This article was downloaded by: [University of Pennsylvania] On: 31 May 2013, At: 08:54 Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK North American Actuarial Journal Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/uaaj20 Pricing Term Insurance in the Presence of a Family History of Breast or Ovarian Cancer Jean Lemaire A.S.A., Ph.D. a, Krupa Subramanian A.S.A. b, Katrina Armstrong M.D. c & David A. Asch M.D., M.B.A. d a Insurance and Risk Management Department, University of Pennsylvania, CPC 310, 3641 Locust Walk, Philadelphia, Pennsylvania 19104-6218 b Department of Risk, Insurance, and Healthcare Management, Temple University, 479 Ritter Annex (004-00), Philadelphia, Pennsylvania 19122 c School of Medicine of the University of Pennsylvania, 708 Blockley, Philadelphia, Pennsylvania 19104-6021 d School of Medicine of the University of Pennsylvania, CPC 210, 3641 Locust Walk, Philadelphia, Pennsylvania 19104-6218 Published online: 04 Jan 2013. To cite this article: Jean Lemaire A.S.A., Ph.D., Krupa Subramanian A.S.A., Katrina Armstrong M.D. & David A. Asch M.D., M.B.A. (2000): Pricing Term Insurance in the Presence of a Family History of Breast or Ovarian Cancer, North American Actuarial Journal, 4:2, 75-87 To link to this article: http://dx.doi.org/10.1080/10920277.2000.10595904 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
PRICING TERM INSURANCE IN THE PRESENCE OF A FAMILY HISTORY OF BREAST OR OVARIAN CANCER Jean Lemaire,* Krupa Subramanian, Katrina Armstrong, and David A. Asch ABSTRACT We estimate the increased mortality and term life insurance costs for women who have a family history of breast or ovarian cancer. Using data from the medical literature on age-specific and family history-specific incidence rates, we develop double-decrement models to evaluate the actuarial impact of breast cancer and ovarian cancer in the family. We also calculate the increased mortality and term insurance costs for women who test positive for the BRCA1 or BRCA2 gene mutation. We find that the type of affected relative and her age at onset of the disease are key underwriting factors. We find substantial mortality increases (up to 100%) for women with two relatives with cancer and women with a first-degree relative who developed cancer at an early age. Mortality increases for women with the BRCA gene mutation reach 150%. While some females with a family history of cancer can be accepted at standard rates, others may need to be quoted substandard rates, depending on the underwriting policy of the company. Females with the gene mutation can possibly be accepted at a rate that incorporates a severe mortality surcharge. 1. INTRODUCTION Approximately one in nine women in the U.S. will develop breast cancer (BC) in her lifetime; one in forty will die from the disease (American Cancer Society 1992). Ovarian cancer (OC) is less prevalent, but more deadly: 1.79% of women will get the disease, and more than 60% of them will die from it (Hartge et al. 1994). The vast majority of these cancers are the result of diet, lifestyle, environmental exposures, social interactions, and other factors known and unknown. *Jean Lemaire, A.S.A., Ph.D., is Professor and Chairperson of the Insurance and Risk Management Department at the University of Pennsylvania, CPC 310, 3641 Locust Walk, Philadelphia, Pennsylvania 19104-6218, e-mail, lemaire@wharton.upenn.edu. Krupa Subramanian, A.S.A., is Assistant Professor in the Department of Risk, Insurance, and Healthcare Management at Temple University, 479 Ritter Annex (004-00), Philadelphia, Pennsylvania 19122, e-mail, ksubrama@sbm.temple.edu. Katrina Armstrong, M.D., is Assistant Professor in the School of Medicine of the University of Pennsylvania, 708 Blockley, Philadelphia, Pennsylvania 19104-6021, e-mail, karmstro@mail.med. upenn.edu. David A. Asch, M.D., M.B.A., is Associate Professor in the School of Medicine of the University of Pennsylvania, CPC 210, 3641 Locust Walk, Philadelphia, Pennsylvania 19104-6218, e-mail, asch@ wharton.upenn.edu. For instance, it is known that a late age at first childbirth and an early first menstruation slightly increase the likelihood of developing BC (Gail et al. 1989). Women with more pregnancies, or longer use of oral contraceptives, or who underwent tubal ligation or hysterectomy, have a somewhat reduced probability of developing OC (Hartge et al. 1994). However, some cancers are inherited. A twofold to threefold increase in the risk of BC development has been associated with a family history of BC in a mother or sister (Claus, Risch, and Thompson 1990). OC risk is multiplied by 5.4 in the presence of family history (Hartge et al. 1994). A small percentage of women (estimates range from one woman out of 833 to one out of 100) have a dominant mutated gene called BRCA1 or BRCA2 (Ford, Easton, and Peto 1995). However, the gene mutation is much more frequent in some subgroups of the population for instance, 2.3% of Ashkenazi Jews carry the BRCA1 mutation (Struewing et al. 1997). Women with a BRCA mutation are at extreme risk to develop BC or OC. Estimates of the probability of developing either of these cancers by age 70 range as high as 0.945 (Easton et al. 1995). Medical data suggest that BRCA mutations are responsible for 80% of all inher- 75
76 NORTH AMERICAN ACTUARIAL JOURNAL, VOLUME 4, NUMBER 2 ited BC (Claus et al. 1998) and 5% of all BC (Wooster et al. 1995). Late in 1996, a reliable genetic test became available for detecting these mutations. Genetic testing is a source of concern for insurers, who fear adverse selection if they do not have access to the same information as applicants. Women who learn through genetic tests that they are at higher risk of death may purchase more insurance, which to them seems inexpensive because it is priced at rates set for average risks. Women who learn they are at lower risk may purchase less insurance. These two forces combine to increase the aggregate mortality of the purchasers of insurance. If insurers do not have access to the test results, they are unable to identify which women are at higher risk and which are not. They have to increase premiums for everyone, driving those at lower risk out of the pool. This creates a spiral of increasing prices and decreasing number of policies issued, which could, in a worst-case scenario, threaten the financial solvency of the insurer. The debate about insurer access to genetic screening information has industry representatives pointing to the risk of adverse selection. They advocate mandates requiring that all test results provided to individuals also be made available to insurers. This insurers request for a level playing field contrasts with opposite efforts by consumer groups to increase the privacy protection of genetic information. Consumers are concerned that test information may find its way to employers and result in employment and social discrimination. They fear that the use of genetic testing by insurers could result in the creation of a biological underclass of uninsurable individuals. The issue is highly emotional and very political. Underlying conflicts in fundamental values have prompted legislators to regulate the use of genetic testing. Wisconsin was the first state to introduce a genetic testing law, in 1992. Thirty-four states have now enacted laws prohibiting insurers of different types from using genetic information in their underwriting decisions. In this paper, we attempt to provide an actuarial insight into the debate by quantifying the impact of family history and BRCA1 and BRCA2 mutations on forces of mortality and on the costs of term insurance. In Section 2, we estimate the increase in the cost of term insurance when there is a family history of BC. We develop a double-decrement model to reveal that the presence of breast cancer in one or two firstdegree relatives may justify a significant increase in the net single premium. The younger the age at onset, the higher the surcharge. In their application forms, insurers may consequently consider requesting not only a list of all relatives affected with BC, but the ages at onset as well. In Section 3, we develop a similar double-decrement model that estimates the increase in the cost of term insurance for a woman with one first-degree relative affected with OC. Due to the high case-fatality rate for OC, premium increases are substantial. In Section 4, we compute term insurance premium increases for a woman who has a BRCA mutation. We use a triple-decrement model to incorporate the risk of both BC and OC. The resulting forces of mortality can make women with a BRCA mutation uninsurable at standard rates. Section 5 provides a short discussion of the degree of conservatism of our estimates. Section 6 presents our conclusions, in the form of suggestions for improving underwriting procedures. The results of our research should be applied with caution. They are based on the most recent data available from the medical literature, but new medical articles are published regularly that often provide very different estimates of BC and OC risks, depending on the demographic group studied. For instance, estimates of the lifetime probability of developing ovarian cancer for a woman with a BRCA1 mutation range from 11% to 84%. Also, there might be a systematic bias in medical studies due to the selection of the sample, usually families with a strong family history. Our premium surcharges are consequently point estimates, subject to high uncertainty. In order to aggregate data from a wide variety of sources, it has been necessary to use some actuarial approximations, such as a uniform-distribution-of-deaths assumption or formulas leading to an occasional double-counting of some early cancers. These approximations lead to second-order errors, which we believe are negligible when compared with the uncertainties in the medical literature. 2. TERM INSURANCE IN THE PRESENCE OF A FAMILY HISTORY OF BREAST CANCER Women with a family history of BC form a high-risk subset of the general population. Incidences of BC in the family may indicate an increased susceptibility to the disease, due to the presence of a BRCA mutation, common environmental factors and lifestyles, or other unknown risk factors. Claus, Risch, and Thompson (1994) have used data from the Cancer and Steroid Hormone Study, conducted by the Centers for Disease
PRICING TERM INSURANCE IN THE PRESENCE OF A FAMILY HISTORY OF BREAST OR OVARIAN CANCER 77 Table 1 Cumulative Probability of BC for a Woman Who Has One First-Degree Relative Affected with BC, by Age of Onset of the Affected Relative Age of Woman Age of Onset in Affected Relative 20 29 30 39 40 49 50 59 60 69 70 79 29 0.007 0.005 0.003 0.002 0.002 0.001 39 0.025 0.017 0.012 0.008 0.006 0.005 49 0.062 0.044 0.032 0.023 0.018 0.015 59 0.116 0.086 0.064 0.049 0.040 0.035 69 0.171 0.130 0.101 0.082 0.070 0.062 79 0.211 0.165 0.132 0.110 0.096 0.088 Figure 1 Double-Decrement Model for BC Control, to calculate age-specific risk estimates of BC. Probabilities of developing BC vary as a function of the number and type of family relatives who developed BC and of the ages at which these relatives became affected. For instance, Table 1 indicates the predicted cumulative probability of BC for a woman with a mother or sister affected, by age of onset of this firstdegree relative (FDR). Onset is defined as the moment BC is diagnosed. The paper by Claus, Risch, and Thompson (1994) was selected from the vast number on this topic in the medical literature because it reports the results of a major study, conducted by the Centers for Disease Control, involving 4,730 patients with confirmed BC and 4,688 control subjects matched to patients by geographic region and five-year age intervals. This large sample allowed the authors to obtain accurate probabilities of developing BC for a wide variety of family histories. A double-decrement model, shown in Figure 1, was built to evaluate the increased death probability of a woman with a family history of BC, and the resulting increase in the net single premium of term insurance. Denote k p x the survival probabilities for females given by the U.S. Decennial Life Tables for 1989 91, published by the U.S. Department of Health and Human Services. We chose to use population data rather than tables for insured lives to provide estimates of increased mortality for the general population. Insurers wishing to use these results may need to adjust for the relationship between population and insured lives ( ) mortality. Let k p x be the probabilities of a doubledecrement model, where the first cause of decrement (1) is dying from causes other than BC, without being affected by BC, and the second cause of decre- ( ) ment (2) is developing BC. So k px is the probability that a female age x does not develop BC and does not (1) die in time interval (x, x k). Let q x be the probability that a female age x dies from causes other than (2) BC within one year, and qx be the probability that a female age x develops BC within one year. Superscripts B and INC indicate, respectively, probabilities for baseline and increased risks. These probabilities are derived from interpolation (sum-of-the-digits method) in the tables of Claus, Risch, and Thompson (1994). Calculations can be summarized as follows. First, baseline double-decrement probabilities are obtained by the relationship ( ),B (2),B kp x kp x(1 kq x ). This formula introduces some double-counting into our calculations, as the U.S. Decennial Table includes some women who have already developed BC and some early deaths due to BC. The impact of this approximation is believed to be very small, as the mean age at onset for BC is close to 69, annual survival probabilities with BC are high, and the above formula is mostly applied to young ages. Once a woman has developed BC, a singledecrement model, specific to the disease, is used. Let BC kq x ( j) be the probability that a woman, now age x, who develops BC at age x j, dies from BC or other causes within k years. The notation allows for the fact that probabilities can depend not only on the age of the patient, but also on the time since onset of the disease. For most cancers, survival probabilities are extremely dependent on the time since diagnosis; death rates are high during the first five years and drop significantly after that. In the case of BC, however, time since diagnosis is less relevant for annual survival probabilities, as they exhibit exponential de-
78 NORTH AMERICAN ACTUARIAL JOURNAL, VOLUME 4, NUMBER 2 cay. A fit of observed probabilities, obtained from the SEER Cancer Statistics Review, 1973 1995 (National Cancer Institute 1995), proved to be satisfactory. The annual probability that a woman affected with BC will die from the disease is estimated to be 0.036, irrespective of the time since diagnosis and age at onset. The (unconditional) probability to die with BC between k and k 1 for baseline risks, for a woman who is BC-free at age x, is k 1 BC,B ( ),B (2),B BC BC k x j x x j k j 1 x j 1 x k j 0 q p q p ( j)q ( j) where the BC-specific probabilities are given by and l p BC ( j) (0.964) k j 1 x k k j 1 x j 1 l x j 1 l q BC ( j) 1 p BC ( j) 1 (0.964) x k 1 x k x k. l x k To die from BC between k and k 1, the woman has to (1) stay alive and free from BC for j years, (2) develop BC between j and j 1, (3) survive BC for k j 1 years, and (4) die. This formulation excludes the possibility that a woman dies from BC the same year the disease is diagnosed, a realistic assumption. BC is usually detected following a mammogram or the discovery of a lump after examination; death is unlikely for several months after discovery. BC,B Once the probabilities qx k of dying from BC have (1) been calculated, probabilities qx k of dying from other causes are obtained by simple difference (1) BC,B q x k qx k q x k. Then, increased death probabilities k q BC,INC x are cal- culated from the formula above, replacing (2),B (2),INC ( ),B ( ),INC q x j by q x j and k px by k p x. Finally, increased death probabilities, combining all causes, are calculated as 1 q q q q q 2 INC (1) BC,INC (1) BC,INC x k x k x k x k x k for k 0,1,2,... 1 (1) BC,INC The correction term 2q x kq x k reflects the fact that, due to increased BC deaths, the number of deaths from other causes will somewhat decrease, using a uniform-distribution-of-deaths assumption. From these death probabilities, the net single premiums of a 5, 10, 15, and 20 year discrete term insurance are calculated, for a 30, 40, and 50 year old woman not affected with BC. A force of interest Table 2 Net Single Premium of 5, 10, 15, and 20 Year Term Insurance, per $1,000 of Coverage, by Age of Applicant, When There Is No Family History of BC Age of Applicant Term 5 Year 10 Year 15 Year 20 Year 30 3.80 7.83 11.30 16.50 40 7.45 16.75 25.57 38.52 50 19.24 42.40 63.12 91.32 of 5% is used; benefits are paid mid-year. Table 2 presents these net single premiums, when no family history of BC is recorded. We then compute the net single premiums for the same policies, in the presence of BC in the family. Each premium is compared to the corresponding net single premium for a woman with no family history of BC, as listed in Table 2. Ratios are presented in Tables 3 through 7 for various family histories of BC. Each figure represents the cost of term with family history, when the premium with no family history of BC is 100. Second-degree relative (SDR) refers to a grandmother or an aunt. Cost differentials exist between Tables 6 and 7 although each represents the impact of an affected mother and aunt. The risk of developing BC is higher with an affected mother and maternal aunt because of direct blood relationship between these two women. If both women had BC, there is a higher probability that the BRCA mutation is present in the family, leading to an increased risk for the woman under consideration. These tables could prove to be very useful for underwriting purposes. In policy applications, insurers should consider asking prospective insureds to indicate all family members affected with BC, as well as the age at onset. If the applicant has a sister or a mother who contracted the disease before the age of 40, she may experience higher mortality, especially if she is still young. If the applicant has two relatives who contracted the disease, the probability is high that the gene is present in the family. Consequently, she is subject to much higher mortality rates. The increase in death probabilities is higher when BC is present in the mother s side of the family. Note that BC affecting a second-degree relative, or affecting a firstdegree relative late in life, should not lead to much concern for the applicant or the insurer.
PRICING TERM INSURANCE IN THE PRESENCE OF A FAMILY HISTORY OF BREAST OR OVARIAN CANCER 79 Table 3 Relative Cost of Term Insurance for a Woman with One First-Degree Relative Affected with BC, by Age of Onset of the Relative Age Term Age of Onset in Affected Relative 20 29 30 39 40 49 50 59 60 69 70 79 Unknown 30 5 104.28 102.56 101.71 100.85 101.28 100.28 101.19 40 5 104.14 102.64 101.61 100.87 101.43 100.14 101.18 50 5 102.14 101.40 100.81 100.45 100.22 100.11 100.61 30 10 113.51 108.11 105.39 102.70 100.90 100.90 103.60 40 10 111.81 107.55 104.59 102.50 101.24 100.41 103.37 50 10 106.00 103.93 102.27 101.28 100.63 100.31 101.77 30 15 118.85 111.35 107.53 103.78 101.29 101.23 105.29 40 15 115.13 109.70 105.90 103.21 101.60 100.54 104.35 50 15 107.57 104.97 102.88 101.63 100.81 100.39 102.19 30 20 122.33 113.65 108.92 104.54 101.71 101.33 106.08 40 20 115.97 110.31 106.25 103.43 101.71 100.61 104.62 50 20 107.58 104.96 102.90 101.66 100.85 100.40 102.25 Table 8 provides the -ratio, the ratio of the force of mortality with a family history of BC and the baseline force of mortality, computed from our annual death probabilities, using a uniform-distribution-ofdeaths assumption. In all three cases, the -ratio increases until year 11, when it reaches a maximum, and then slowly declines. Consequently the common assumption of a constant frailty (increased forces of mortality are a constant multiple of the basic force) is not verified here. The -ratio increases are substantial, exceeding 100% in the 2FDR worst-case scenario. 3. TERM INSURANCE IN THE PRESENCE OF A FAMILY HISTORY OF OVARIAN CANCER Table 9 indicates the probability of developing OC by age, for the general population. It is estimated that Table 4 Relative Cost of Term Insurance for a Woman with One Second-Degree Relative Affected with BC, by Age of Onset of the Relative Age of Onset in Affected Relative Age Term 20 29 30 39 40 49 50 59 60 69 70 79 Unknown 30 5 101.99 101.14 100.57 100.57 100.28 100.00 100.57 40 5 101.76 101.17 100.75 100.29 100.43 100.00 100.44 50 5 100.98 100.63 100.34 100.17 100.17 100.05 100.28 30 10 106.30 103.60 101.80 101.79 100.90 100.00 101.80 40 10 105.03 103.34 102.08 100.83 101.24 100.00 101.55 50 10 102.76 101.77 100.96 100.47 100.47 100.15 100.79 30 15 108.77 105.05 102.55 102.46 101.29 100.00 102.49 40 15 106.48 104.30 102.67 101.07 101.58 100.00 101.62 50 15 103.50 102.24 101.22 100.60 100.60 100.18 101.01 30 20 110.26 106.08 103.22 102.66 101.70 100.00 102.85 40 20 106.96 104.60 102.80 101.16 101.63 100.06 102.13 50 20 103.53 102.25 101.24 100.64 100.64 100.18 101.03
80 NORTH AMERICAN ACTUARIAL JOURNAL, VOLUME 4, NUMBER 2 Table 5 Relative Cost of Term Insurance for a Woman with Two First-Degree Relatives Affected with BC, by Age of Onset of the Second Relative (Age of Onset of First Relative: 20 29) Age Term Age of Onset in Affected Relative 20 29 30 39 40 49 50 59 60 69 70 79 Unknown 30 5 113.01 112.42 111.53 110.36 108.90 107.45 110.36 40 5 113.60 112.64 111.65 110.52 109.08 107.37 110.37 50 5 107.39 106.85 106.31 105.58 104.73 103.83 105.51 30 10 140.80 138.97 136.20 132.55 128.01 123.48 132.55 40 10 138.20 135.55 132.83 129.67 125.68 120.89 129.37 50 10 120.32 118.89 117.43 115.46 113.14 110.69 115.27 30 15 156.67 154.09 150.27 145.26 139.06 132.69 145.23 40 15 148.31 145.02 141.64 137.69 132.67 126.64 137.16 50 15 125.18 123.45 121.68 119.27 116.43 113.41 119.04 30 20 167.00 163.70 159.24 153.48 146.25 138.64 153.31 40 20 150.05 146.75 143.35 139.24 134.07 127.90 138.87 50 20 124.67 123.13 121.40 119.07 116.30 113.36 118.87 these probabilities need to be multiplied by 5.4 for women reporting one mother or sister diagnosed with OC (Hartge et al. 1994). Detailed data by age at onset of the FDR are not available; neither are estimates for other family histories. A double-decrement model, similar to the model developed in Section 2, is built to evaluate the increased death probability of a woman with an FDR diagnosed with OC, and the resulting increase in the net single premium of term insurance. The probability of developing OC for basic risks, q x, is derived from inter- (3),B polation in Table 9. Once a woman has developed OC, a single-decrement model specific to the disease is OC used. Let k q x ( j) be the probability that a woman now age x, who develops OC at age x j, dies within k years. Unlike BC, time since diagnosis is critical for OC survival rates. Table 10 provides raw observed sur- Table 6 Relative Cost of Term Insurance for a Woman with a Mother and One Maternal Aunt Affected with BC, by Age of Onset of the Maternal Aunt (Age of Onset of Mother: 20 29) Age of Onset in Affected Relative Age Term 20 29 30 39 40 49 50 59 60 69 70 79 Unknown 30 5 112.12 111.82 110.94 110.07 108.62 107.17 109.78 40 5 112.30 111.82 111.31 110.05 108.92 107.36 110.04 50 5 106.69 106.45 105.95 105.43 104.59 103.83 105.29 30 10 138.03 137.10 134.38 131.66 127.11 122.58 130.76 40 10 134.63 133.29 131.88 128.38 125.23 120.86 128.30 50 10 118.45 117.82 116.47 115.04 112.77 110.67 114.68 30 15 152.80 151.48 147.81 143.99 137.79 131.50 142.81 40 15 143.88 142.22 140.42 136.09 132.10 126.61 136.02 50 15 122.91 122.14 120.51 118.76 115.98 113.38 118.32 30 20 162.19 160.51 156.62 151.85 144.97 137.52 150.74 40 20 145.62 143.98 141.97 137.71 133.44 127.87 137.50 50 20 122.58 121.83 120.29 118.57 115.90 113.32 118.16
PRICING TERM INSURANCE IN THE PRESENCE OF A FAMILY HISTORY OF BREAST OR OVARIAN CANCER 81 Table 7 Relative Cost of Term Insurance for a Woman with a Mother and One Paternal Aunt Affected with BC, by Age of Onset of the Paternal Aunt (Age of Onset of Mother: 20 29) Age Term Age of Onset in Affected Relative 20 29 30 39 40 49 50 59 60 69 70 79 Unknown 30 5 105.72 105.15 104.86 104.26 104.28 104.28 104.57 40 5 105.67 105.06 104.60 104.44 104.29 104.14 104.45 50 5 103.03 102.70 102.45 102.26 102.14 102.08 102.38 30 10 118.05 116.24 115.32 113.53 113.51 113.51 114.43 40 10 116.12 114.39 113.10 112.66 112.22 111.81 112.89 50 10 108.47 107.57 106.87 106.35 106.01 105.84 106.69 30 15 125.17 122.65 121.35 118.93 118.88 118.85 120.12 40 15 120.62 118.43 116.80 116.20 115.64 115.12 116.25 50 15 110.64 109.53 108.65 108.01 107.59 107.37 108.42 30 20 129.87 126.86 125.16 122.72 122.51 122.38 123.85 40 20 121.77 119.50 117.78 117.06 116.43 115.90 117.41 50 20 110.61 109.51 108.65 108.03 107.62 107.40 108.40 vival rates for all cohorts observed longitudinally since 1973. Table 10 demonstrates a clear pattern of improvement in survival rates; thus rates observed in 1973 do not reflect the increased survival rates seen today. Using Taylor s separation method (Taylor 1977), summarized in the Appendix, we estimate 20-year survival rates with 1992 as year of onset. These estimates are presented in Table 11. We need to fit these probabilities to the continuous survival function s(x) P(survival x), because we must estimate mid-year survival rates and because the Year Table 8 -ratios for Three Family Histories 1 FDR (20 29) 1 SDR (20 29) 2 FDR (20 29) 1 1.0000 1.0000 1.0000 3 1.0345 1.0161 1.1051 5 1.0999 1.0465 1.3034 7 1.1822 1.0848 1.5518 9 1.2627 1.1225 1.7927 11 1.3385 1.1580 2.0159 13 1.3004 1.1391 1.9045 15 1.2976 1.1358 1.8999 17 1.3026 1.1362 1.9167 19 1.3174 1.1414 1.9586 estimates above are not monotonically decreasing. The best fit is ax s(x) 1 N(1 e ) with N 0.63 and a 0.333. Using a mid-year approximation, the (unconditional) probability of dying from OC between k and k 1 is, for basic risks, k 1 OC,B ( ),B (3),B OC OC k x j x x j k j 1/2 x j 1/2 x k j 0 q p q p ( j)q ( j) where Table 9 Probability of Developing Ovarian Cancer before Selected Ages Age Probability 30 0.04% 40 0.10 50 0.28 60 0.61 70 1.07 80 1.49 Ever 1.79 ( ),B (3),B OC kpx qx k 1/2q x k 1/2(k)
82 NORTH AMERICAN ACTUARIAL JOURNAL, VOLUME 4, NUMBER 2 Table 10 Survival Probabilities after Onset of OC by Year of Diagnosis and Years since Diagnosis Year of Diagnosis 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1 59.9% 64.4% 59.6% 63.7% 66.2% 67.7% 67.5% 69.8% 69.3% 70.6% 70.1% 73.1% 72.1% 69.1% 71.0% 73.6% 75.5% 76.1% 76.5% 78.3% 2 45.7 48.7 45.0 47.8 51.0 52.0 51.5 53.9 52.5 52.7 53.8 56.2 55.5 52.4 53.9 62.0 62.1 64.0 64.3 3 40.8 43.5 39.7 42.2 43.0 44.5 44.1 46.6 45.7 44.6 47.8 48.3 48.0 46.0 46.3 55.5 54.4 56.4 4 38.1 40.8 36.5 39.4 40.1 40.5 40.1 41.9 41.9 40.9 43.7 43.2 42.6 42.2 42.3 51.4 49.4 5 36.0 38.1 34.1 37.8 38.7 38.4 37.7 39.0 40.0 38.1 42.5 40.6 39.6 38.5 38.8 48.3 6 35.2 35.8 33.9 36.6 37.8 36.4 36.2 37.0 38.5 36.8 40.0 39.6 37.5 36.7 37.3 7 34.9 35.4 33.3 35.3 36.4 35.8 34.7 36.6 38.5 35.8 39.0 38.8 36.2 35.6 8 33.7 34.7 32.5 34.4 36.0 35.1 34.0 35.5 37.6 35.2 37.2 37.8 35.7 9 33.1 34.1 32.2 34.4 35.8 34.6 33.6 34.1 36.9 35.0 37.0 36.4 10 32.5 34.1 32.2 34.4 35.8 34.6 33.4 33.5 36.3 34.8 36.3 11 32.5 34.0 32.2 34.0 35.7 34.3 33.4 33.5 36.3 34.5 12 32.5 33.7 32.2 33.7 35.1 33.7 33.4 33.0 36.3 13 32.1 33.3 32.2 33.7 35.1 33.2 33.4 32.2 14 31.9 33.2 32.2 33.4 34.8 33.0 33.4 15 31.6 33.1 32.2 32.2 34.8 32.8 16 30.5 33.1 32.2 31.6 34.8 17 30.2 33.1 32.2 31.1 18 30.2 33.1 32.2 19 30.1 33.0 20 30.1 Source: National Cancer Institute, 1995.
PRICING TERM INSURANCE IN THE PRESENCE OF A FAMILY HISTORY OF BREAST OR OVARIAN CANCER 83 Table 11 Estimates of Survival Probabilities for Ovarian Cancer Diagnosed in 1992 p Year OC k j 1/2 x j 1/2 Probability 1 78.3% 2 65.8 3 58.2 4 52.3 5 50.9 6 46.3 7 44.9 8 43.3 9 42.6 10 42.4 11 42.1 12 42.5 13 39.0 14 40.7 15 39.2 16 40.3 17 37.5 18 39.5 19 38.2 20 36.3 ( j) s(k j 1/2) l x k l x j 1/2 s(k j 1/2)l q OC ( j) 1 p OC ( j) 1 x k 1 x k x k s(k j 1/2)l x k OC OC 1/2q x k 1/2(k) 1 1/2p x k 1/2(k) l x k 1 1 s(1/2). l x k 1/2 Table 12 Relative Cost of Term Insurance for a Woman with an FDR Affected with OC Compared with No Family History (Age at Onset Unknown) Age Term Cost 30 5 104.23 40 5 106.50 50 5 104.64 30 10 109.01 40 10 112.52 50 10 108.87 30 15 110.07 40 15 112.45 50 15 108.67 30 20 112.20 40 20 112.20 50 20 107.92 The second term in k q OC x reflects the fact that, unlike with BC, it cannot be assumed that a woman diagnosed with OC will survive the year of onset. Increased probabilities of death are then computed using the procedure developed in Section 2. Table 12 summarizes the results and provides the relative increase of the cost of term insurance, for selected ages and terms. Compared with Table 3, the increases for a family history of OC are more substantial than the corresponding increases for BC. This is due to the fact that an FDR with OC multiplies the chances of developing OC by 5.4, versus less than 2 in the case of BC. Also, a higher case-fatality rate exists for OC. Table 13 provides -ratios; the excess mortality nears 100% in some cases. Table 13 -ratios for a Woman with a Mother or Sister Affected by OC, by Age of Woman Year Age 30 Age 40 Age 50 1 1.0302 1.0489 1.0378 3 1.1946 1.3025 1.2240 5 1.4011 1.5892 1.4286 7 1.5958 1.7929 1.5927 9 1.7350 1.9236 1.6878 11 1.7070 1.8210 1.6008 13 1.5812 1.5337 1.3946 15 1.6926 1.5271 1.3334 17 1.8143 1.5919 1.3541 19 1.9083 1.6395 1.3579
84 NORTH AMERICAN ACTUARIAL JOURNAL, VOLUME 4, NUMBER 2 4. TERM INSURANCE FOR A WOMAN WITH BRCA 4.1 Increase Due to Breast Cancer Estimates of the penetrance (the percentage of those with the gene mutation who will become ill) of BRCA1 and BRCA2 vary widely across studies. There is a huge ethnic diversity in the sites of mutations and in the number of people who will develop BC in each group. A study by Easton et al. (1995) found a penetrance of 85% for BC in a selected group of families used for genetic linkage studies. More recent articles, for instance Struewing et al. (1997), obtain lower penetrance figures for a population of Ashkenazi Jews. More recent medical data (Claus et al. 1998) suggest a penetrance of 62.8% in a study involving more than 9,000 women. We will adopt a conservative estimate of 65%, as suggested by Lowden (1998). BRCA mutations not only increase the probability of developing BC, they also lead to earlier cancers. The Cancer and Steroid Hormone Study, 1980 82, estimated that the age at onset of BC for women without the mutation is normally distributed around a mean of 68.99 years and a standard deviation of 15.39. With a BRCA mutation, the mean age at onset drops to 55.435, while the standard deviation is unaffected (Claus, Risch, and Thompson 1994). The knowledge of the penetrance and of the distribution of age at onset allows the application of the double-decrement model from Section 2 to compute increased mortality and term insurance costs for women with a mutation. Table 14 indicates that forces of mortality can be increased by as much as 150%. Table 15 presents the increased cost of term insurance for a woman aged 30, 40, or 50. The preceding calculations assume that genetic testing leads to no medical benefits in the form of improved risk reduction. There is some hope that women found to carry BRCA mutations can reduce their risk of BC mortality by increased mammogram Table 15 Relative Cost of Term Insurance for a Woman with a BRCA Mutation (BC Only) Term Age 30 Age 40 Age 50 5 119.76 119.80 110.71 10 161.67 155.07 129.05 15 185.00 168.98 135.54 20 198.52 170.27 134.39 surveillance, prophylactic mastectomy, or chemoprevention with tamoxifen. This is another source of conservatism in the model term premium increases are probably somewhat overstated. 4.2 Increase due to Ovarian Cancer As with BC, estimates of the likelihood of developing OC for a woman with BRCA mutations vary widely across studies. The probability ranges from 11% to 84%, depending on the type of mutation (BRCA1 or BRCA2), the specific allele of BRCA1, and the population under consideration (Easton et al. 1995, Ford et al. 1994, Struewing et al. 1997). For a general population, an average of 40% seems conservative and will be used here. Table 16 presents selected -ratios. Table 17 shows the increases in term insurance costs. 4.3 Total Increase BRCA1 and BRCA2 mutations increase the probability of developing both BC and OC. Clinical data suggest independence between the events developing BC and developing OC (Easton et al. 1995). To study the joint impact of the two cancers on term insurance rates, a triple-decrement model is needed. Table 18 provides selected -ratios from this model. Table 19 provides term insurance increases. As expected, mortality surcharges are very high. Table 14 Selected -ratios for a Woman with a BRCA Mutation (BC Only) Table 16 Selected -ratios for a Woman with a BRCA Mutation (OC Only) Year Age 30 Age 40 Age 50 6 1.6385 1.5811 1.3134 11 2.5283 2.1548 1.6157 16 2.3188 1.8187 1.4083 Year Age 30 Age 40 Age 50 6 1.4984 1.7033 1.5186 11 1.7070 1.8210 1.6008 16 1.7574 1.5585 1.3411
PRICING TERM INSURANCE IN THE PRESENCE OF A FAMILY HISTORY OF BREAST OR OVARIAN CANCER 85 Table 17 Relative Cost of Term Insurance for a Woman with a BRCA Mutation (OC Only) Table 19 Relative Cost of Term Insurance for a Woman with BRCA (OC BC) Age 30 Age 40 Age 50 5 120.69 131.99 123.55 10 143.82 160.96 144.06 15 149.28 160.12 142.43 20 158.61 157.98 137.94 30 40 50 5 140.42 161.39 134.20 10 205.20 240.68 172.36 15 233.58 256.98 176.51 20 255.51 250.24 170.23 5. CONSERVATISM OF ASSUMPTIONS Our analyses are subject to several limitations of the medical literature. The wide range of estimates of probabilities to develop the disease creates a major source of uncertainty. Also, BC has been studied much more than OC; thus the development of BC under a wide variety of family situations has been modeled. Similar studies concerning OC are underway, and some results have been published very recently. Our benchmark values for probabilities have been selected in a prudent way, so that term insurance increases in the above tables can be considered conservative. Note however two elements not introduced in the preceding model that may lead to a slight underestimation of the premiums: 1. The presence of BC in the family impacts the probability to develop BC but also, indirectly, the probability to develop OC. If an FDR has BC, this increases the likelihood of a BRCA mutation in the family, thereby increasing the chances of developing OC. Given that medical data concerning family history and OC considers only one case (one FDR, age unknown), a model incorporating this relationship could not be built. The effect of this restriction on our model is expected to be very small, as less than 6% of BC and less than 3% of OC are due to BRCA mutations. 2. We have not incorporated in the model the possibility that a woman can develop BC, be completely cured of that disease, and subsequently contract Table 18 Selected -ratios for a Woman with BRCA (OC BC) Year 30 40 50 6 2.1370 2.5661 1.8320 11 3.2351 3.4904 2.2164 16 3.0761 2.6192 1.7495 OC and die. Except in the case of a woman with a BRCA mutation, the probability of such a double cancer is very small. Therefore we believe that the -ratios and premium surcharges recommended in this article are conservative, in the sense that they are more likely to be overstated than understated. 6. CONCLUSIONS: PRACTICAL ISSUES IN LIFE INSURANCE UNDERWRITING Our analyses suggest that insurance companies could consider gathering as much information about family history as possible during the underwriting process and use BC and OC information in setting premiums. The simple knowledge that the mother of the applicant has been affected by BC may not be sufficient for an accurate assessment. Companies could possibly request that applicants list all relatives affected with cancers, as well as the ages at onset. It does not seem that insurers are currently putting much weight on family history in their underwriting and rating procedures. Quicken Insuremarket provides online quotes for term insurance for a set of large U.S. companies. The only question asked online is Has cancer resulted in the death of any immediate family members ( parents or siblings) before the age of 60? Table 20 provides annual premiums quoted by six major insurers for a $100,000, 20-year term insurance on a nonsmoking female life age (30), as a function of the answer to the previous question. Besides the large range in quotes it is noteworthy to observe that only three companies seem to use the answer to the cancer question as a rating variable in this preliminary phase of the underwriting process. A major insurer kindly provided us with details of its life insurance underwriting process. On the policy application, customers are asked if they have a family history (parents or siblings) of cancer, diabetes, heart disease or high blood pressure. Applicants must provide ages at onset and ages at death of affected rela-
86 NORTH AMERICAN ACTUARIAL JOURNAL, VOLUME 4, NUMBER 2 Table 20 On-line Quotes for Six U.S. Insurers Insurer No Yes A $590 $590 B 760 760 C 630 700 D 830 830 E 710 820 F 455 535 It is concluded that while many women with a family history of BC or OC can be accepted at standard rates, females with two family members with cancer, or one FDR with cancer at an early age, probably can only be accepted at substandard rates. Females with a BRCA mutation will generally not be accepted at standard rates. Companies may accept these women in one of their substandard rate classes, corresponding to a higher mortality surcharge. Insured women would then be requested to undergo increased surveillance, such as quarterly mammograms. tives. A family history of cancer is taken into account in a very moderate way in the evaluation of the applicant, but age at onset is not an underwriting factor. A family history of cancer may trigger a small premium increase, but the increase does not vary by age at onset of the affected relative. Quite often a decision to accept a borderline case may depend on family history. About 5% of the applicants are deemed to be medically uninsurable. Of those accepted, about 93% of policies are issued at standard or preferred rates. Others are accepted at substandard rates. The company uses a set of substandard tables, corresponding to various levels of excess mortality. As indicated in Tables 8 and 13, women with a family history of BC or OC can in some cases exhibit mortality ratios exceeding 200%. From Table 18, we see that women with a BRCA mutation have mortality ratios up to 350%. Table 21 presents mortality ratios for common diseases and conditions (Brackenridge and Elder 1998). It shows that the effect on mortality of a family history of BC or OC is comparable to the effect of several common diseases. Table 21 Mortality Ratios for Common Conditions Disease Measurement -Ratio Systolic blood pressure 158 167 (men) 2.06 Systolic blood pressure 178 187 (women) 2.78 Diabetes mellitus Men 2.50 Build 40% overweight (women) 1.62 Build 60% overweight (men) 2.60 Epilepsy All types 2.78 Alcoholism 5 drinks a day 3.00 Smoking Average (men) 1.70 Smoking 40 cigarettes/day (men) 2.00 HIV 35-year-old male 50.00 APPENDIX TAYLOR S SEPARATION METHOD Let C ij be the probability to have survived OC for i years after diagnosis in year j, where i, j 1,...,k. These probabilities are given in Table 10. Note that in this table, columns represent years of diagnosis, rows years since diagnosis. Diagonals are calendar years. Define c ij to be the improvement in survival probability between onset years j 1 and j c C C. ij ij i, j 1 The separation method postulates that c ij can be expressed as c p ij j i j 1 k where j 1 p j 1. The increase in survival rates results from the multiplicative effect of a column factor (improvement in diagnostic techniques) and a diagonal factor (better treatment methods). The model parameters p j and can be estimated as follows. Let i j 1 h h h l 1 l,h l 1 h l 1 l d c p h 1,...,k be the sum of the terms of a diagonal. Let k j 1 k j i 1 ij j l j l v c p j 1,...,k be the sum of the terms of column j. So dk k(p1 p2 p k). k Since p j 1, ˆ j 1 k d k.asc 1k p k k v k, ˆp k v k / ˆ k. Then d (p p p ) (1 p ). k 1 k 1 1 2 k 1 k 1 k Hence,
PRICING TERM INSURANCE IN THE PRESENCE OF A FAMILY HISTORY OF BREAST OR OVARIAN CANCER 87 Then and d k 1 ˆ k 1. (1 ˆp k ) c c p ( ) v 1, k 1 2,k 1 k 1 k 1 k k 1 c1, k 1 c2,k 1 vk 1 ˆp k 1. ˆ ˆ ˆ ˆ Step by step, we obtain k 1 k k 1 k d h k h ˆ h 1,...,k h ˆp j 1 ˆp v j k ˆ l l j j 1 h j j 1,...,k. The estimation of the ˆ h (h 1,...,k) and of the ˆp j ( j 1,...,k) having been carried out, the triangle of the ĉ ˆ ij ˆp j i j 1 can be built. This enables the comparison of the observations c ij and the estimations ĉ ij in order to test the validity of the model. In order to complete the triangle of the c ij into a rectangle, it is necessary at this stage of the method to estimate the effect of future medical improvements by extrapolating the ˆ h (h k). In this case a linear fit of the estimates ˆ 1,..., ˆ k provides the extrapolated ˆ, ˆ k 1 k 2,.... This enables the computation of the square matrix ĉ ˆ ij ˆp j i j 1. The last column of this matrix is the set of survival probabilities for the last diagnosis year, provided in Table 11. REFERENCES AMERICAN CANCER SOCIETY. 1992. Cancer Facts and Figures. Atlanta. BRACKENRIDGE, R. D. C., AND ELDER, W. J. 1998. Medical Selection of Life Risks. London: Macmillan. CLAUS, E., RISCH, N., AND THOMPSON, W. D. 1990. Age at Onset as an Indicator of Familial Risk of Breast Cancer, American Journal of Epidemiology 131:961 72. CLAUS, E., RISCH, N., AND THOMPSON, W. D. 1994. Autosomal Dominant Inheritance of Early-Onset Breast Cancer, Cancer 73:643 51. CLAUS, E., ET AL. 1998. Effect of BRCA1 and BRCA2 on the Association Between Breast Cancer Risk and Family History, Journal of the National Cancer Institute 90:1824 9. EASTON, D., ET AL. 1995. Breast and Ovarian Cancer Incidence in BRCA1-Mutation Carriers, American Journal of Human Genetics 56:265 71. FORD, D., ET AL. 1994. Risks of Cancers in BRCA1 Mutation Carriers, Lancet 343:692 5. FORD, D., EASTON, D., AND PETO, J. 1995. Estimates of the Gene Frequency of BRCA1 and Its Contribution to Breast and Ovarian Cancer Incidence, American Journal of Human Genetics 57:1457 62. GAIL, M., ET AL. 1989. Projecting Individualized Probabilities of Developing Breast Cancer for White Females Who Are Being Examined Annually, Journal of the National Cancer Institute 81:1879 86. HARTGE, P., ET AL. 1994. Rates and Risks of Ovarian Cancer in Subgroups of White Women in the United States, Obstetrics and Gynecology 84:760 4. LOWDEN, J. A. 1998. The Current State of Genetic Testing in Life Insurance, In Genetic Testing: Implications for Insurance, 19 28. Schaumburg, Ill.: The Actuarial Foundation. NATIONAL CANCER INSTITUTE. 1995. SEER Cancer Statistics Review 1973 1995. Bethesda: National Institutes of Health. STRUEWING, J., ET AL. 1997. The Risk of Cancer Associated with Specific Mutations of BRCA1 and BRCA2 among Ashkenazi Jews, New England Journal of Medicine 336: 1401 8. TAYLOR, G. 1977. Separation of Inflation and Other Effects from the Distribution of Non-Life Insurance Claim Delays, ASTIN Bulletin 9:219 30. WOOSTER, R., ET AL. 1995. Identification of the Breast Cancer Susceptibility Gene BRCA2, Nature 378:789 92. Discussions on this paper can be submitted until October 1, 2000. The authors reserve the right to reply to any discussion. See the Submission Guidelines for Authors on the inside back cover for detailed instructions on the submission of discussions.