adding a new app to your - scor global life americas€¦ · american academy of actuaries 2014...

American Academy of Actuaries 2014 Actuarial Software Now 5

Adding a New App to Your Actuarial Smart Devices

Smart analytics can be an important tool in influencing study reliability.

By Zhiwei Zhu

isto

ck P

Ho

to

What Is Smart Analytics?Predictive analytics is viewed by many as a sort of black box that market-ing and underwriting departments use to target potential customers or to determine to which underwriting class policy applicants belong. While these uses are valuable, like the smart-phone they represent only a portion of the power of predictive analytics and are a good example of smart ana-lytics. Various types of smart analytics emphasize different features, such as prediction, volatility, simulation, and optimization.

Fortunately, we live in an era when a smartphone can do more than make calls and predictive analytics can do more than make predictions. And businesses are competing to find new ways to best explore smart analytics for insights, productivity, efficiency, and optimization.

If the magic that makes a smart-phone smart is its ability to digitize and process the seemingly incompat-ible mediums of sound, image, light, text, and numbers under the control of one operating system, then by ex-tension the “secret sauce” of what we call smart analytics is its capacity to analyze apparently different data sets such as sales, claims, defaults, lapse rates, lab results, underwriting deci-

sions, demographics, and social media by following unified scientific princi-ples (e.g., statistics and computer sci-ence). Above all, like a smartphone, smart analytics is a platform that not only gives users a multifunctional tool set but also empowers innovative minds to expand the platform’s capa-bilities by creating new apps. Smart analytics involves the transformation and integration of quantitative sci-ences, such as statistics, mathematics, and computer science to deliver data-driven business insights.

What Can Predictive Analytics Do?A better understanding of predictive analytics can help us comprehend smart analytics. In order to generate objective and data-driven predictions, predictive analytics customizes and applies a range of statistical proce-dures to mine data for evidence, to test ideas for reliability, to standardize data analyses for efficiency, to create models for patterns, and to quantify uncertainty with probabilities. For example, when predictive analytics is used as a risk analysis tool for insured mortality studies, it performs not only the traditional descriptive rate and credibility analyses but also some or all of the statistical inference proce-dures to quantify uncertainty as listed in Figure 1. In practice, these proce-

Figure 1. Predictive Analytics Performs Data, Credibility, and Pattern Analyses

Mortality Study

Traditional analyses Rate by driver

Data credibility

Univariate analyses Hypothesis test

Variance analysis

Distribution analysis

Imputation

Multiple variable analyses and model development

Statistical models

Variable selection

Correlation

Parameterization

Normalization

Intercept

Interaction

Model application Estimation

Extrapolation

Smoothing

Scoring

Predictive value

Incremental value

Model fit Sensitivity

Specificity

Fit validation

Model generalization Reliability test

6 2014 Actuarial Software Now American Academy of Actuaries

dures have a wide range of applica-tions, such as:1. To identify additional risk drivers

when new data become available (e.g., do people who consume olive oil or work as teachers have low mortality?);2. To generate normalized value

estimation (does olive oil have the same effect on Italian, American, and Chinese mortality, all other mor-tality factors held constant?);3. To quantify the reliability of

studies (can we tell which mortal-ity study is statistically more reliable if one study uses as many claims as available and another uses only select-ed but more relevant claims?);4. To estimate mortality for seg-

ments that have less or no credible data (what is the best estimate of insured mortality at age 100 or old-er based on the study of other age groups?);5. To smooth, grade, and extrap-

olate (how should select mortality grade to ultimate mortality?); and6. To classify and select risks (how

do some applicants with a high body mass index qualify for preferred rates?).

With appropriate business guid-ance, predictive analytics can also be customized as new apps for other specific needs in target marketing, underwriting, pricing optimization, capital cost reduction, enterprise risk management, and other areas.

How Does Predictive Analytics Work?The low-frequency nature of mortali-ty poses a unique challenge to life and

annuity insurance experience studies; that is, the lack of sufficient claims for in-depth and credible conclusions. But predictive analytics can be tai-lored partially to mitigate this prob-lem. Let’s examine a case study that applies predictive analytics to insured mortality experiences. The following information is taken from “Logistic Regression for Insured Mortality Ex-perience Studies,” a paper that was presented at the 2014 Living to 100 Symposium.

The Study Case: As a life reinsurer with one of the largest U.S. life rein-surance mortality portfolios, SCOR Global Life Americas employs smart analytics to maximize useful mortal-ity insights at population, segment, and client levels. In this illustrative ex-ample, we apply predictive analytics to 1) measure the predictive values of nine mortality drivers (e.g., for pricing adjustments), 2) estimate mortality slopes by age and duration and mor-tality differentials among insured sub-groups (for future mortality assump-tions), 3) quantify study reliability (for quality control and optimization), and 4) generate mortality best estimates

(for experience table construction). The Study Data: The completely

de-identified study data come from an industry mortality study and from a global reinsurer’s experience data-base. The study aggregates the in-dividual life experience of approxi-mately two-thirds of the industry for a period of 10 calendar years. Nearly 200 million exposure years are avail-able for study. To demonstrate the potential of predictive analytics to ef-ficiently use a limited amount of data tailored for a specific purpose, we se-lected policies issued on or after 1950 with insured amounts of $50,000 and higher to represent a hypothetical tar-get segment.

The Predictive Analytics: The applied predictive analytics consists of two major steps: creating predic-tive models and generating modeled scores. The model building process involves many steps, such as model selection, parameter estimation, and performance validation. For this case study, we chose logistic regression models to estimate a mortality rate (q) because of the models’ good fit to mortality data, flexibility for many applications, and intuitiveness for interpretations. A logistic model for mortality has a general form of:

where q is the probability of death in an

exposure year given that the policy-holder has survived to the beginning of the year. In statistics, q is also called

...)**...(

...)**...(

313,1212,12211

313,1212,12211

1

xxxxxx

xxxxxx

eeq

The low-frequency nature of mortality

poses a unique challenge to life and

annuity insurance experience studies; that is, the lack of sufficient claims for in-depth and

credible conclusions. But predictive analytics can be tailored partially

to mitigate this problem.


the dependent variable of the model. xi are the observable mortality pre-

dictors (e.g., age, sex, duration, and product). In general, they are also called independent variables or ex-planatory variables.� is a parameter related to a nor-

malized mortality level. In statistics, it is called the intercept and is to be estimated with experience data and a maximum likelihood method. �i are parameters related to mor-

tality slopes and differentials. In sta-tistics, they are called the coefficients of the independent variables and are to be estimated with experience data and a maximum likelihood method.

We built four such models: male nonsmokers, male smokers, female nonsmokers, and female smokers. This split modeling design allows for better comparisons against other studies later in this article. The nine studied mortality predictors were is-sue age, duration, gender, smoker sta-tus, study year, face band, underwrit-ing class, product, and issue year.

The Findings (and Power): Skip-ping the technical details, we’ll focus on reviewing four of the many types of analyses performed in the model-ing processes. For readers who are familiar with the Statistic Analysis System (SAS), the statistical model-ing tool used for our study, we have retained the original titles of the SAS outputs for easy reference.

To better appreciate the power of predictive analytics, readers can also think of how or whether these many analyses could be conducted with conventional descriptive methods and

with the amount of selected data. For appropriate interpretation of the analysis outputs, let us recall two sta-tistical concepts:

a) p-value, which is used to measure statistical significance in hypothesis tests. A rule of thumb is that when p-value ≥ 0.05, the null hypoth-esis should be accepted. Frequently, a null hypothesis is related to “no difference.”

b) Odds of death q/(1-q), which is the ratio of probability of death and probability of survival. Since mortal-ity q is generally very small for most insured segments, the odds of death q/(1-q) are approximately the same as mortality q. Therefore, we will sim-

ply approximate mortality ratios (or mortality relativity) with odds ratios. For example, we use the odds ratio of males and females as an estimate of the mortality ratio between the two groups.

Output 1: “Type 3 Analysis of Effects” for testing whether observed mortality variation by predictor is credible (or a study’s variable is a good predictor, Figure 2).

The tests are conducted sepa-rately for each of the four insured subgroups. The four columns to the right represent outputs from the four models. A p-value ≥ 0.05 implies that mortality does not significantly vary statistically by the corresponding predictor while controlling the other studied variables.

For example, the two highlighted p-values are greater than 0.05, which implies that for the female smoker and male nonsmoker segments mor-tality does not vary statistically sig-nificantly by product. Hence, the predictive value of products is low for these two subgroups. Bear in mind that the models intrinsically ac-

We built four such models: male non-

smokers, male smokers, female nonsmokers, and female smokers. This split modeling

design allows for better comparisons against

other studies.

Predictor \ p-valueDegree of Freedom

Female Male

Nonsmoker Smoker Nonsmoker Smoker

Duration 1 <.0001 <.0001 <.0001 <.0001

Issue age 1 <.0001 <.0001 <.0001 <.0001

Study year 1 0.1714 0.4597 0.1719 0.0017

Face band 2 0.0051 0.004 <.0001 <.0001

Product 1 0.0157 0.9533 0.1363 <.0001

Issue year 2 <.0001 0.0003 <.0001 <.0001

Underwriting class 2 <.0001 <.0001 <.0001 <.0001

Figure 2: Type 3 Analysis of Effects


count for (i.e., normalize) the underly-ing differences in the distributions of the other listed variables between the permanent and term policies. This type of normalized test is difficult to perform with a conventional method.

Output 2: “Odds Ratio Estimates” for gauging how much mortality var-ies by predictor (Figure 3).

This output contains model-esti-mated odds ratios and their 95 percent confidence intervals. As mentioned at the beginning of this section, we can simply interpret the numbers in this table as mortality ratios, defined in the “Predictor” column.

According to the design and theory of logistic regression, odds ratios for a continuous variable such as dura-

tion or issue age reflect the change in mortality when the variable value in-creases by one unit. For example, the four ratios highlighted in yellow are around 1.1, which tells us that mor-tality increases by about 10 percent when issue age increases by one year for all four insured segments. These estimations are in line with the find-ings from various large general and insured population studies. This indi-cates that, although only a small por-tion of the insured experience data are used, this predictive analytics pro-duces findings that can be confirmed by studies using much more data.

Take the cells highlighted in blue as another example. The four segments’ mortality ratios between preferred

and residual standard classes range from 0.73 to almost 0.77, which im-plies that preferred mortality is about 27 percent to 23 percent lower than that of the residual standard class. This finding is also in line with ac-tuaries’ observations and knowledge. Again, this confirms the validity of predictive analytics. These cross-study verifications imply that other study findings are also likely to be credible.

Output 3: “Model Fit” for quanti-fying study reliability (Figure 4).

In this output table, a c-statistic of a model is also known as the area under the ROC (receiver operating characteristic) curve that represents the trade-off between false positive and false negative when the model is

Male Nonsmoker Male Smoker Female Nonsmoker Female Smoker

Predictor Point Estimate

95% Wald Confidence Limits

Point Estimate


Point Estimate


Point Estimate


Duration 1.141 1.139 1.143 1.118 1.114 1.122 1.157 1.153 1.160 1.133 1.126 1.139

Issue age 1.101 1.100 1.102 1.093 1.092 1.094 1.105 1.104 1.105 1.098 1.096 1.099

Study year 0.998 0.995 1.001 1.009 1.003 1.014 0.997 0.992 1.001 1.004 0.994 1.013

Face 100k-499k vs 500k+

1.115 1.096 1.135 1.203 1.143 1.265 1.000 0.971 1.030 0.926 0.855 1.002

Face 50k-99k vs 500k+

1.284 1.258 1.311 1.407 1.335 1.484 1.037 1.003 1.071 0.988 0.911 1.072

UnderW Med vs Non-med

0.920 0.902 0.939 1.018 0.986 1.050 0.950 0.921 0.981 1.044 0.992 1.099

Product perm vs term

1.013 0.996 1.030 0.923 0.890 0.958 1.033 1.006 1.060 0.998 0.939 1.061

Class one-class vs standard

1.042 1.027 1.057 0.930 0.893 0.967 1.038 1.014 1.062 0.938 0.881 0.999

Class preferred vs standard

0.730 0.719 0.741 0.748 0.717 0.781 0.740 0.722 0.758 0.767 0.715 0.823

Figure 3: Odds Ratio Estimates (Mortality Ratio Estimates)


applied for prediction with the study data. The values of a c-statistic range from 0 to 1, and a higher value implies a better model fit to the data. In many situations, a c-statistic greater than 0.6 is considered good.

All four c-statistics are reasonably high, which implies that all four of our models fit the four insured sub-groups reasonably well, especially the two smoker groups. This is an indica-tion that smoking is such a significant mortality driver that smokers’ mor-tality can be more accurately esti-mated than that of nonsmokers when the same amount of information is available.

More broadly, this type of analy-sis can be applied to compare studies conducted by different parties. Driven by the concern of not having a cred-ible amount of claim data, it is com-mon for actuaries to simply trust stud-ies that use more claim data. In fact, many other factors can influence study reliability, such as data quality, data relevance, and study design. There-fore, the number or amount of claims should not be the only criterion for judging the reliability of studies.

Output 4: “Modeled Mortality” (scoring) for extrapolation and table construction (Figure 5a-b).

With properly crafted predictive models, model-estimated mortality can be generated for any cell defined

Figure 4: Association of Predicted Probabilities and Observed Responses

Figure 5a–b: Modeled Mortality for Observed Cohorts

by the studied mortality drivers—even for cells in which scarce claims can be observed (e.g., advanced ages). The modeled mortality estimates can also be organized in table formats that ac-tuaries are more familiar with and that enable them to perform further refine-ments. Instead of presenting large ta-

bles, the following two charts compare one age group’s mortality from our model-generated mortality tables and two SOA industry tables.

The comparison suggests that the model projections fit the actual expe-rience well (the chart for males) when a credible number of claims are avail-able. Otherwise, the model projections are reasonably similar to the SOA 2008 Valuation Basic Tables (the chart for females), since the experience data for our study and the SOA 2008 VBT cover a similar time period. This is an-

Association of Predicted Probabilities and Observed Responses

Female Male

Nonsmoker Smoker Nonsmoker Smoker

c-statistic (ROC) 0.682 0.753 0.679 0.747

male, Nonsmoker, issue ages 48–52

Female, Nonsmoker, issue ages 48–52


other validation of the predictive ana-lytics for mortality experience studies.

Flexible, Expanding, and EvolvingApplications of smart analytics are flexible, expanding, and evolving. As mentioned earlier, predictive analyt-ics is only one type of smart analytics and the case study is just a drop in the ocean in terms of smart analytics uses. Some companies can adopt smart ana-lytics by buying an off-the-shelf system such as a risk-scoring tool and using its designed features. Others may want to gain more benefits by developing their own apps to better serve their needs or those of their customers. If banks can

develop iPhone apps to serve custom-ers’ online payment demands, life in-surance companies might want to cus-tomize smart analytics to understand their target segments’ mortality trends.

However, smart analytics requires a strategic investment and multidisci-plinary collaboration. As illustrated in the case study, maximizing the benefits of smart analytics requires specialized skills, expertise, strategy, execution, and tools. If banks rely on profession-als such as software engineers, data-base administrators, and communica-tions specialists to create smartphone apps designed to attract wireless pay-ment customers, insurance companies will need to engage outside profession-

als and vendors such as statisticians, predictive modelers, and analytics tool developers to innovate broad applica-tions of smart analytics that will help them compete in risk management.

It is not hard to imagine the conse-quences if a communications company decided not to take advantage of the capabilities of smartphones for inter-nal communications or external cus-tomer services. So, one way or another, insurance firms and other companies that depend upon data and analytics will need to invest in smart analytics. n

ZHIWEI ZHU is vice president of Risk Model-ing & Analytics at SCOR Global Life Americas.

adding a new app to your - scor global life americas€¦ · american academy of actuaries 2014...

Documents