1. Assessing the Effects of Time-varying Predictors or Treatments: A Conceptual Discussion Daniel Almirall VA Medical Center, HSRD Duke Medical Center, Dept. of Biostatistics September 25, 2007 In-house HSRD Research Meeting

2. Outline of Our Talk 1.Two Motivating Examples 2.What is the Data Structure? 3.Ways to formalize Scientific Questions? 4.Primary Challenge in the Data Analysis Time-varying confounders 5.Some Design Considerations

3. Motivating Example 1: Weight Loss Low-carb (vs. Low-fat) diet study Weight & QOL at 0, 4, 8, 12, 16, 20, 24 wks Majority of patients lose weight over time Finds more weight loss in low-carb group Finds improvements in QOL measures Finds that QOL, along some dimensions, may be differential by diet group Next natural question: Does weight loss, in turn, improve quality of life?

4. Motivating Example 2: PTSD Guided Imagery Study RCT of an intervention (GIFT) for women experiencing MST First step: analyze the effect of GIFT as usual (ITT) Suppose that after randomization to either GIFT or music therapy, some patients begin medication use An opportunity: What is the effect of GIFT possibly augmented by medication use on PTSD symptoms?

5. Data Structure For simplicity, we consider only 2 time points for the majority of this talk.

6. Data Structure: Main Ingredients Time, Time-varying treatments, Outcome A1A2 Y3 Time Interval 1Time Interval 2End of Study Weight at 4 weeksWeight at 8 weeks GIFT? at baselineMEDS? at 8 weeks Ex1: Ex2:......... Ex1: QOL Ex2: PTSD Symptoms

7. Data Structure: More Outcomes? Outcome May be Time-Varying, But... A1A2 Y3 Y1 Y2 Time Interval 1Time Interval 2End of Study

8. Data Structure: Main Ingredients Time, Time-varying treatments, Outcome A1A2 Y3 Time Interval 1Time Interval 2End of Study Weight at 4 weeksWeight at 8 weeks GIFT? at baseline Ex1: Ex2:......... Ex1: QOL Ex2: PTSD Symptoms MEDS? at 8 weeks

9. Data Structure: Covariates? May have Baseline Covariates X1 X1 A1A2 Y3 Time Interval 1Time Interval 2End of Study Weight at 4 weeksWeight at 8 weeks QOL age, race, diet, exer0,...

10. Data Structure: Covariates? Covariates May Be Time-Varying, As Well X1 X2 A1A2 Y3 Time Interval 1Time Interval 2End of Study Weight at 4 weeksWeight at 8 weeks QOL exer4-8, comply4-8,... age, race, diet, exer0,...

11. Data Structure: Covariates? Covariates May Be Time-Varying, As Well X1 X2 A1A2 Y3 Time Interval 1Time Interval 2End of Study GIFT?MEDS? PTSD Symptoms severity at week 8,... race, baseline severity,...

12. Formalizing Scientific Questions What are ways we can operationalize this?

13. Motivating Example 1: Weight Loss Low-carb (vs. Low-fat) diet study Question: Does weight loss over time improve quality of life? Formalized: What is the effect of the rate of weight loss on subsequent QOL scores? E(QOL 24 (WEIGHT 0,4,8,12,16,20,24 ) ) = β0 + β1 WTSLP Why not just do regression QOL 24 ~ WTSLP?

14. Motivating Example 2: PTSD Guided imagery study Question: What is the effect of GIFT subsequently augmented by meds on PTSD symptoms? Formalized: E(PTSD (GIFT, MED) ) = β0 + β1 GIFT + β2 MED + β3 GIFT x MED Why not just regress PTSD ~ GIFT, MED?

15. Data Analysis The challenge of time-varying confounders Will ordinary regression work?

16. Motivating Example 1: Weight Loss Unadjusted Linear Effect = -2.623

17. Data Analysis We want the effect of f(A1,A2) on Y3 A1A2 Y3 Time Interval 1Time Interval 2End of Study Note: This effect may occur in a multitude of ways. Weight at 4 weeksWeight at 8 weeks GIFT? at baselineMeds? at 8 weeks Ex1: Ex2:......... Ex1: QOL Ex2: PTSD

18. Data Analysis Confounders at baseline X1 A1A2 Y3 Time Interval 1Time Interval 2End of Study Weight at 4 weeksWeight at 8 weeks QOL diet, exer0,...

19. Data Analysis Confounders at baseline X1 A1A2 Y3 Time Interval 1Time Interval 2End of Study spurious Adjusting for X1 in ordinary regression is a legitimate strategy in this case. Weight at 4 weeksWeight at 8 weeks QOL diet, exer0,...

20. Data Analysis What about time-varying confounders? Ex1 X1 X2 A1A2 Y3 Time Interval 1Time Interval 2End of Study Weight at 4 weeksWeight at 8 weeksQOL exer4-8, comply4-8,... diet, exer0,...

21. Data Analysis What about time-varying confounders? Ex2 X1 X2 A1A2 Y3 Time Interval 1Time Interval 2End of Study GIFT?MEDS?PTSD Symptoms severity at week 8,... race, baseline severity,...

22. Data Analysis Need to adjust for time-varying confounders X1 X2 A1A2 Y3 Time Interval 1Time Interval 2End of Study spurious Adjusting for X2 in ordinary regression may be problematic in this case. Why?...

23. Data Analysis The first problem with conditioning on X2. X2 A1A2 Y3 Time Interval 1Time Interval 2End of Study X cut off

24. Data Analysis The first problem with conditioning on X2. X2 A1A2 Y3 Time Interval 1Time Interval 2End of Study X cut off Weight at 4 weeks Weight at 8 weeks QOL exer4-8, comply4-8,...

25. Data Analysis The second problem with conditioning on X2. X2 A1A2 Y3 Time Interval 1Time Interval 2End of Study U spurious non-causal path

26. Data Analysis The second problem with conditioning on X2. X2 A1A2 Y3 Time Interval 1Time Interval 2End of Study U spurious non-causal path Weight at 4 weeksWeight at 8 weeks QOL exer4-8, comply4-8,... Motivation, social support,...

27. Data Analysis: What do we do? There exist weighted regression methods... X1 X2 A1A2 Y3 Time Interval 1Time Interval 2End of Study XX That eliminate/reduce confounding in the sample. Requires that we have all confounders of A1 and A2. Weights: function of E(A1| X1) and E(A2| A1, X1, X2). X Does not require knowledge about U.

28. Design Recommendations Clear definition of time-varying treatment How time is defined becomes important Alignment of time, time-varying txts, and Y Brainstorm about the most important factors affecting your time-varying predictor or treatment –Ex1: What are the things that affect weight loss? –Ex2: What are all the reasons the patient might have been assigned medication subsequent to GIFT?

29. References Robins. (1999). Association, causation, and marginal structural models. Synthese, 121:151- 179.Association, causation, and marginal structural models Hernán, Brumback, Robins. (2001). Marginal structural models to estimate the joint causal effect of nonrandomized treatments. Journal of the American Statistical Association, 96(454):440-448.Marginal structural models to estimate the joint causal effect of nonrandomized treatments Bray, Almirall, Zimmerman, Lynam & Murphy(2006). Assessing the Total Effect of Time-varying Predictors in Prevention Research. Prevention Science 7(1):1-17. Assessing the Total Effect of Time-varying Predictors in Prevention Research.

30. More research on the timing and sequencing of treatments in medicine Time-varying effect moderation (my thesis) Effect of time-varying adaptive decision rules (dynamic treatment regimes)? Developing optimal dynamic treatment regimes –New sequentially randomized trials are available to help accomplish this

31. Thank you.