1. Modelling the development of, and treatments for, heart disease and stroke. Tushar Chatterjee, Angus Macdonald & Howard Waters Heriot-Watt University, Edinburgh Presentation: IME, 10-12 July 2007

2. 2 Plan of Talk 1.Background 2.Model 3.Parameter estimation 4.Applications  Treatments (Statins)  Obesity  Smoking 5.Questions

3. 3 Background Increasing life expectancy Year UK Males - Age 0305070 198170.842.724.110.1 199173.244.726.011.1 200175.746.928.312.5 Year UK Females - Age 0305070 198176.848.229.213.3 199178.749.730.614.3 200180.451.232.115.2 (UK Office of National Statistics)

4. 4 Background  Ischaemic Heart Disease (IHD) Angina Coronary Insufficiency Myocardial Infarction (MI)  Stroke Transient Ischaemic Attack Hard Stroke (HS) (Ischaemic and Haemorrhagic)  Major risk factors Age Sex Smoking Hypertension Hypercholesterolaemia Diabetes Body Mass Index

5. 5 Model  Continuous time/age, finite state space Markov model  Specified by transition intensities (hazard rates) between states IHD IHD + Stroke Stroke DeadHealthy

6. 6 Model  Healthy has 160 sub-states: Risk FactorLevels Body Mass Index 5 Hypertension 4 Diabetes 2 Hypercholesterolaemia 4 Smoking modelled deterministically  Model allows for multiple cases of MI and HS  IHD and/or Stroke = 10 separate states (x 160)  Total number of states = 160 + 10 x 160 + 1 = 1761  Probabilities Calculated by solving the Kolmogorov Forward Equations  System of 1761x1761 simultaneous differential equations

7. 7 Parameter estimation  Framingham data sets – longitudinal data  Original Cohort 1948-1986  Offspring & Spouses Cohort 1971-1998  Estimates of transition intensities  Identify significant explanatory variables  Smoothed using GLM  Health Survey of England (2003)  Adjust parameters to match UK prevalence rates

8. 8 Parameter estimation TransitionAgeSexSmokingBMIH’tensH’cholDiabetesCohort effectIHDStroke → MI (1 st )(1)(2)(4)(5)(3)(6)(7) 1.60- → HS (1 st )(1)(3)(2)(4) 2.05- H’tens → ←●●●-- H’chol → ←●●-● Diabetes →●●●-● ←●-● BMI → ←●●-- → Dead(1)(6)(5)(7)(2)(10)(9)(8) 0.59(3)(4) Significant factors

9. 9 Applications - Treatment  Statins  Cholesterol lowering drugs  First licensed in the UK in 1987  Rosuvastatin licensed in 2003  Effect  Standard dose reduces cholesterol by 1.8 mmol/l  Reduction in IHD risk increases over 5 years  Reduction in stroke risk is constant  % reduction in IHD/stroke risk is independent of baseline cholesterol level

10. 10 Applications - Treatment ConditionYears of treatment% reduction in risk 1 mmol/l1.8 mmol/l IHD 111%19% 224%39% 3-533%51% 6 +36%55% StrokeAll durations10%17% Duration dependence → Semi-Markov model

11. 11 Applications - Treatment SexSmoking category Expected time to IHD, stroke or death Expected time to death No treatment Treatment NCEP Guideline No treatment Treatment NCEP Guideline Male Never51.552.557.858.4 Ex48.549.754.955.7 Current44.345.950.251.2 Female Never56.256.961.161.4 Ex53.654.358.659.0 Current49.350.354.054.6  Population profile  Starting age = 20  UK prevalence at age 20  Deterministic smoking profile (Never, started before age 20 and given up at age 49 (Ex), Current)

12. 12 Questions?