Institute of Actuaries of Australia. Disability Claims - Does Anyone Recover?

Transcription

1 Institute of Actuaries of Australia Disability Claims - Does Anyone Recover? David Service FIA, ASA, FIAA David Pitt BEc, BSc, FIAA 2002 The Institute of Actuaries of Australia This paper has been prepared for issue to, and discussion by, Members of the Institute of Actuaries of Australia. The Council wishes it to be understood that opinions put forward herein are not necessarily those of the Institute and the Council is not responsible for those opinions. The Institute of Actuaries of Australia Level 7 Challis House 4 Martin Place Sydney NSW Australia 2000 Telephone: Facsimile: Website:

2 Disability Claims Does Anyone Recover? Abstract The common feature in all recent reports of disability experience has been the deterioration of claims termination rates. The adequate analysis of termination rates requires very material amounts of data. In this study the authors have had access to claims data submitted to the Institute of Actuaries of Australia Disability Committee over the period 1980 to 1998 covering 106,000 claims. The authors have analysed this major dataset using conventional approaches Actual/Expected and using the latest Generalised Linear Modeling techniques. Also presented is a comparison of a stochastic approach to the setting of reserves for outstanding claims liabilities with the corresponding deterministic method. Nineteen characteristics of the experience are reported using Actual/Expected techniques. Most show material differences between different values of the characteristic. The analysis confirms the deterioration of experience but suggests that 1997 and 1998 showed significant improvement. The authors ask whether this is a real improvement or merely a pause before even worse experience. David Service Centre for Actuarial Research Australian National University david.service@anu.edu.au David Pitt Centre for Actuarial Research Australian National University david.pitt@anu.edu.au 2

3 1. INTRODUCTION The common feature in all recent reports of disability experience has been the deterioration of claims termination rates. The adequate analysis of termination rates requires very material amounts of data. In this study we have had access to claims data submitted to the Institute of Actuaries of Australia Disability Committee over the period 1980 to 1998 covering 106,000 claims. The authors have analysed this major dataset using conventional approaches Actual/Expected and using the latest Generalised Linear Modeling techniques. Also presented is a comparison of a stochastic approach to the setting of reserves for outstanding claims liabilities with the corresponding deterministic method. This paper is set out in 6 sections and several Appendices, as follows Section 1 Introduction This introduction Section 2 Data A description of the data, its characteristics and the selection criteria used Section 3 Comparison of Actual vs Expected Claim Terminations A comparison of actual terminations vs those expected on the basis of IAD Section 4 Generalised Linear Model of Claim Termination Rates A description of the GLM fitted to claim termination rates on the basis of the data Section 5 Stochastic Claims Reserving The results of calculating claims reserves with stochastic methods Section 6 Further Research Some notes on further research opportunities in regard to the use of GLMs in connection with disability business Appendix A Some Data Specifications Details of the data selection specifications Appendix B Actual vs Expected Detailed results of the actual vs expected analysis 3

4 Appendix C GLM Full details of the GLM Acknowledgements This research could not have been carried out without significant support by the Institute of Actuaries of Australia, the authors received a research grant from the IAAust 2001 Research Grants Scheme, and the IAAust Disability Committee was prepared to supply the authors with their extensive claims database. The authors gratefully acknowledge this support. The original version of this paper was presented to the Horizon meetings in July The discussion at those meetings has informed this final version. Health Warnings In interpreting these results readers should note that the quality of data submitted to the Disability Committee has materially improved over the period covered by this analysis and we have, necessarily, taken the data supplied at face value. It has, of course, already been through the Committee s own validation process. However, in some cases the interpretation used by companies in submitting data may have changed over the period. In using these results for any particular company it should be borne in mind that the Disability Committee s reports have consistently shown wide variation in experience by individual companies. As no company information was supplied it was not possible to investigate the possible intercompany variations for any of the characteristics analysed. 4

5 2. DATA The IAAust Disability Committee supplied the authors with their claims database for the period 1980 to This database had all identifiers relating to company or policy removed prior to its being provided to the authors. The database contained records relating to 106,000 individual claims and their various characteristics. Each claim record contained the following data Country Disability Definition Gender Deferment Accident Deferment Sickness Date of Policy Commencement Benefit Period Accident Benefit Period Sickness Occupation Date of Birth Expiry Age Benefit Rate Benefit Type Medical Evidence Coverage Type Contract Type Cause of Claim Smoker Status Benefit Proportion Date Disability Commenced Date Claim Ceased Some of these characteristics were summarised to reduce the number of data points but without sacrificing data quality. The summarised characteristics were Deferment Claim cause Coterminus benefits Proportionate benefit Benefit rate Age at claim The detailed specifications used to determine these summarised characteristics are set out in Appendix A. Certain records were excluded from the analysis due to missing data or to match the primary data selection criteria used by IAAust Disability Committee. The exclusion criteria are set out in Appendix A. 5

6 After these records were excluded 101,000 claims with 875,000 months of exposure remained for the analyses. Not all claims remained in the original Disability Committee database from commencement to termination. Some claims commenced prior to 1980, some remained open at the end of 1998 and some companies only contributed data to some of the years between 1980 and Nevertheless, each claim contributed to the exposure for the months for which data was available for it and contributed to actual terminations only if it terminated in the data available for it. Claim cessation due to death, recovery or lump sum payment was defined as a claim termination. Claim cessations due to benefit expiry were not treated as a claim termination. Claims which terminated due to death comprised 1.1% of all claims terminated and lump sum terminations comprised 0.3% of all claims terminated. Claim durations were taken at monthly intervals from the date disability commenced regardless of the deferment period. The first month was duration 0. In the Actual/Expected analyses only benefits classified as Full were included except for the comparison of Partial and Full benefits. Claims were classified as Partial if less than full benefits had been paid at any time in the claims payment history. 13% of all claims were so classified. 6

7 3. COMPARISON of ACTUAL vs EXPECTED CLAIMS TERMINATIONS The IAAust Disability Committee primarily reports claim termination experience by using average duration of claims for the first three years of claims. This makes sense given that each report concentrates on the four years covered. However, as noted in those reports, average claim duration needs to be interpreted with care as it can change due to changes in new claims volumes without any change in underlying termination rates. For this paper we have concentrated on actual vs expected claim terminations (by claim numbers) as the measure of termination rate experience. For the calculation of expected terminations we have used IAD The results are presented as an index which is the inverse of Actual/Expected in order that as results deteriorate the ratio increases. Fewer terminations than expected is bad news! The base data includes only claims which satisfied the following criteria Individual coverage (excluding Business Overheads) Contract type not Cancellable Not a partial benefit at any point in the claim payment history Detailed Actual vs Expected results are set out in Appendix B. The more important conclusions are summarised in following paragraphs. In this section only a one-dimensional view is taken of the experience. There are simply too many possible cells to allow a reasonable analysis to be conducted using actual/expected techniques. However, the section dealing with the generalised linear model does, of course, take a multidimensional approach. IT will be noted that the data for the period 1989 to 1993 does not have an index of 100%, i.e. the data does not agree with IAD89-93 for the same period. This is due to three sources of difference The data provided to the authors was of later origin than that used to derive IAD89-93 due to subsequent revisions and submission of additional data by contributors, The analysis in this paper has summarised some data, and IAD89-93 uses an artificial approach to setting termination rates at longer durations. Since the comparisons used here are based on the relative values of the index the small difference between our 1989 to 1993 results and IAD89-93 is not significant in the interpretation of the results. 7

8 3.1 Experience over Time In this analysis the year is the year of exposure (and claim termination). Table 1: Comparison of Actual and Expected Experience over Time Year Expected Actual Index % % % % % % % % % % % % % % % % % % % % This analysis confirms the general deterioration of experience over time but interestingly suggests that in the last two years (1997 & 1998) some improvement may be evident. Is this a real improvement or, like the periods 1986 to 1988 and 1990 to 1992, a mere fluctuation before the deterioration resumes its course? Because of this very material change in aggregate experience over time the results of the analyses by each of seventeen characteristics are presented in a two dimensional form to show the experience over time as well as by the values for each individual characteristic. The only exceptions to this presentation style were experience by benefit size, age at claim, duration and year of policy commencement where the number of individual values for each characteristic were too great to allow such an analysis. 3.2 Summary of Results Table 2 shows the results for each characteristic presented as the Index for the total period ignoring differences by year. The experience by year for each characteristic is to be found in Appendix B. This table 8

9 identifies which values for which characteristics are material in impacting the termination experience. Table 2: Index of Termination Rates by Characteristic Characteristic Value Index Gender Male 112% Female 125% Occupation A 126% B 111% C 107% D 111% Deferment 7 days 66% 14 days 108% 30 days 125% 90 days 245% Definition Own / Any 2 years 110% Own 126% Any 95% Benefit Type Level 105% Increasing 119% Medical Evidence Medical 83% Non Medical 101% Other 126% Coverage Individual 113% Business Overheads 126% Contract Type Level Guaranteed 114% Level 109% Stepped Guaranteed 97% Stepped 116% Cancellable Level 85% Cancellable Stepped 103% No Claim Bonus No 114% Yes 113% Smoker Status No Differentiation 107% Non Smoker Checks 107% Non Smoker 113% Smoker 127% Claim Cause Unknown 115% W 69% X 147% Y 190% Accident 101% CoTerminus Yes 112% No 117% Benefit Period 2 years 102% 5 years 115% Expiry 127% Lifetime 123% Benefit Proportion Full 113% Partial 196% 9

10 3.3 Some Initial Conclusions These results suggest that the characteristics used in IAD89-93 to differentiate termination rates deferment, gender and occupation ado not capture significant differences in experience according to some other characteristics. In addition, not only is the experience deteriorating to an extent where IAD89-93 is materially overstating the likely termination rates but also its shape for various characteristics may be materially different to that shown in the experience. 10

11 4. GENERALISED LINEAR MODEL of CLAIM TERMINATION RATES 4.1 Background to Generalised Linear Models Generalised linear models (GLMs) were first developed by Nelder and Wedderburn (1972). GLMs extend the basic linear regression model. The linear regression model, when used for the prediction of a dependent variable, Y (for example claim termination rate), with a number of independent variables, X 1, X 2,..,Xp, (for example occupation class, duration of claim, age, smoker status) can be described as follows: 1. The random component: each value of Y is normally distributed with expected value µ and constant variance σ The systematic component: a set of independent variables X 1, X 2,,Xp which combine to produce a linear predictor η given by p η = where the β j are regression coefficients estimated by the 1 x j β j least squares principle. 3. The link between the linear predictor and the mean of Y is µ = η The GLM extends this basic model in two significant ways: 1. The dependent variable, Y, may come from an exponential family distribution rather than just the Normal distribution. The exponential family encompasses most of the statistical distributions used by actuaries in general insurance and includes the Normal, Poisson, Binomial, Gamma and Inverse Gaussian distributions. The advantage of using this broader class of distributions for the response variable is that it gives the user a wider range of possible relationships between the variance of the dependent variable and the mean of that variable. 2. The link function in (3) above can be any monotonic differentiable function. Common link functions are the identity link, the log link, the inverse link and the logit (or log-odds) link. Having fitted a GLM the process of determining whether predictors are adding value to the model is also different to the process used in traditional linear modelling. To assess the adequacy of the fit of a GLM we need to define the deviance statistic. The deviance is the discrepancy between the actual values of the dependent variable and the fitted values of that dependent variable. 11

12 The formula for the deviance is ( ˆ, ) = 2 φ (, φ) ( ˆ, φ) DYY ly ly where φ is the dispersion parameter and l( Y ˆ, φ ) is the log-likelihood function for the observed values. The deviance is therefore the difference in log-likelihoods between a perfectly fitting (or saturated) model and the model for which the deviance is being calculated. The addition of independent variables to a GLM therefore reduces the deviance. The amount of this reduction in deviance (in other words the size of the step taken towards the perfectly fitting model) is used as a measure of whether that particular independent variable is adding significant predictive power to the model. 4.2 Actuarial Use of Generalised Linear Models Actuaries in both life and general insurance have both made use of generalised linear models. General insurance actuaries now routinely use GLMs for pricing a range of both long and short-tail lines of business. Brockman (1992) describes the use of GLMs in motor vehicle insurance pricing and details some of the diagnostic procedures commonly employed to ensure a good model fit. Haberman (1996) summarises the actuarial use of GLMs in a very accessible paper. The first use of GLMs by actuaries in the life insurance domain appears to be by Renshaw (1991). His paper, Generalised linear models and actuarial science, describes how models traditionally used by actuaries in the graduation of mortality rates can be viewed as special cases of GLMs. The traditional Gompertz and Makeham functions for describing the variation in the force of mortality by age and the Wilkie model for mortality are recast as GLMs. The Wilkie model for mortality is qˆ x ( ˆ ηx ) ( ˆ η ) s 1 exp = where ˆ η ˆ x = β j x 1+ exp x j= 0 j It is clear that this is a GLM with a binomial error distribution and logit link function. The first significant mathematical model of disability was that developed by Miller and Courant (1974). GLMs were first used in connection with disability income insurance by Renshaw. Renshaw 12

13 (1995) describes the use of generalised linear modelling for graduating transition intensities in the well known multiple state model used to describe the dynamics of disability income insurance. This model is shown below. ABLE ILL DEAD Figure 1: Multi-state model used for Disability Income Insurance Modelling This paper is concerned with the rate of termination of disability claims. That is, we endeavour to estimate the transition intensity from the ill state to the able state. This transition intensity is denoted ρ and can be thought of as the force of recovery. The 1997 Report of the Disability Committee of the Institute of Actuaries of Australia (IAAust) highlights the significance of rating factors in describing the incidence rates of disability. We suspected that some or all of these rating factors might be significant in the explanation of termination rates. GLMs have been employed to quantify this relationship in a multiple simultaneous predictor setting. 4.3 Advantages of Using Generalised Linear Models for Claim Termination Rates The advantages of using GLMs in describing termination rates are they enable the impact of changing the level of a rating factor to be quantified in a way that does not simultaneously consider the simultaneous change in other rating factors. For example the 1997 Disability Report considers the impact of occupation class on claim duration. The report states that claim duration for occupation class A is longer than that for occupation classes B to D. The GLM enables you to isolate out the impact of the change in occupation class from the changes in other variables which occur when you move from occupation class A to D. For example females are rarely in occupation class D and the fact that occupation class A lives are usually more severely disabled 13

14 before they are unable to work than is the case for say occupation D lives; they provide a predicted value of the termination rate for a particular life with all rating factors specified to be determined along with a variance of this predicted value; they enable suitable modelling of the variance of the mean termination rate unlike conventional linear modelling; and the predicted termination rates will be smooth since they are the output of a mathematical function. This means that premiums and reserves calculated from the model will also be smooth. the results for termination rates are a result of a single model rather than a big range of different tables. 4.4 Analysis The GLM fitted in this paper used data from the whole period 1980 to 1998 but with only a limited set of characteristics in order to facilitate the actual calculations by reducing the number of cells analysed. Fitting a GLM to the full set of characteristics using only data from the latest data period 1995 to 1998 would be a valuable further step. The authors are currently planning that project. The fitting of a suitable GLM requires choices as regards the distribution of the errors, the link function, the predictors to use and whether any transformation of those predictors is useful. In addition it is worthwhile to investigate interactions which may exist between the predictor variables. A number of different GLMs were fit to the termination rate data. After considerable analysis it was found that the Poisson error structure was the most appropriate for describing the mean variance relationship inherent in the data. It was comforting to note that this error family is the same one commonly used for claim inception rates in the modelling of many short-tail lines of general insurance business. The data selection for the final GLM adopted used claims which had a deferment of 14 or 30 days, did not have an Unknown claim cause and had Individual coverage. There were 83,000 such claims with 675,000 months of exposure. The following characteristics were retained 14

15 Definition Gender Occupation Smoker Status Age at Claim Claim Cause Deferment Benefit Rate Year of Exposure Duration There were 275,000 cells in the data. It should be noted that unlike the Actual/Expected analysis the data used to fit the GLM included both Partial and Full benefit claims. In order to give greater weight to those observations which we have more confidence in, the GLMs were fitted using the exposure for each rating factor combination as weights. The results in Appendix C show that all of the following rating factors aid significantly in the prediction of termination rates: age at date of claim, cause of claim, duration of claim, gender, occupation class, smoker status, deferment period, benefit rate and the calendar year at the date of possible claim termination. The dataset includes all claim terminations so that at every possible duration only certain claims will actually be observed to terminate. From the output in Appendix C one can calculate the fitted values for claim termination rates. The formula is Claim Termination Rate = exp( AgeClaim (ClaimCauseW) (AgeClaim*Sqrt(Duration))) It is clear from Appendix C that the model has a significant residual deviance. This result is not surprising given that the nineteen years of data was included in the analysis and only a limited number of rating factors were included as explanatory variables. The interpretation of deviance residuals is explained in McCullagh (1989). A number of other variables and transformations of existing variables could also be explored and these are mentioned in Section 6 which is devoted to further research. Graphs and other comparisons of modelled termination rates versus actual data will be included in a future paper which is currently being written by the authors. This paper will build a model for claim termination rates (and incidence rates) based only on the most recent five years of data. This reduced dataset will allow a considerably 15

16 improved fit to the data to be achieved than was possible in this analysis. Other interesting results of the analysis include: The benefit rate has a statistically significant negative impact on the rate of claim termination; there is a statistically significant interaction between duration and deferment period in determining the termination rate. At shorter durations the predicted termination rate is significantly higher for the shorter deferment period. After durations of approximately 8 months this difference becomes nonstatistically significant; there has been a statistically significant decline, over time, in termination rates when aggregated across all levels of the rating factors. The decline in termination rates is still statistically significant even after the impact of all other rating factors has been allowed for. An alternative to the second method of fitting an interaction term between deferment period and duration is to use break-point predictor terms. This has been employed successfully in the UK by Renshaw (1995). The idea is to include terms of the form (Duration 3) + which are only positive if the duration is greater than 3 and otherwise are zero. Such terms enable the rating factors to exhibit a non-constant linear relationship (after allowing for the link function) with the termination rate. They prove useful in modelling the lower termination rates that one observes at the very shortest durations. 16

17 5. STOCHASTIC CLAIMS RESERVING Given the GLM in Appendix C we aim to find the approximate distribution, using simulation, of the required reserves to ensure different probabilities of adequacy. The analysis is for the average of 100 claims that are new at the date of valuation with a monthly disability payment of $2600. The graph below was generated using a male aged 40, in occupation class A, with a deferred period of 2 weeks who became disabled because of an accident. Reserve Requirements for $2600 Monthly Claim at Duration Zero Reserve($) Percentage Figure 2: Reserve Requirements for varying probabilities of adequacy In the above analysis allowance has been made for deteriorating claims termination rates and for interest at 6% per annum continuously compounding. The calculation above is made using two probability distributions. First the fitted value for the natural log of the termination rate from the GLM is normally distributed. This is the case because this fitted value is a linear combination of coefficient estimates and independent covariate values and the coefficient estimates are maximum likelihood estimates which are themselves (asymptotically) normally distributed. The delta method was then used to find the variance of the actual fitted values for the termination rates. The number of terminating claims, given the termination rate, then comes from a binomial distribution. 17

18 The table shows the reserves required to give a particular probability of the reserve being adequate using the stochastic techniques. Table 3: Reserve Requirements by Probability of Adequacy Probability Claim Reserve at Start of Claim Increase Over 50% 50% 33,764 75% 36,749 9% 90% 39,692 18% 95% 41,180 22% 99% 45,357 34% The reserve using a traditional deterministic approach would be that at the 50% probability level. 18

19 6. FURTHER RESEARCH There is considerable scope for further research into the description of claim termination rates in disability income insurance. For example, the use of generalised additive models which enable the use of a range of smoothers (for example, kernel smoothers and local linear loess estimates); use of the fact that the predicted termination rates are lognormally distributed to derive a numerical approximation to the distribution of outstanding claim reserves; further work on the use of interaction and break-point predictor terms in the fitting of the GLMs; use of economic variables for explaining termination rate experience in addition to the variables considered in this paper; and build a further GLM using data from 1995 to 1998 and a larger set of independent variables to explain variation in claim termination rates over this period. 19

20 References Benjamin B. and Pollard J. H. (1993). The Analysis of Mortality and Other Actuarial Statistics. Published by the Institute and Faculty of Actuaries. Brockman, M. J., and Wright, T. S. (1992). Statistical motor rating: making effective use of your data. Journal of the Institute of Actuaries 119, pp Haberman, S. and Pitacco, E. (1999). Actuarial Models for Disability Insurance. Published by Chapman and Hall/CRC. Haberman, S., and Renshaw, A. E. (1996). Generalised linear models and actuarial science. The Statistician 45, pp McCullagh P. and Nelder J. A. (1989) Generalised Linear Models. Second Edition. Published by Chapman and Hall/CRC. Miller, J.H. and Courant, S. (1974). A Mathematical Model of the Incidence of Disability. Transactions of the Society of Actuaries 25, pp Nelder, J. A. and W. Wedderburn, R. W. M. (1972). Generalised linear models. Journal of the Royal Statistical Society A 135, pp Renshaw, A. E. (1991). Actuarial Graduation and Generalised Linear and Non-Linear Models. Journal of the Institute of Actuaries 118, II, pp Renshaw, A. E. and Haberman, S. (1995). On the graduation associated with a multiple state model for permanent health insurance. Insurance, Mathematics and Economics, 17, pp The Institute of Actuaries of Australia Report of the Disability Committee (1997). Transactions of the Institute of Actuaries of Australia

21 APPENDIX A Some Data Specifications A1. Claims Excluded Country Not Australia Deferment Sickness Not Equal Deferment Period Accident Sickness Only cover or Accident Only cover A2. Summarised Characteristics Deferment The original data has deferment period in days. These were summarized as follows days days days days days days days CoTerminus If Benefit Period Accident = Benefit Period Sickness then CoTerminus. Proportionate Benefit If at any time a claim payment is not the full benefit then the claim is recorded as Partial Age at Claim This is recorded in quinquennial steps starting at 22. A1

22 Benefit Rate Recorded in the following bands ($ per month) , , , , , , , , , ,000 Claim Cause All claims had an alpha cause coded. These were summarized as follows in order to reduce the number of possible cells in the data matrix. The choice of combinations was deliberately made based on the average claim duration as shown in the Disability Committee Reports so as to give three broad groups short, medium and long. Summarised Cause Original Causes V None recorded W A, H, I, J, K, L X C, D, F, G, M. N, P, R, S Y B, E, Z Accident The original causes are the WHO International Classification of Diseases as follows. A B C D E F G H I J Infective and parasitic diseases Neoplasms (MN = Malignant and BN = Benign) Endocrine, Nutritional and Metabolic diseases Diseases of the blood and blood forming organs Mental disorders Diseases of the Nervous system and sense organs Diseases of the circulatory system Diseases of the respiratory system Diseases of the digestive system Diseases of the genito-urinary system A2

23 K Diseases of Pregnancy and childbirth L Diseases of the skin and subcutaneous tissue M Diseases of the musculoskeletal system and connective tissue N Congenital anomalies P Senility and ill defined conditions Q Accidents, poisoning and violence (external causes) R 100 AIDS related complex and full blown AIDS S 101 HIV+ and Lymphadenopathy A3

24 Appendix B Detailed Actual / Experience Results B1. Experience by Calendar Year of Exposure Year Expected Actual Index % % % % % % % % % % % % % % % % % % % % B1

25 B2. Experience by Gender Male Female Year Expected Actual Index Expected Actual Index % 0 0 0% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % B2

26 B3. Experience by Occupation A B C D Year Expected Actual Index Expected Actual Index Expected Actual Index Expected Actual Index % 1 0 0% % % 1 0 0% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % B3

27 B4. Experience by Deferment 7 Days 14 Days 30 Days 90 Days Year Expected Actual Index Expected Actual Index Expected Actual Index Expected Actual Index % % % % % % % % % % % 8 0 0% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % B4

28 B5. Experience by Disability Definition Own / Any 2 Own Any Year Expected Actual Index Expected Actual Index Expected Actual Index % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % B5

29 B6. Experience by Benefit Type Level Increasing Level - Out of Working Hours Increasing - Out of Working Hours Year Expected Actual Index Expected Actual Index Expected Actual Index Expected Actual Index % % % % % % % % 0 0 0% % % 4 0 0% % % 2 0 0% % % 3 0 0% % % 2 0 0% % % 3 0 0% % % 1 0 0% 8 0 0% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % B6

30 B7. Experience by Medical Evidence Medical Non Medical Other Year Expected Actual Index Expected Actual Index Expected Actual Index % % 4 0 0% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % B7

31 B8. Experience by Coverage Type Individual Business Overheads Year Expected Actual Index Expected Actual Index % % % % % % 2 0 0% % 6 0 0% % % % % % % % % % % % % % % % % % % % % % % % % % % B8

32 B9. Experience by Contract Type Year Level - Guaranteed Level - Non Guaranteed Stepped - Guaranteed Stepped - Non Guaranteed Cancellable - Level Cancellable - Stepped Exp. Actual Index Exp. Actual Index Exp. Actual Index Exp. Actual Index Exp. Actual Index Exp. Actual Index % % % % % 4 0 0% % % % % % % % % % % % % % 3 0 0% % % % % 6 0 0% % % % % 6 0 0% % % % % 1 0 0% 5 0 0% % % % % 3 0 0% % % % % % 6 0 0% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % B9

33 B10. Experience by No Claim Bonus No Yes Year Expected Actual Index Expected Actual Index % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % B10

34 B11. Experience by Smoker Status No Differentiation Non Smoker - Periodic Checks Non Smoker Smoker Year Expected Actual Index Expected Actual Index Expected Actual Index Expected Actual Index % % 0 0 0% 0 0 0% % 1 0 0% 3 0 0% % 3 0 0% 7 0 0% % 0 0 0% 2 0 0% % % 4 0 0% 7 0 0% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % B11

35 B12. Experience by Claim Cause Unknown Combined Cause W Combined Cause X Combined Cause Y Accident Year Exp. Actual Index Exp. Actual Index Exp. Actual Index Exp. Actual Index Exp. Actual Index % % 5 0 0% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % B12

36 B13. Experience by CoTerminus Status Yes No Year Expected Actual Index Expected Actual Index % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % B13

37 B14. Experience by Benefit Period 2 Years 5 Years Expiry Lifetime Year Expected Actual Index Expected Actual Index Expected Actual Index Expected Actual Index % 0 1 6% % % % % 5 0 0% % % % 8 0 0% % % % 5 0 0% % % % 8 0 0% % % % 3 0 0% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % B14

38 B15. Experience by Benefit Proportion Full Benefit Partial Benefit Year Expected Actual Index Expected Actual Index % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % B15

39 B16. Experience by Age at Claim Age At Claim Expected Actual Index % % % % % % % % % % B16

40 B17. Experience by Duration Duration (Months) Expected Actual Index % % % % % % % % % % % % % % % % % % % % % % % % % % % % % B17

41 B18. Experience by Year of Policy Commencement Year of Entry Expected Actual Index % % % % % % % % % % % % % % % % % % % % % % % % % % % % % B18

42 B19. Experience by Benefit Size Benefit $per month Expected Actual Index % % % % % % % % % % % B19

43 APPENDIX C - GLM Poisson model Response: termrate Terms added sequentially (first to last) Df Deviance Resid. Df Resid. Dev NULL ageclaim claimcausew claimcausex claimcausey duration sqrt(duration) male occupationa occupationb occupationc smoker deferment benefitrate APeriod ageclaim:duration ageclaim:sqrt(duration) Call: glm(formula = termrate ~ ageclaim + claimcausew + claimcausex + claimcausey + duration + sqrt(duration) + ageclaim + ageclaim * duration + ageclaim * sqrt(duration) + male + occupationa + occupationb + occupationc + smoker + deferment + benefitrate + APeriod, family = poisson(link = log), weights = COpen) Deviance Residuals: Min 1Q Median 3Q Max C1

44 Coefficients: Value Std. Error t value (Intercept) 3.23e e ageclaim -8.08e e claimcausew 3.71e e claimcausex -3.29e e claimcausey -5.61e e duration -1.86e e sqrt(duration) 2.58e e male 1.41e e occupationa -1.35e e occupationb -8.56e e occupationc -4.24e e smoker -6.05e e deferment 2.38e e benefitrate -7.60e e APeriod -1.67e e ageclaim:duration 1.82e e ageclaim:sqrt(duration) -6.52e e (Dispersion Parameter for Poisson family taken to be 1 ) Null Deviance: on degrees of freedom Residual Deviance: on degrees of freedom Number of Fisher Scoring Iterations: 6 C2