Factored stochastic tree modeling for medical decision making Gordon Hazen Northwestern University Rowland Chang Northwestern University James Pellissier Loyola University/Merck Pharmaceuticals

2 What is a stochastic tree? –Basic concepts……………………………….. –Stochastic tree transformation and rollback…. –Approximating human survival………………. –Factoring out mortality……………………….. Factoring stochastic trees…………………. Discounting / Risk aversion………………. Influence diagrams for stochastic models… Our THA model…………………………... The StoTree modeling environment………. Cost-effectiveness for THA……………….. Outline of talk

3 What is a stochastic tree? A stochastic tree is –A decision tree with stochastic nodes added –A continuous-time Markov chain with chance and decision nodes added –A multi-state DEALE model –A continuous-time version of a Markov cycle tree Stochastic Trees Continuous-time MCs Decision Trees Discrete-time MCs / Markov cycle trees DEALE

4 …What is a stochastic tree? Matchar & Pauker (1986): Transient ischemic attacks in a man with coronary artery disease

5 …What is a stochastic tree? Roach et al. (1988): Prostate cancer in a man with asymptomatic HIV

6 Markov cycle tree

7 Transforming stochastic trees = Superposition / Decomposition

8 …Transforming stochastic trees = Eliminating self-transitions

9 …Transforming stochastic trees

10 Stochastic tree rollback = v(x) = Quality rate at x L(x) = Mean quality-adjusted duration beginning at x Recursive formula:

11 Stochastic tree rollback

12 Approximating human survival

13 Coxian approximation to human mortality

14 Coxian approximation to human mortality

15 Factoring out mortality

16 …Factoring out mortality Background mortality Stroke morbidity

17 …Factoring out mortality Background mortality Stroke morbidity

18 Equivalent product tree

19 Rollback with Coxian mortality

20 Factored stochastic trees Cancer AIDS Background mortality

21 …Factoring stochastic trees Systemic embolism Pulmonary embolism Systemic hemorrhage Tsevat et al. (1986): Warfarin for dilated cardiomyopathy

22 Discounting / Risk aversion G = Utility function yielding quality-adjusted duration Utility function yielding discounted quality-adjusted duration Rollback with discounting

23 Modeling risk attitude ~ Vaccine scenario: What chance p of immediate death would you take to reduce your ongoing mortality rate by a percentage c? Undiscounted quality-adjusted duration forces: p = c Discounted quality-adjusted duration allows p < c (risk aversion)

24 Continuous-risk utility assessment

25 Influence diagrams Decision treeInfluence diagram

26 Influence diagrams with stochastic nodes

27 THA model

28 ACR functional status

29 THA vs. Conservative Management

30 ACR Functional Status / Initial THA Outcome

31 Prosthesis Status After THA

32 Last Surgery

33 Conservative Management

34 The StoTree modeling environment

35 …StoTree modeling environment

36...StoTree modeling environment

37 Rollback in the THA model 85-year-old white male

38 Cost-effectiveness for THA 85-year-old white male

39 THA Cost-Effectiveness Results