Underwriting Critical Illness Insurance: A model for coronary heart disease and stroke
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1 Underwriting Critical Illness Insurance: A model for coronary heart disease and stroke Presented to the 6th International Congress on Insurance: Mathematics and Economics. July Lisbon, Portugal. Angus Macdonald Howard Waters Chessman Wekwete Department of Actuarial Mathematics and Statistics Heriot-Watt University, Edinburgh 1
2 Abstract The paper presents a model for assessing premium ratings for applicants of stand-alone Critical Illness insurance. Using Markov models, and Norberg s differential equations we calculate the costs of insurance for applicants, considering the specific risk factors for coronary heart disease and stroke; sex, smoking, body mass index, diabetes, hypertension, and hypercholesterolaemia. We discuss the application of this model to quantifying the impact of genetic information on the insurance costs. 2
3 Background Swiss Re funding Impact of genetic information on life insurance Breast & Ovarian Cancers Coronary Heart Disease and Stroke Critical Illness Insurance 3
4 Breast & Ovarian Cancers Two single genes BRCA 1 & BRCA 2 Account for 5% - 10% of BC/OC cases Increased risk = 40(?) Refs: Macdonald, Waters & Wekwete I& II Scandinavian Actuarial Journal, 2003 Conclusions for CI underwriting: Family History: family size/structure is important Genetic information does not add much to family history 4
5 CHD & Stroke - Objectives Impact of genetic information Multifactorial disorder Diabetes Hypertension Hypercholesterolaemia Environmental factors Underwriting models Critical Illness Insurance Life assurance 5
6 Risk Factors Age. Fixed; Sex, Smoking status, BMI. Cholesterol: Total Cholesterol (TC) in mg/dl Stage 0: TC < 200 Stage 1: 200 TC < 240 Stage 3: 240 TC Blood pressure: (sbp and dbp) in mm/hg Category dbp sbp Optimal/Normal High Normal [85, 90) [130, 140) H tension Stage I [90, 100) [140, 160) H tension Stages II-III Diabetes: Blood Sugar Level (bsl) in mg/dl. Diabetes: 126 bsl 6
7 Model for CHD & Stroke Time (Age) inhomogeneous Markov model: Separate parameterisations for: Sex (2): Smoking (2): BMI (3) 24 transient states: Blood pressure (4): Cholesterol (3): Diabetes (2) Require transition intensities between these. 3 absorbing states: CHD, Stroke, Dead Require transition intensities to these. Data requirements! 7
8 chol1 bp1, diab chol2 bp2, diab The Model: Example λ bp12 bp2, chol1 λ CHD λ Stroke λ D CHD Stroke Dead chol1 bp2, diab λ bp23 bp2, diab λ chol01 chol1 bp3, diab 8
9 The CHD and stroke model Óн¾ Óо Óн¾ Ô¼½ Óм½ Óм½ Ô½ Óо Óн Óн Ô½ Ô¾ Óн¾ Óм½ Óн¾ Ô¼½ ½¼ Ô½ ½½ Óо Óн Ô½ Ô½¾ Óм½ Ô½¾ ½¾ Ô¾ ½ Óн Ô¾ ½ Ô½¾ Óн¾ Ô½¾ Ô¾ Óн¾ Óм½ Óм½ Ô¾ Ô¼½ ½ Óо Ô½ Ô½¾ ½ Óн ¾¼ Óо Ô¾ À ÀÀÀÀ ½ Ô¾ ¾ À À ½ Óн Ê Ô¼½ ½ Ô Ô½ Óо Ô¾ Óн À ÀÀÀÀ Ô¾ Óн¾ À Ê À Óн¾ Ô¾ À ÀÀÀÀ Ô¾ À À ¼ Óм Ô¼ À ÀÀÀÀ Óм½ À Ô¼½ À ¾½ Ô Óо ¾ Óо Ô Óм½ ¾¾ Óн Ô Ô½¾ ½ Ô Óн Ô¾ Ô ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ÅÁ Ü Ø Û ¹ ¾ ÅÁ Ü Ø Û ½¾ À ÅÁ Ü Ø Û ËØÖÓ Ü Ø ¹ ¾ ËØÖÓ ËØÖÓ Ü Ø Ü Ø ¹ ¾ Ü Ø 9
10 Data - Framingham Heart Study Small town near Boston, USA Large scale longitudinal study men women aged in 1949 Exposure = 99,000 years 581 Heart attacks 304 Strokes Biennial examinations, recording Smoking status Blood sugar level Total cholesterol SBP & DBP Height & Weight Dates of: MI, Stroke,..., Death 10
11 Modelling Occurrence/exposure rates GLMs, Poisson errors Transitions to CHD & Stroke Highest ever values for BP, Chol & BSL Time trends Hypercholesterolaemia 11
12 Fitted Models Factor λ CHD λ STR λ Chol01 λ Chol12 Age Y Y Y Y Sex Y Y Y Y Smoking Y Y BMI BP Y Y Chol Y - - Diab Y Y Factor λ BP01 λ BP12 λ BP23 λ Diab Age Y Y Y Y Sex Y Y Smoking BMI Y Y BP Chol Diab - 12
13 Model Validation Incidence rates: Morbidity Statistics from General Practice UK, First ever diagnosis of Hypertension, Hypercholesterolaemia & Diabetes Prevalence rates: Health Surveys of England 1994 and 1998 Prevalence rates of Hypertension, Hypercholesterolaemia & Diabetes Incidence rates: Dinani et al (2000) UK incidence rates of CHD & Stroke Probabilities: Anderson et al (1991) Probabilities of CHD & stroke based on Framingham data. 13
14 Model Validation CHD (Males) CHD (Females) Incidence rate Our model Dinani et al s rates Incidence rate Our model Dinani et al s rates Age Age Stroke (Males) Stroke (Females) Incidence rate Our model Dinani et al s rates Incidence rate Our model Dinani et al s rates Age Age 14
15 Application to CI Insurance Extend CHD and Stroke model for other CI claim causes. Cancers, Kidney failure, minor claim causes. Type 1 diabetes and Type 2 diabetes modelled separately. Allow for 28 day survival for claim eligibility. 36 transient states and 4 absorbing states. 15
16 Modelling - Other CI Cancer Data: Cancer registrations UK Lung Cancer : Age, Sex, Smoking. Other Cancers: Age, Sex. Kidney Failure Data: Renal Data System, U.S.A Diabetes status, Age, Sex. Other claim causes 15% 20% of incidence of CHD, Stroke & Cancers Mortality: ELT 15 (- CI related deaths) 16
17 Numerical Results Norberg: I:ME 1995 Base: Non-smokers, Normal BMI Sum assured 100,000, Force of interest 5% p.a. Age/Term 35/20 45/10 45/20 Males Premium % CI (Sim) Females Premium
18 Numerical Results: Ratings Age/Term 35/20 45/10 45/20 Non-smokers Type 1 Diab +169% +118% +82% Type 2 Diab +44% +36% +27% Chol2 +27% +24% +19% BP3 +82% +79% +64% Chol2, BP3 +149% +142% +111% Chol2, BP3, Type 2 Diab +239% +223% +170% Smokers Type 1 Diab +209% +170% +140% Type 2 Diab +86% +87% +86% Chol2 +71% +78% +80% BP3 +144% +151% +139% 18
19 Impact of assumed genetic mutations Assumption: Genetic mutation leads to increased hypertension incidence. Policy terms: Age 35, term 10 years Risk Increased BP incidence factors None 0% +2% +36% +82% Diab Type % +250% +294% +356% Type 2 +60% +63% +107% +169% Chol1 +4% +7% +42% +91% Chol2 +33% +37% +89% +160% BP1 +6% +8% +55% +87% BP2 +43% +45% +76% +92% 19
20 Impact of assumed genetic mutations Assumption: Genetic mutation leads to increased CHD incidence. Policy terms: Age 35, term 10 years Risk Increased CHD incidence factors None 0% +48% +432% +2288% Diab Type % +310% +808% +3206% Type 2 +60% +123% +621% +3020% Chol1 +4% +55% +465% +2416% Chol2 +33% +114% +758% +3829% BP1 +6% +61% +490% +2506% BP2 +43% +131% +825% +4080% 20
21 Conclusions Model can be used for CI insurance underwriting, Quantifying the impact of genetic mutations on insurance costs. Underwriting: Decisions comparable with practice apart from decisions for Type 2 Diab and Chol2. Genetics Mutations affecting CHD/Stroke directly: Significant impact. Mutations affecting risk factors: Minor impact. 21
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