Underwriting Critical Illness Insurance: A model for coronary heart disease and stroke

Underwriting Critical Illness Insurance: A model for coronary heart disease and stroke Presented to the 6th International Congress on Insurance: Mathematics and Economics. July 2002. Lisbon, Portugal. Angus Macdonald Howard Waters Chessman Wekwete Department of Actuarial Mathematics and Statistics Heriot-Watt University, Edinburgh 1

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

Background Swiss Re funding 1998-2001 Impact of genetic information on life insurance Breast & Ovarian Cancers Coronary Heart Disease and Stroke Critical Illness Insurance 3

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

CHD & Stroke - Objectives Impact of genetic information Multifactorial disorder Diabetes Hypertension Hypercholesterolaemia Environmental factors Underwriting models Critical Illness Insurance Life assurance 5

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 85 130 High Normal [85, 90) [130, 140) H tension Stage I [90, 100) [140, 160) H tension Stages II-III 100 160 Diabetes: Blood Sugar Level (bsl) in mg/dl. Diabetes: 126 bsl 6

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

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

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

Data - Framingham Heart Study Small town near Boston, USA Large scale longitudinal study 1949-1984 2336 men + 2873 women aged 28-62 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

Modelling Occurrence/exposure rates GLMs, Poisson errors Transitions to CHD & Stroke Highest ever values for BP, Chol & BSL Time trends Hypercholesterolaemia 11

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

Model Validation Incidence rates: Morbidity Statistics from General Practice UK, 1991-92 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 1993-94 of CHD & Stroke Probabilities: Anderson et al (1991) Probabilities of CHD & stroke based on Framingham data. 13

Model Validation CHD (Males) CHD (Females) Incidence rate 0.0 0.010 0.020 Our model Dinani et al s rates 30 40 50 60 70 80 Incidence rate 0.0 0.002 0.006 Our model Dinani et al s rates 30 40 50 60 70 80 Age Age Stroke (Males) Stroke (Females) Incidence rate 0.0 0.010 0.020 Our model Dinani et al s rates Incidence rate 0.0 0.004 0.008 0.012 Our model Dinani et al s rates 30 40 50 60 70 80 30 40 50 60 70 80 Age Age 14

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

Modelling - Other CI Cancer Data: Cancer registrations UK 1990-92 Lung Cancer : Age, Sex, Smoking. Other Cancers: Age, Sex. Kidney Failure Data: Renal Data System, U.S.A. 1994-97 Diabetes status, Age, Sex. Other claim causes 15% 20% of incidence of CHD, Stroke & Cancers Mortality: ELT 15 (- CI related deaths) 16

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 362 514 764 95% CI (Sim) 311 420 453 583 696 842 Females Premium 353 531 698 17

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

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 1 2 10 50 None 0% +2% +36% +82% Diab Type 1 +247% +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

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 1 2 10 50 None 0% +48% +432% +2288% Diab Type 1 +247% +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

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