SOME NEW ACTUARIAL MODELS OF THE INSURANCE IMPLICATIONS OF GENETIC TESTING FOR BREAST AND OVARIAN CANCER. Baopeng Lu

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1 SOME NEW ACTUARIAL MODELS OF THE INSURANCE IMPLICATIONS OF GENETIC TESTING FOR BREAST AND OVARIAN CANCER By Baopeng Lu Submitted for the Degree of Doctor of Philosophy at Heriot-Watt University on Completion of Research in the School of Mathematical and Computer Sciences May This copy of the thesis has been supplied on the condition that anyone who consults it is understood to recognise that the copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without the prior written consent of the author or the university (as may be appropriate).

2 I hereby declare that the work presented in this thesis was carried out by myself at Heriot-Watt University, Edinburgh, except where due acknowledgement is made, and has not been submitted for any other degree. Baopeng Lu (Candidate) Professor Angus S. Macdonald (Supervisor) Professor Howard R. Waters (Supervisor) Date ii

3 Abstract There have been many controversial debates between the public and insurance companies as to whether genetic information (or more specifically, the results of genetic testing) should be available to insurance companies. The public fears genetic discrimination over access to insurance, while insurance companies prefer to work according to fairness and traditional insurance principles. These conflicting views may be compounded by ambiguous government policies that may not be clear to the public or insurers. Actuaries have been attempting to tackle this problem by formulating quantitative approaches and this thesis forms part of the growing actuarial literature in this field. Insurers access to genetic test results is often restricted and the only genetic information that might be collected during underwriting in some countries is family history. In this thesis, we propose a new family history model which is simple and dynamic, where the onset of a family history is represented explicitly as a transition between states, hence as part of the applicant s own life history. This helps to adapt family history into multiple state models, which are intrinsically suitable for modelling genetic disorders. Furthermore, the effect of a moratorium on the use of family history can be modelled straightforwardly. iii

4 We then applied this family history model to life insurance, critical illness insurance and income protection insurance to: (a) estimate premium ratings depending on genotype or family history; and (b) model the potential cost of adverse selection. By investigating various insurance markets, our models help to answer two core questions about genetics and insurance: (a) How large would the impact be if genetic tests or family history are allowed to be used in underwriting? (b) How large would the impact be if genetic tests or family history are not allowed to be used in underwriting? iv

5 Acknowledgements First, I would like to express my deepest appreciation to my dearest supervisors, Professor Angus Macdonald and Professor Howard Waters for their advice, encouragement and help throughout this study. Their insightful guidance directs me to the end of the thesis and they help me to grow from a boy to a man. I owe them too much. I would like to thank Dr. Chessman Wekwete for his kind help and involvement in my first-year study. His friendship helped me to adapt to a new life abroad. I would love to thank my parents. Their love accompanied me through this study and will continue further in my whole life. They give me the strength and the desire for success, and in return, I realise their dreams. I would love to thank my fiancee, Fan Yan, for her everlasting support and encouragement. Only one thing I would like to say here is: my future will be shared by her. I would like to thank Dr. Mark Robson from the Memorial Sloan-Kettering Cancer Center in New York and Dr. William Foulkes and Dr. Pierre Chappuis of McGill University and the Jewish General Hospital in Montreal, for providing the underlying datasets of this study. v

6 I would like to thank all my friends for their friendship and support during this study. I express my special appreciation to Chenming Bao, Keli Zhang, Shenglai Xie, and Jiangchun Bi. Finally, I would like to thank the sponsors for funding this study, and members of the Genetics and Insurance Research Centre in Heriot Watt University for helpful comments at various stages. vi

7 Contents Abstract Acknowledgements iii v Introduction 1 1 Background Basic Genetics DNA, Genes, and Chromosomes Mendelian Inheritance Mutations and Diseases Breast Cancer and Ovarian Cancer Genetic Testing Introduction of Genetic Testing Genetic Testing and Insurance in the UK Quantitative Basis Multiple State Models Parameterising Multiple State Models The Epidemiology of Breast Cancer and Ovarian Cancer Breast Cancer Ovarian Cancer The Genetic Literature on Breast Cancer and Ovarian Cancer The Development of BC/OC Genetics The BRCA1 Gene The BRCA2 Gene Mutation Frequencies Genetics in Clinical Practice Genetic Testing and Insurance A Family History Model of Breast Cancer and Ovarian Cancer Risk Subpopulations Definition of Subpopulations The Distribution of Families in Subpopulations A Model of Family History Modelling Family History Estimating Incidence Rates of BC and OC Estimating the Rate of Mortality Excluding BC and OC vii

8 3.2.4 The Rate of Onset of a Family History Discussion Application of the Family History Model to Life Insurance Life Underwriting The Underwriting Process The OR Rate Genetic Underwriting Our Purpose A Life Insurance Model Including Family History Modelling Requirements The Model Premium Ratings for Temporary Life Insurance Numerical Procedures Premium Ratings Based on Genotype Premium Ratings Based on Family History Conclusions The Cost of Adverse Selection in a Temporary Life Insurance Market Moratoria and Underwriting Classes Parameterisation Numerical Procedures Moratoria on Genetic Test Results Alone A Moratorium on Family History and Genetic Test Results Conclusions Application of the Family History Model to Critical Illness Insurance Critical Illness Insurance Overview Development A Model of a Critical Illness Insurance Market Parameterisation Premium Ratings for Critical Illness Insurance Premium Ratings Based on Genotype Premium Ratings Based on Family History The Costs of Adverse Selection in a CI Insurance Market Moratoria on Genetic Test Results Alone A Moratorium on Family History and Genetic Test Results Conclusions Premium Ratings The Effect of Lower Penetrance of BRCA1 and BRCA2 Mutations The Impact of Adverse Selection viii

9 6 A Life History Model of an Applicant At Risk of Breast Cancer for Income Protection Insurance Income Protection Insurance Policy Design IPI Underwriting Our Purpose Actuarial Models of IPI The CMIB s IPI Model An Extension of the IPI Model to Breast Cancer Stages of Breast Cancer Extent and Staging of Breast Cancer Non-invasive Breast Cancer Invasive Breast Cancer Recurrent Breast Cancer The Diagnosis of Breast Cancer Diagnostic Approaches The Participation Rate and Sensitivity The Tumour Detection Model The Tumour Progression Model The Tumour Detection Model Breast Cancer Treatment I: The General Population Forms of Treatment Mastectomy versus BCS Treatment Options Breast Cancer Treatment II: BRCA1/2 Mutation Carriers Increased Risk Associated with BRCA1 and BRCA2 Mutations Treatment for BRCA1/2 Mutation Carriers: BCS versus Bilateral Mastectomy Treatment Procedures and Recovery Treatment Procedures Rates of Recovery Based on Treatment Options Rates of Breast Cancer Recurrence Recurrence Rates After Primary Treatment of BCS for Early Breast Cancer Recurrence Rates After Primary Treatment of Mastectomy for Locally Advanced Breast Cancer for Non-carriers Recurrence Rates After Primary Treatment of Bilateral Mastectomy for Locally Advanced Breast Cancer for Mutation Carriers Conclusions Application of the Life History Model to Income Protection Insurance Intensities for Sicknesses Other Than Breast Cancer The Onset Rate of Other Sicknesses The Rates of Claim Recovery From Other Sicknesses Mortality ix

10 7.2.1 Baseline Mortality Mortality since Diagnosis of Breast Cancer Mortality after Onset of Other Sickness Risk Subpopulations and the Onset of Family History Risk Subpopulations The Development of a Family History of BC Application of the Life History Model to IPI Business Numerical Procedures Premium Ratings for the General Population Premium Ratings for Mutation Carriers Premium Ratings for Women With a Family History The Effect of Reduced Onset Rates The Cost of Adverse Selection in an IPI Market The Life History Model of a Woman at Risk of Breast Cancer in an IPI Market Parameterisation Numerical Procedures Underwriting Classes Based on Various Moratoria Moratoria on Genetic Test Results Alone A Moratorium on Family History and Genetic Testing Results Conclusions Conclusions, Contributions and Further Research Conclusions A New Family History Model Premium Ratings The Effect of Reduced Penetrance of BRCA1 and BRCA2 Mutations Adverse Selection Contributions Further Research A Estimating the Rate of Mortality after Onset of BC or OC 221 A.0.1 Post-onset Mortality after Breast Cancer A.0.2 Post-onset Mortality after Ovarian Cancer A.0.3 Improvements in Survival Rates A.0.4 Discussion B BC Mortality Data 237 C OC Mortality Data 239 References 240 x

11 List of Tables 2.1 BC risk factors. Source: Veronesi et al. (2005) Heterogeneity analysis based on the CASH model. Source: Ford et al. (1998) Prevalence of BRCA1 and BRCA2 gene mutations. Source: Peto et al. (1999), Johannesdottir et al. (1996) and Struewing et al. (1997) Published penetrance estimates of BRCA1 mutations, expressed as the cumulative probability of onset of BC and OC at ages 50 and 70, with 95% confidence intervals where available Published penetrance estimates of BRCA2 mutations, expressed as the cumulative probability of onset of BC and OC at ages 50 and 70, with 95% confidence intervals where available Estimates of the population frequency of mutations in BRCA1 and BRCA2 alleles Cumulative risks of BC for a woman with one affected first- or seconddegree relative according to the Claus model. Source: Claus et al. (1994) Calculation of the probability of at least one of the applicant s parents being a BRCA1 mutation carrier. q 1 = 2p 1 is approximately the probability that any given grandparent is a mutation carrier Proportions of the five subpopulations in the whole population Estimated rates of onset of breast cancer (and 95% confidence intervals) in respect of BRCA1 and BRCA2 mutation carriers, based on the meta-analysis of Antoniou et al. (2003) Estimated rates of onset of ovarian cancer (and 95% confidence intervals) in respect of BRCA1 and BRCA2 mutation carriers, based on the meta-analysis of Antoniou et al. (2003) Distribution of the number of the applicant s sisters. Source: Macdonald et al. (2003a) Types of regulations concerning: (a) the requirement to take new genetic tests; (b) the requirement of disclosure of current genetic testing results when underwriting; and (c) insurers use of current genetic testing results if disclosed by applicants willingly. Source: Lemaire and Macdonald (2004) Expected present value of temporary life insurance cover of unit benefit, for non-mutation carriers (NC) and persons with a known BRCA1 or BRCA2 mutation. Excess BC/OC incidence rates are 100% and 50% of those observed xi

12 4.15 Expected present value of an annuity of 1 per annum payable continuously while in the insured and BC/OC states of Figure 4.17, for non-mutation carriers (NC) and persons with a known BRCA1 or BRCA2 mutation. Excess BC/OC incidence rates are 100% and 50% of those observed Level net premium for temporary life insurance cover of unit benefit, expressed as absolute values, absolute extra premiums and a percentage of the premium for standard risks, for non-mutation carriers (NC) and persons with a known BRCA1 or BRCA2 mutation. Excess BC/OC incidence rates are 100% and 50% of those observed Proportions of lives with and without a family history of BC and/or OC at age 20, 30, 40 and 50 yeas, respectively. Subpopulations labeled with index i are defined in Section Level net premium for temporary life insurance cover of unit benefit, expressed as both absolute values and a percentage of the premium for standard risks, for women with and without a family history of BC and/or OC, respectively (FH = family history present). Excess BC/OC incidence rates are 100% and 50% of those observed Possible underwriting classes within the five sub-populations, labelled by index i, defined in Section (T) denotes persons who have had a genetic test and (NT) denotes that persons who have not. (F) denotes persons who have developed a family history and (NF) denotes persons who have not. (ALL) denotes all of the insured states Percentage increases in premium rates for life insurance, under a moratorium on all genetic test results and adverse results, for a market operating between ages 20 and Percentage increases in premium rates for life insurance, using a moratorium on all genetic test results and adverse results respectively, under severe adverse selection, with annual rate of testing 0.04, for a market operating between ages 20 and Percentage increases in premium rates for life insurance, under a moratorium on genetic test results and family history, for a market operating between ages 20 and Expected present value of CI insurance cover of unit benefit, for nonmutation carriers (NC) and persons with a known BRCA1 or BRCA2 mutation. Excess BC/OC incidence rates are 100% and 50% of those observed Expected present value of an annuity of 1 per annum payable continuously while in the insured and BC/OC states of Figure 5.19, for non-mutation carriers (NC) and persons with a known BRCA1 or BRCA2 mutation. Excess BC/OC incidence rates are 100% and 50% of those observed xii

13 5.25 Level net premium for CI insurance cover of unit benefit, expressed as both a absolute value and a percentage of the premium for standard risks, for non-mutation carriers (NC) and persons with a known BRCA1 or BRCA2 mutation. For comparison, results from Macdonald et al. (2003b) are reproduced in brackets.excess BC/OC incidence rates are 100% and 50% of those observed Level net premium for CI cover of unit benefit, expressed as both a absolute value and a percentage of the premium for standard risks, for women with and without a family history of BC and/or OC, respectively (FH = family history present). Excess BC/OC incidence rates are 100% and 50% of those observed Percentage increases in premium rates under a moratorium on all genetic testing results and adverse results respectively, for a CI insurance market operating between ages 20 and Percentage increases in premium rates using a moratorium on all genetic testing results and adverse results respectively, under severe adverse selection, with annual rate of testing 0.04, for a CI insurance market operating between ages 20 and Percentage increases in premium rates under a moratorium on genetic testing results and family history, for a CI insurance market operating between ages 20 and Published participation rates in the UK breast cancer screening program. Source: NHS Breast Screening Programme 2005 Review Progression rates from Duffy et al. (1995, 1997) MLEs of transition intensities of the model in Figure Source: Chen et al. (2002) The detection rates of invasive types of breast cancer, based on SEER 9 Regs Public-use database. COUNT is the number of BC cases detected during the age interval and TE is the total exposure to risk. Rates are per 100,000 women years The modified detection rates of invasive types of breast cancer, based on SEER 9 Regs Public-use database. COUNT is the number of breast cancer detected during the age interval and TE is the total exposure to risk. Rates are per 100,000 women years Twenty-year results of an Italian randomised trial of breast cancer surgery. Source: Veronesi et al. (2002) Twenty-year results of a US randomised trial of breast cancer surgery. Source: Fisher et al. (2002) Ten-year results of breast cancer recurrence after primary treatment of BCS. Source: Robson et al. (2004) Parameter estimates of rates of onset of various types of recurrence for BRCA1/2 mutation carriers Recurrences after mastectomy. Source: Overgaard et al. (1997) Recurrences after bilateral mastectomy. Source: Peralta et al. (2000) and Herrinton et al. (2005) The modifying factor M inception of claim inception rates based on the standard female experience for Source: CMIR 20 (2001) xiii

14 7.42 The modifying factor M recovery of claim recovery rates based on the standard female experience for Source: CMIR 20 (2001) The modifying factor M sick mort of mortality rates after onset of sickness other than BC based on the standard female experience for Source: CMIR 20 (2001) Expected present values of the IPI claim annuity of 1 per annum payable continuously while sick with duration exceeding the DP, according to the standard female experience for and based on the model in Figure Expected present values of an annuity of 1 per annum payable continuously while healthy or sick with duration less than the DP, according to the standard female experience for and based on the model in Figure Level net premium for the IPI claim annuity of 1 per annum, according to the standard female experience for and based on the model in Figure Expected present values of the IPI claim annuity of 1 per annum payable continuously while sick with duration exceeding the DP, according to the standard female experience for and based on the basic model in CMIR Expected present values of an annuity of 1 per annum payable continuously while healthy or sick with duration less than the DP, according to the standard female experience for and based on the basic model in CMIR Level net premium for the IPI claim annuity of 1 per annum, according to the standard female experience for and based on the basic model in CMIR Level net premiums for IPI cover of unit benefit, expressed as both absolute values and a percentage of the premium for standard risks, for persons with a known BRCA1 or BRCA2 mutation Proportions of lives with and without a family history of BC at age 20, 30, 40 and 50 years, respectively. Subpopulations labeled with index i are defined in Section Level net premiums for IPI cover of unit benefit, expressed as both absolute values and a percentage of the premium for standard risks, for women with and without a family history of BC, respectively (FH = family history present) Level net premiums for IPI cover of unit benefit, expressed as both absolute values and a percentage of the premium for standard risks, for persons with a known BRCA1 or BRCA2 mutation. Excess BC incidence rates are 50% of those observed Level net premiums for IPI cover of unit benefit, expressed as both absolute values and a percentage of the premium for standard risks, for women with and without a family history of BC, respectively (FH = family history present). Excess BC incidence rates are 50% of those observed xiv

15 7.55 Percentage increases in premium rates for IPI cover with DP for 1 week, under a moratorium on all genetic test results and adverse results respectively, for a market operating between ages 20 and Percentage increases in premium rates for IPI cover with DP for 4 weeks, under a moratorium on all genetic test results and adverse results respectively, for a market operating between ages 20 and Percentage increases in premium rates for IPI cover with DP for 13 weeks, under a moratorium on all genetic test results and adverse results respectively, for a market operating between ages 20 and Percentage increases in premium rates for IPI cover with DP for 26 weeks, under a moratorium on all genetic test results and adverse results respectively, for a market operating between ages 20 and Percentage increases in premium rates for IPI cover, using a moratorium on all genetic test results and adverse results respectively, under severe adverse selection, with annual rate of testing 0.04, for a market operating between ages 20 and Percentage increases in premium rates for IPI cover with DP for 26 weeks, under a moratorium on all genetic test results and family history, for an IPI market with different DPs operating between ages 20 and A.61 Results of test for differences of BC mortality rates by duration since diagnosis A.62 Results of test for differences of OC mortality rates by duration since diagnosis. Degrees of freedom for χ 2 test given in parenthesis A.63 Mortality Trends A.64 SEER Mortality Trends xv

16 xvi

17 List of Figures 1.1 A three-state model for sickness and death Age-standardised mortality rates because of BC, for women in England and Wales between Source: O.N.S. (1997) Age-standardised mortality rates because of OC, for women in England and Wales between Source: O.N.S. (2005) Double-decrement model for BC. Source: Lemaire et al. (2000) A Markov model for the i th relative of the insured woman, with genotype g i. Relative No.1 is the woman herself. Source: Macdonald et al. (2003a) Population incidence rates of breast cancer and ovarian cancer. Source: Macdonald et al. (2003a) Rate of onset of BC for BRCA1 mutation carriers Rate of onset of BC for BRCA2 mutation carriers Rate of onset of OC for BRCA1 mutation carriers Rate of onset of OC for BRCA2 mutation carriers Crude and graduated proportion of total deaths that are due to Breast Cancer and Ovarian Cancer, for females. Source: Macdonald et al. (2003a) Rate of onset of family history for the non-mutation-carrying subpopulation, i = Rate of onset of family history for the BRCA1 subpopulations, i = 1 and i = 2, based on the recent meta-analysis by Antoniou et al. (2003) (original rates and our fitted functions, respectively) with, for comparison, rate of onset of family history from Macdonald et al. (2003a), which was based on earlier studies Rate of onset of family history for the BRCA2 subpopulations, i = 3 and i = 4, based on the recent meta-analysis by Antoniou et al. (2003) (original rates and our fitted functions, respectively) with, for comparison, rate of onset of family history from Macdonald et al. (2003a), which was based on earlier studies Rate of onset of family history for the BRCA1 subpopulations, i = 1 and i = 2, based on the recent meta-analysis by Antoniou et al. (2003) (original rates, our fitted functions and 95% confidence intervals) Rate of onset of family history for the BRCA2 subpopulations, i = 3 and i = 4, based on the recent meta-analysis by Antoniou et al. (2003) (original rates, our fitted functions and 95% confidence intervals) xvii

18 4.17 A semi-markov model of family history, genetic testing, insurance purchase and life insurance events for a person in the ith subpopulation (FH = family history present). Intensities are functions of current age, x + t, and duration since onset of BC or OC, d A Markov model for a woman with genotype g, buying CI insurance. Source: Macdonald et al. (2003b) A Markov model of family history, genetic testing, insurance purchase and CI insurance events for a person in the i th risk subpopulation (FH = family history present) Crude and graduated incidence rates of cancers other than BC and OC, for females. Source: Macdonald et al. (2003b) Crude and graduated incidence rates of strokes, for females. Source: Macdonald et al. (2003b) Crude and graduated incidence rates of all first heart attacks, for females. Source: Macdonald et al. (2003b) Crude and graduated proportion of total deaths that are from CI claim causes, for females. Source: Macdonald et al. (2003b) A sample path for an individual conventional IPI policy. H = Healthy, S = Sick, d = deferred period, NRA = normal retirement age, P = Premiums, and B = Benefits The CMIB s three-state semi-markov model for sickness A semi-markov model of the life history of a woman in the ith subpopulation with breast cancer. ➀: treatment of BCS with radiotherapy; ➁: combined treatment of mastectomy (bilateral mastectomy for BRCA1/2 mutation carriers), radiotherapy and chemotherapy; ➂: chemotherapy for ipsilateral recurrence or combined treatment for contralateral recurrence; and ➃: systematic treatment. Intensities are functions of current age, x + t, and duration at current state, z Three-state Markov model of the progression of breast cancer A Markov model of the detection of breast cancer Comparison of incidence rates of breast cancer, based on the SEER 9 Regs Public-use ( ) database and UK fitted rates from Macdonald et al. (2003a) Non-parametric and parametric estimates for the probability of survival free of ipsilateral recurrence for non-carriers of BRCA1/2 mutations Parametric rates of onset of ipsilateral recurrence for non-carriers of BRCA1/2 mutations Q-Q plots to test model adequacy of ipsilateral recurrence for noncarriers of BRCA1/2 mutations Non-parametric and parametric estimates for the probability of survival free of contralateral recurrence for non-carriers of BRCA1/2 mutations Parametric rates of onset of contralateral recurrence for non-carriers of BRCA1/2 mutations Q-Q plots to test model adequacy of contralateral recurrence for noncarriers of BRCA1/2 mutations xviii

19 6.36 Non-parametric and parametric estimates for the probability of survival free of distant recurrence for non-carriers of BRCA1/2 mutations Parametric rates of onset of distant recurrence for non-carriers of BRCA1/2 mutations Q-Q plots to test model adequacy of distant recurrence for noncarriers of BRCA1/2 mutations Non-parametric and parametric estimates for probability of free of ipsilateral recurrence for BRCA1 mutation carriers Parametric rates of onset of ipsilateral recurrence for BRCA1 mutation carriers Q-Q plots to test model adequacy of ipsilateral recurrence for BRCA1 mutation carriers Non-parametric and parametric estimates for probability of free of contralateral recurrence for BRCA1 mutation carriers Parametric rates of onset of contralateral recurrence for BRCA1 mutation carriers Q-Q plots to test model adequacy of contralateral recurrence for BRCA1 mutation carriers Non-parametric and parametric estimates for probability of free of distant recurrence for BRCA1 mutation carriers Parametric rates of onset of distant recurrence for BRCA1 mutation carriers Q-Q plots to test model adequacy of distant recurrence for BRCA1 mutation carriers Non-parametric and parametric estimates for probability of free of contralateral recurrence for BRCA2 mutation carriers Parametric rates of onset of contralateral recurrence for BRCA2 mutation carriers Q-Q plots to test model adequacy of contralateral recurrence for BRCA2 mutation carriers Non-parametric and parametric estimates for probability of free of distant recurrence for BRCA2 mutation carriers Parametric rates of onset of distant recurrence for BRCA2 mutation carriers Q-Q plots to test model adequacy of distant recurrence for BRCA2 mutation carriers Onset rates of sickness other than BC for different DPs, based on the standard female experience for Crude and graduated proportions of total deaths that are due to BC, for females Relative survival rate for women who develop early breast cancer Relative survival rate for women who develop locally advanced breast cancer Relative survival rate for women who develop metastatic breast cancer Rates of onset of family history of BC in risk subpopulations, following the same approach as in Section xix

20 7.60 A semi-markov model of family history, genetic testing and IPI purchase for a person in the i th risk subpopulation (FH = family history present) A.61 Crude BC mortality rates at selected durations after diagnosis A.62 Crude and fitted BC mortality rates and 95% confidence intervals for the crude rates A.63 Fitted BC mortality rates for all durations A.64 Fitted BC mortality rates with fitted mortality at adjacent durations. 228 A.65 Crude OC mortality rates at selected durations after diagnosis A.66 Crude and fitted OC mortality rates and 95% confidence intervals for the crude rates A.67 Fitted OC mortality rates for all durations A.68 Fitted OC mortality rates with fitted mortality at adjacent durations. 232 A.69 Crude BC mortality rates for UK and SEER populations A.70 Crude OC mortality rates for UK and SEER populations xx

21 Introduction The last decade will prove to be significant in human history. Huge numbers of genes were located by the Human Genome Project, whose purpose is to locate genes easier, faster and cheaper. Their studies have led to the location of genes responsible for disorders including, but far beyond, cystic fibrosis, Huntington s disease (HD), breast cancer (BC), ovarian cancer (OC), and some forms of Alzheimer s disease. Tests for these, and many other genetic disorders, are becoming more commonly available and could soon become inexpensive. However, the development of human genetics bring not only benefits, but also creates numerous ethical and social issues. Questions around fairness and discrimination are intensely debated. Who are eligible to undergo genetic testing? How will the serious implications for privacy and confidentiality be handled? Who should have the right to use the genetic test results? Should persons with adverse test results be treated differently and what is fair? Insurers, along with their customers and regulators, are confronted with the complexities of risk classification and the consequences of using genetic information. More specifically, may an insurance company classify its applicants based on their genetic status? Different opinions on behalf of different groups have been expressed to answer this question. While consumers fear that insurers could be reluctant to provide coverage on the basis of adverse genetic test results, insurers are concerned that adverse selection will occur if applicants have genetic information that is not known by them. These debates have resulted in quasi-legislative intervention, however, no significant attention has been paid directly to this issue. In the UK, the key concern concentrates on the effect of genetic test results on eligibility for health-related insurance. However, recently the debates have broadened 1

22 and embraced the use of family history in underwriting. Following a lead by the UK actuarial profession, studies have started to seek quantitative insights about the financial implications of genetics and insurance; we expect these to throw some light on the social and ethical issues generated by the development of genetics. At the same time, industry actuaries have been involved in work on behalf of the insurance companies to construct a firm and reasonable basis for seeking permission to make use of the results of certain predictive genetic tests for insurance purposes. During the exploring process, two modelling approaches have appeared in the actuarial literature: top-down and bottom-up. A top-down approach is applied if the analysis focuses on broad, inclusive classes of mutations, without specific reference to individual genetic diseases. Macdonald (1997, 1999) are two examples which investigated the entire class of multifactorial disorders, and Macdonald (2003a) considered the entire class of single-gene diseases similarly. A bottom-up approach models each genetic disorder specifically and aggregates the individual costs. To date, genetic diseases modelled by this approach are: Alzheimer s Disease and longterm care by Macdonald and Pritchard (2000, 2001), Adult Polycystic Kidney Disease (APKD) by Gutiérrez and Macdonald (2003), Huntington s Disease (HD) by Gutiérrez and Macdonald (2004), and Early-onset Alzheimer s Disease (EOAD) by Gui and Macdonald (2002). However, the above genetic disorders are all single-gene diseases that have no causes other than mutations in a single gene. The interpretation of this kind of family history is simple and can be calculated straightforwardly given relevant mutation frequencies. Models for estimating financial consequences of these diseases have been well developed. Conclusions have also been drawn in terms of costs for mutation carriers and the financial impacts on various insurance markets. On the other hand, disorders like BC and OC have many causes, where only a small proportion of cases are inherited through defects in single genes, others being usually associated with environmental causes. In this case, onset of the disease does not identify mutation carriers, and a family history could arise by chance in any family. Previous studies about these disorders mainly chose BC and OC as their subjects, since they are the only ones currently being investigated by the 2

23 Association of British Insurers (ABI) as possibly relevant for insurance purpose. Subramanian et al. (1999) and Lemaire et al. (2000) analysed BC and OC in respect of life insurance, while Macdonald et al. (2003a,b) proposed a model of BC and OC leading to estimates of the probabilities that an applicant has a BRCA1/BRCA2 mutation given complete or incomplete knowledge of her family history, and applied the model to critical illness (CI) insurance underwriting. The purpose of this thesis is to discuss the actuarial issues arising in connection with BC and OC, and various insurance products. In this thesis, we expand and update previous studies as follows: (a) We present a simplified but more dynamic model of family history of BC and OC that greatly reduces the computational burden of the approach used by Macdonald et al. (2003a,b). (b) We incorporate more recent estimates of rates of onset associated with these mutations, from epidemiological studies that better control the selection of subjects. (c) We estimate survival rates after onset of BC and OC and extend the previous study to life insurance. (d) We investigate and model a comprehensive life history of a woman with BC, including events such as diagnosis, treatment, recovery and recurrence; and apply this model to study income protection insurance (IPI). We begin by introducing some background knowledge of human genetics and genetic testing as well as some actuarial modelling tools in Chapter 1. In this chapter we also discuss the impact of genetic testing on insurance and describe the development of using genetic information for insurance purposes in the UK. In Chapter 2, we review the current genetic epidemiology of BC and OC. Both BC and OC are severe and common diseases, especially BC which is the most common cancer in women. OC is less prevalent, but more lethal. The majority of BC and OC is the result of a combination of risk factors, such as diet, lifestyle, environmental exposures, and others known and unknown. However, both BC and OC have inherited variants, accounting for a small proportion of all cases, that are now known to be caused primarily by mutations in the BRCA1 and BRCA2 genes. These two 3

24 genes account for a significant proportion of families with multiple cases of BC and OC. A literature review of mutation frequencies and penetrances is given. Genetic tests with respect to BRCA1 and BRCA2 cancer-predisposing gene mutations have been available in clinical practice since the mid 1990s, and inevitably this has led to a debate about the use of such test results in insurance underwriting. Therefore, we discuss some issues about the genetic testing and insurance at the end of this chapter. In some countries, the applicant s genetic makeup is strictly forbidden to be used for insurance purposes (except perhaps for very large policies). Actuaries then can only estimate the probabilities that the applicant is or is not a mutation carrier, given his or her family history. In Chapter 3, we propose a family history model which is based on underwriting practice and uses first-degree relatives only. This model is dynamic in nature, where the presence of a family history is regarded as an event in the applicant s life history. We then calculate the rate of onset of a family history of BC and OC given fitted onset and mortality rates (and corresponding morbidity and mortality rates for causes other than BC and OC). In the above family history model, the development of a family history is represented explicitly as a transition between states. This allows the impact of a moratorium to be modelled. We then apply this family history model to life insurance in a semi-markov framework in Chapter 4 and to CI insurance in a Markov framework in Chapter 5 to: (a) estimate premium ratings depending on genotype or family history; and (b) model the potential cost of adverse selection. We are interested to extend the dynamic family history model to income protection insurance, a more complicated application. In Chapter 6, we construct and parameterise a semi-markov model for a comprehensive life history of a woman with BC, in which events such as diagnosis, treatment, recovery and recurrence are incorporated. We then show: (a) estimates of IPI premium ratings depending on genotype or family history; and (b) the impact of adverse selection in the IPI market under various moratoria on the use of genetic information, in Chapter 7. Our conclusions, contributions and possible directions for further research are given in Chapter 8. 4

25 The results of Chapters 3, 4, and 5 were the basis of the paper Gui et al. (2006) to appear in Scandinavian Actuarial Journal. The results concerning IPI in Chapters 6 and 7 were presented to the 10th I:ME (Insurance: Mathematics & Economics) International Congress (Leuven, Belgium) in July 2006 with the title Stochastic Modeling of Breast Cancer for Income Protection Insurance. 5

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27 Chapter 1 Background 1.1 Basic Genetics Genetics is far too large a subject to be described in detail here. We introduce only as much human genetics as is needed to study insurance related issues. Some good references are Pasternak (1999); Strachan and Read (1999) and Griffiths et al. (2004) DNA, Genes, and Chromosomes DNA Each person has a unique set of chemical blueprints that determines how his or her body looks and works. These blueprints are embedded in a complex molecule called deoxy-ribonucleic acid (DNA), which is found inside each cell in the body. DNA molecules are among the largest molecules now known, each of which is made up of two strands that wind around each other like a twisted ladder (known as the double helix ), whose sides are connected by rungs of nitrogen-containing chemicals called bases. Each strand is a linear arrangement of repeating similar units called nucleotides. There are four different bases present in DNA: adenine (A), thymine (T), cytosine (C), and guanine (G). The specific order of the bases arranged along the strand is called the DNA sequence; the sequence determines the exact genetic rules required to create a particular organism with its own unique characteristics. An 7

28 organism s complete set of DNA is called its genome, and it contains the governing blueprint for all molecular structures and functions for the lifetime of the cell or organism. The two DNA strands are held together by weak bonds between the bases on each strand, forming base pairs. Genome size usually refer to the total number of base pairs; the human genome contains roughly three billion base pairs. When a cell divides into two daughter cells, its full genome is duplicated. During cell division the DNA molecule unwinds and the strands separate by breaking the weak bonds between the base pairs. Each strand will act as a template for the construction of a complementary new strand as free nucleotides match up with their counterparts on the strand. Strict rules are obeyed on base-pairing: adenine will combine only with thymine (an A-T pair) and cytosine with guanine (a C-G pair). Each daughter cell receives one old and one new DNA strand. The base-pairing rules make sure that the new strand is an exact copy of the old one, barring errors in copying called mutations. Genes and Alleles Specific segments of DNA that contain the rules for producing particular proteins are called genes, so a gene consists of a linear sequence of nucleotide bases in the DNA. A gene is the basic unit of inheritance and each gene is located at a precise position on a chromosome. Human genes vary greatly in length, often extending over thousands of bases, but only about 10% of the genome is known to include the protein-coding sequences (exons) of genes, along with intron sequences, which have no coding meanings. The balance of the genome is considered to consist of other non-coding regions, such as control sequences and intergenic regions, whose functions are obscure. All living organisms are composed largely of proteins; humans can synthesise at least 100,000 different kinds. Proteins are large, complex molecules made up of long chains of subunits called amino acids. Twenty different kinds of amino acids are found in human proteins. Within the gene, each specific sequence of three DNA bases (codons) controls the cell s protein-synthesising mechanism to create particular 8

29 amino acids. For example, the base sequence A-T-G codes for the amino acid methionine. The genetic code is thus a series of codons which specify which amino acids are needed to produce specific proteins. Evidence shows that any gene may occasionally mutate to present as a new equally stable unit, called an allele, which has more or less similar but not identical effects on the same trait. For example, the gene for seed shape in pea plants exists in two forms, one form (or allele) for round seed shape (A) and the other for wrinkled seed shape (a). Organisms have two alleles for each trait. An organism in which both copies of the gene (alleles) are identical is called homozygous while an organism which has two different alleles of the gene is said to be heterozygous one is dominant and the other is recessive. The genotype of a single gene or multiple genes, sometimes with environmental factors, may determine the physical appearance of an individual organism, which is referred to as the phenotype. The dominant allele is expressed in the phenotype and the recessive allele is not. Using the previous example, the phenotype is the seed shape, with round seed shape (A) being dominant and wrinkled seed shape (a) being recessive. Alternatively, a round phenotype indicates that the genotype is (AA) or (Aa) and a wrinkled phenotype must have a genotype (aa). Chromosomes All genes (except those present in mitochondria, which we ignore) are arranged into 24 distinct, physically separate units called chromosomes. Most human cells contains 2 sets of chromosomes, 1 set given by each parent. Each set has 23 single chromosomes: 22 autosomes and an X or Y sex chromosome. Women have a pair of X chromosomes and men have a X and Y pair. This means that the Y chromosome, which determines the sex of the child, will only be from the father. When stained with certain dyes, chromosomes can be seen under a microscope, revealing an interspersed combination of light and dark bands which reflect regional differences in the number of A-T vs C-G base pairs. Variation in size and the banding order makes the 24 chromosomes visually distinct from each other. 9