Model Markov models are a typemathematical model based on matrix algebra which de-scribes the transitions a cohort of patients make among anumber of mutually exclusive and exhaustive health statesduring a series of short intervals or cycles In this model apatient is always in one of the finite number of health statesevents are modeled as transitions from one state to anotherand contribution of utility to overall prognosis depend onlength of time spent in health states [19] +e components ofa Markov model are shown below (Figure 1)

(i) States the set of distinct health states under con-sideration in the model together with the possibletransitions between them

(ii) Cycle length the length of time represented by asingle stage (or cycle) in a Markov process Markovmodels are developed to simulate both short-cycleand long-term processes (eg cardiovasculardiseases)

(iii) Transition probabilities the matrix of probabilitiesof moving between health states from one stage tothe next

22 Process of Mathematical Modeling Based on MarkovApproach Before starting the data collection and the cal-culation we first defined our model by specifying the dif-ferent states that can be included based on the literature andexpert opinions

S S1 S2 S31113864 1113865 set of states in the process (1)

Having specified the structure of the model in terms ofthe possible transitions between states we defined thetransition probabilities based on available data

+e transition probability (TPij) is defined as a condi-tional probability (Pt(sjsi)) of making a transition (mov-ing) from state i to state j during a single cycle (t)Additionally transition probabilities are stratified by sex andage groups ag isin c1 c2 cg1113966 1113967 where c1 c2 cg repre-sents a set of age groups [19 22]

One of the goals of the Markov model is to study thepotential effects of some health promotion interventionsWe modeled first a baseline scenario and then the in-tervention scenarios

For the baseline scenario we assumed no change willhappen during the period ldquoTrdquo of study (20 years) in eitherthe present uptake rates of medical therapies or populationlevel uptakes of specific nutrients

Based on the model structure in Figure 1 we assume thatwe will apply three interventions to study their impact onmortality in the future (over the 20 years from t year 1 toyear 20)

We define a policy Π (I0 I1 I2 I3) as a set of thehealth promotion interventions

I0 refers the baseline scenario we assumed no changewill happen during 20 yearsI1 scenario aimed to improve medical treatments inacute phase

Healthypopulation

Dead

SickTP11

TP12

TP13 TP23

TP22

Figure 1 Markov diagram states and transition probabilities (eachcircle represents a Markov state and arrows indicate transitionprobabilities)















(2)








formula

1113945

Ii

e





NHPlit NHPli


Ii

e

⎛⎝ ⎞⎠

NSlit NSli


NDlit NDli



e

⎛⎝ ⎞⎠

LYlit NHPli

t minusNDlit

(5)



DPPlist

NDlit minusND

l0t (6)

LYligt

LYlit minus LY

l0t (7)













end forend for




LYt NHPt + NDt

end forend for




for t 1 T

NHPlit NHPli


NSlit NSli


NDlit NDli



LYlit NHPli

t minusNDlit



st 1113936

T1 ND

lit minusND

l0t

LYligt

1113936T1 LY

lit minus LY

l0t end for

end forend for


end forend for



















3 Results



Inputs (TPij)

















4 Discussion



TP44

TP24

TP11 TP12

TP15

TP16TP16

TP13

TP33

TP25

TP23TP26 TP35

TP36

TP46

TP45

Minorstroke and

TIAMinor

stroke andTIA


Majorstroke

Nonstrokeand IHD

deaths

Stroke andIHD

deaths






timal policy























WomenMenBoth

15000

10000

5000

0

Life

yea

rs



Primaryprevention

Policy total

Strategies











minus172









5 Conclusions






Data Availability


Disclosure






Acknowledgments


700600500400300200100

0TP12 TP16

38

646St

roke

and

IHD

dea

ths

13 7 6


TP26 TP33






References





















































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of
































(2)








formula

1113945

Ii

e





NHPlit NHPli


Ii

e

⎛⎝ ⎞⎠

NSlit NSli


NDlit NDli



e

⎛⎝ ⎞⎠

LYlit NHPli

t minusNDlit

(5)



DPPlist

NDlit minusND

l0t (6)

LYligt

LYlit minus LY

l0t (7)













end forend for




LYt NHPt + NDt

end forend for




for t 1 T

NHPlit NHPli


NSlit NSli


NDlit NDli



LYlit NHPli

t minusNDlit



st 1113936

T1 ND

lit minusND

l0t

LYligt

1113936T1 LY

lit minus LY

l0t end for

end forend for


end forend for



















3 Results



Inputs (TPij)

















4 Discussion



TP44

TP24

TP11 TP12

TP15

TP16TP16

TP13

TP33

TP25

TP23TP26 TP35

TP36

TP46

TP45

Minorstroke and

TIAMinor

stroke andTIA


Majorstroke

Nonstrokeand IHD

deaths

Stroke andIHD

deaths






timal policy























WomenMenBoth

15000

10000

5000

0

Life

yea

rs



Primaryprevention

Policy total

Strategies











minus172









5 Conclusions






Data Availability


Disclosure






Acknowledgments


700600500400300200100

0TP12 TP16

38

646St

roke

and

IHD

dea

ths

13 7 6


TP26 TP33






References





















































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of



























end forend for




LYt NHPt + NDt

end forend for




for t 1 T

NHPlit NHPli


NSlit NSli


NDlit NDli



LYlit NHPli

t minusNDlit



st 1113936

T1 ND

lit minusND

l0t

LYligt

1113936T1 LY

lit minus LY

l0t end for

end forend for


end forend for



















3 Results



Inputs (TPij)

















4 Discussion



TP44

TP24

TP11 TP12

TP15

TP16TP16

TP13

TP33

TP25

TP23TP26 TP35

TP36

TP46

TP45

Minorstroke and

TIAMinor

stroke andTIA


Majorstroke

Nonstrokeand IHD

deaths

Stroke andIHD

deaths






timal policy























WomenMenBoth

15000

10000

5000

0

Life

yea

rs



Primaryprevention

Policy total

Strategies











minus172









5 Conclusions






Data Availability


Disclosure






Acknowledgments


700600500400300200100

0TP12 TP16

38

646St

roke

and

IHD

dea

ths

13 7 6


TP26 TP33






References





















































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of



































3 Results



Inputs (TPij)

















4 Discussion



TP44

TP24

TP11 TP12

TP15

TP16TP16

TP13

TP33

TP25

TP23TP26 TP35

TP36

TP46

TP45

Minorstroke and

TIAMinor

stroke andTIA


Majorstroke

Nonstrokeand IHD

deaths

Stroke andIHD

deaths






timal policy























WomenMenBoth

15000

10000

5000

0

Life

yea

rs



Primaryprevention

Policy total

Strategies











minus172









5 Conclusions






Data Availability


Disclosure






Acknowledgments


700600500400300200100

0TP12 TP16

38

646St

roke

and

IHD

dea

ths

13 7 6


TP26 TP33






References





















































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of
































4 Discussion



TP44

TP24

TP11 TP12

TP15

TP16TP16

TP13

TP33

TP25

TP23TP26 TP35

TP36

TP46

TP45

Minorstroke and

TIAMinor

stroke andTIA


Majorstroke

Nonstrokeand IHD

deaths

Stroke andIHD

deaths






timal policy























WomenMenBoth

15000

10000

5000

0

Life

yea

rs



Primaryprevention

Policy total

Strategies











minus172









5 Conclusions






Data Availability


Disclosure






Acknowledgments


700600500400300200100

0TP12 TP16

38

646St

roke

and

IHD

dea

ths

13 7 6


TP26 TP33






References





















































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of






















timal policy























WomenMenBoth

15000

10000

5000

0

Life

yea

rs



Primaryprevention

Policy total

Strategies











minus172









5 Conclusions






Data Availability


Disclosure






Acknowledgments


700600500400300200100

0TP12 TP16

38

646St

roke

and

IHD

dea

ths

13 7 6


TP26 TP33






References





















































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of























WomenMenBoth

15000

10000

5000

0

Life

yea

rs



Primaryprevention

Policy total

Strategies











minus172









5 Conclusions






Data Availability


Disclosure






Acknowledgments


700600500400300200100

0TP12 TP16

38

646St

roke

and

IHD

dea

ths

13 7 6


TP26 TP33






References





















































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of
























5 Conclusions






Data Availability


Disclosure






Acknowledgments


700600500400300200100

0TP12 TP16

38

646St

roke

and

IHD

dea

ths

13 7 6


TP26 TP33






References





















































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of






















References





















































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of










































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of



















comparing strategies to prevent stroke and ischemic heart...

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