1. Overview of Adaptive Treatment Regimes Sachiko Miyahara Dr. Abdus Wahed

2. Before starting the presentation… ≠ Adaptive Treatment Regimes Adaptive Experimental Design

3. Adaptive Treatment Regimes vs. Adaptive Experimental Design Adaptive Treatment Regimes “…adaptive as used here refers to a time- varying therapy for managing a chronic illness” (Murphy,2005) Adaptive Experimental Design “…such as designs in which treatment allocation probabilities for the present patients depend on the responses of past patients” (Murphy,2005)

4. Outline 1. What is Adaptive Treatment Regime? -Definition -Example -Objective 2. How to decide the best regime? - 3 different study designs - Comparison of 3 designs 3. Trial Example (STAR*D) 4. Inference on Adaptive Treatment Regimes

5. What is Adaptive Treatment Regime? Definition: a set of rule which select the best treatment option, which are made based on subjects’ condition up to that point.

6. What is Adaptive Treatment Regime? A A’ B1B1 B 1 ’ B2B2 B 2 ’ B2B2 Non Responder Non Responder Patient B1B1 B 1 ’

7. 8 Possible Policies (1) Trt A followed by B 1 if response, else B 2 (AB 1 B 2 ) (2) Trt A followed by B 1 if response, else B 2 ’ (AB 1 B 2 ’) (3) Trt A followed by B 1 ’ if response, else B 2 (AB 1 ’B 2 ) (4) Trt A followed by B 1 ’ if response, else B 2 ’ (AB 1 ’B 2 ’) (5) Trt A’ followed by B 1 if response, else B 2 (A’B 1 B 2 ) (6) Trt A’ followed by B 1 if response, else B 2 ’ (A’B 1 B 2 ’) (7) Trt A’ followed by B 1 ’ if response, else B 2 (A’B 1 ’B 2 ) (8) Trt A’ followed by B 1 ’ if response, else B 2 ’ (A’B 1 ’B 2 ’ )

8. What is the objective of the Adaptive Treatment Regimes? Objective: To know which treatment strategy works the best, given a patient’s history.

9. A treatment naïve patient comes to a physician’s office. Questions: 1. What treatment strategy should the physician follow for that patient? 2. How should it be decided? What is the objective of the Adaptive Treatment Regime?

10. If one knew… (T be the outcome measurement) 1. E(T| AB 1 B 2 ) = 15 2. E(T| AB 1 B 2 ’) = 14 3. E(T| AB 1 ’B 2 ) = 18 4. E(T| AB 1 ’B 2 ’) = 17 5. E(T| A’B 1 B 2 ) = 20 6. E(T| A’B 1 B 2 ’) = 19 7. E(T| A’B 1 ’B 2 ) = 13 8. E(T| A’B 1 ’B 2 ’ ) = 12 Best Regime for the patient

11. In Reality… Problems: 1. E(T|. ) are not known (need to estimate) 2. How can one accurately and efficiently estimate E(T|. )?

12. How to estimate the expected outcome? Three study designs: 1. A clinical trial with 8 treatments 2. Combine existing trials 3. SMART (Sequential Multiple Assignment Randomized Trials)

13. Design 1: A clinical trial with 8 Treatment Policies AB 1 B 2 AB 1 B 2 ’ AB 1 ’B 2 AB 1 ’B 2 ’ Sample = Randomization A’B 1 B 2 A’B 1 B 2 ’ A’B 1 ’B 2 A’B 1 ’B 2 ’

14. Design 2: Combining Existing Trials A A’ B1B1 B1’B1’ + Trial 1Trial 5Trial 3Trial 2Trial 4 +++ Responder to A only Responder to A’ only Non Responder to A only Non Responder to A’ only B1B1 B1’B1’ B2B2 B2’B2’ B2B2 B2’B2’

15. Sequential Multiple Assignment Randomized Trials (SMART) proposed by Dr. Murphy The SMART designs were adapted to: - Cancer (Thall 2000) - CATIE (Schneider 2001) – Alzheimer's Disease - STAR*D (Rush 2003) – Depression Design 3: SMART

16. A A’ B1B1 B 1 ’ B2B2 B 2 ’ B2B2 B 1 ’ B1B1 Non Responder Non Responder Sample = Randomization

17. Comparisons of 3 Study Designs Question: A Trial with 8 Trts Combined Trial SMART 1. Does it serve the purpose of finding the best strategy? 2. Is it feasible? 3.Can we assess the trt effects using a standard statistical method? Yes Maybe No Maybe No

18. Sequenced Treatment Alternatives To Relieve Depression (STAR*D) 1.What is STAR*D? 2.The Study Design

19. What is STAR*D? Multi-center clinical trial for depression Largest and longest study to evaluate depression N=4,041 7 years study period Age between 18-75 Referred by their doctors 4 stages (3 randomizations)

20. STAR*D Study Design: Level 1 Non Responder Eligible Subjects CIT Go to Level 2

21. STAR*D Study Design: Level 2 CIT+CT BUP CT VEN SER Switch Add on Lev 1 Non Responder = Subject’s Choice = Randomization CIT+BUS CIT+BUP

22. STAR*D Study Design: Level 3 Lev3 Med+Li NTP MIRT Switch Add on Lev 2 Non Responder = Subject’s Choice = Randomization

23. STAR*D Study Design: Level 4 VEN+MIRT TCP Lev 3 Non Responder = Randomization

24. Details on Inference from SMART Remember the goal is to estimate E(T|AB 1 B 2 ) First, how can we construct an unbiased estimator for E(T|AB 1 B 2 )?

25. Details on Inference from SMART Let us ask ourselves, what would we have done if everyone in the sample were treated according to the strategy AB 1 B 2 ? A B1B1 B2B2 Non Responder Patient

26. What would we have done if everyone in the sample were treated according to the strategy AB 1 B 2 ? Answer: E(T|AB 1 B 2 ) = ΣT i /n Details on Inference from SMART Applies to 8-arm randomization trial

27. But in SMART, we have not treated everyone with AB 1 B 2 Details on Inference from SMART A B1B1 B 1 ’ B2B2 B 2 ’ Non Responder Sample

28. Let C(AB 1 B 2 ) be the set of patients who are treated according to the policy AB 1 B 2 Details on Inference from SMART A B1B1 B 1 ’ B2B2 B 2 ’ Non Responder Sample

29. We define R = Response indicator (1/0) Z 1 = Treatment B 1 indicator (1/0) Z 2 = Treatment B 2 indicator (1/0) Then C(AB 1 B 2 ) = {i: [R i Z 1i + (1-R i )Z 2i ]=1} Details on Inference from SMART

30. One would define E(T|AB 1 B 2 ) = Σ[R i Z 1i + (1-R i )Z 2i ]T i /n ’ Where n ’ is the number of patients in C(AB 1 B 2 ). This estimator would be biased as it ignores the second randomization.

31. There are two types of patients in the set C(AB 1 B 2 ) who were treated according to the policy AB 1 B 2 A responder who received B 1 and A nonresponder who received B 2 Details on Inference from SMART

32. A B1B1 B 1 ’ B2B2 B 2 ’ Non Responder Sample

33. Assuming equal randomization, A responder who received B 1 was equally eligible to receive B 1 ’ A responder who received B 2 was equally eligible to receive B 2 ’ Details on Inference from SMART

34. Thus A responder who received B 1 in C(AB 1 B 2 ) is representative of another patient who received B 1 ’ and A non-responder who received B 2 in C(AB 1 B 2 ) is representative of another patient who received B 2 ’ Details on Inference from SMART

35. We define weights as follows A responder who received B 1 in C(AB 1 B 2 ) receives a weight of 2 [1/(1/2)], also A non-responder who received B 2 in C(AB 1 B 2 ) receives a weight of 2 [1/(1/2)] While everyone else receives a weight of zero. Details on Inference from SMART

36. Unbiased estimator E(T|AB 1 B 2 ) = Σ[R i Z 1i + (1-R i )Z 2i ]T i /(n/2) And, in general, E(T|AB 1 B 2 ) = Σ[R i Z 1i /π 1 + (1-R i )Z 2i /π 2 ]T i /n This estimator is unbiased under certain assumptions

37. Issues Compare treatment strategies Wald test possible but needs to derive covariance between estimators (which may not be independent of each other) In survival analysis setting, how to derive formal tests to compare survival curves under different strategies Is log-rank test applicable? Can the proportional hazard model be applied here?

38. Issues Efficiency issues How can one improve efficiency of the proposed estimator How to handle missing data (missing response information, censoring, etc.) How to adjust for covariates when comparing treatment strategies And most importantly,

39. Issues Is it possible to tailor the best treatment strategy decisions to individual characteristics? For instance, could we one day hand over an algorithm to a nurse (not physician) which would provide decisions like “If the patient is a caucacian female, age 50 or over, have normal HGB levels, bla bla bla…the best strategy for maintaining her chronic disease would be……..”

40. ATSRG link http://www.pitt.edu/~wahed/ATSRG/main.htm