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Assessing the Effects of Time-varying Predictors or Treatments: A Conceptual Discussion

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. Two Motivating Examples What is the Data Structure ?

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Assessing the Effects of Time-varying Predictors or Treatments: A Conceptual Discussion

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

  3. Motivating Example 1: Weight LossLow-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: PTSDGuided 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 IngredientsTime, Time-varying treatments, Outcome Y3 Ex1: QOL Ex2: PTSD A1 A2 Symptoms Ex1: Weight at 4 weeks ......... Weight at 8 weeks Ex2: GIFT? at baseline ......... MEDS? at 8 weeks Time Interval 1 Time Interval 2 End of Study

  7. Data Structure: More Outcomes?Outcome May be Time-Varying, But... Y2 Y3 Y1 A1 A2 Time Interval 1 Time Interval 2 End of Study

  8. Data Structure: Main IngredientsTime, Time-varying treatments, Outcome Y3 Ex1: QOL Ex2: PTSD A1 A2 Symptoms Ex1: Weight at 4 weeks ......... Weight at 8 weeks Ex2: GIFT? at baseline ......... MEDS? at 8 weeks Time Interval 1 Time Interval 2 End of Study

  9. Data Structure: Covariates?May have Baseline Covariates X1 Y3 QOL A1 A2 Weight at 4 weeks Weight at 8 weeks X1 age, race, diet, exer0,... Time Interval 1 Time Interval 2 End of Study

  10. Data Structure: Covariates?Covariates May Be Time-Varying, As Well Y3 QOL A1 A2 Weight at 4 weeks Weight at 8 weeks X2 X1 exer4-8, comply4-8,... age, race, diet, exer0,... Time Interval 1 Time Interval 2 End of Study

  11. Data Structure: Covariates?Covariates May Be Time-Varying, As Well Y3 PTSD Symptoms A1 A2 GIFT? MEDS? X2 X1 severity at week 8,... race, baseline severity,... Time Interval 1 Time Interval 2 End of Study

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

  13. Motivating Example 1: Weight LossLow-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(QOL24 (WEIGHT0,4,8,12,16,20,24) ) = β0 + β1 WTSLP Why not just do regression QOL24 ~ WTSLP?

  14. Motivating Example 2: PTSDGuided 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 AnalysisThe challenge of time-varying confounders • Will ordinary regression work?

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

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

  18. Data AnalysisConfounders at baseline Y3 QOL A1 A2 Weight at 4 weeks Weight at 8 weeks X1 diet, exer0,... Time Interval 1 Time Interval 2 End of Study

  19. Data AnalysisConfounders at baseline Adjusting for X1 in ordinary regression is a legitimate strategy in this case. Y3 spurious spurious QOL A1 A2 Weight at 4 weeks Weight at 8 weeks X1 diet, exer0,... Time Interval 1 Time Interval 2 End of Study

  20. Data AnalysisWhat about time-varying confounders? Ex1 Y3 Weight at 4 weeks Weight at 8 weeks QOL A1 A2 X2 X1 exer4-8, comply4-8,... diet, exer0,... Time Interval 1 Time Interval 2 End of Study

  21. Data AnalysisWhat about time-varying confounders? Ex2 Y3 GIFT? MEDS? PTSD Symptoms A1 A2 X2 X1 severity at week 8,... race, baseline severity,... Time Interval 1 Time Interval 2 End of Study

  22. Data AnalysisNeed to adjust for time-varying confounders Adjusting for X2 in ordinary regression may be problematic in this case. Y3 spurious spurious Why? ... A1 A2 X2 X1 Time Interval 1 Time Interval 2 End of Study

  23. Data AnalysisThe first problem with conditioning on X2. Y3 A1 A2 cut off X X2 Time Interval 1 Time Interval 2 End of Study

  24. Data AnalysisThe first problem with conditioning on X2. Y3 QOL A1 A2 Weight at 8 weeks Weight at 4 weeks cut off X X2 exer4-8, comply4-8,... Time Interval 1 Time Interval 2 End of Study

  25. Data AnalysisThe second problem with conditioning on X2. spurious non-causal path Y3 U A1 A2 X2 Time Interval 1 Time Interval 2 End of Study

  26. Data AnalysisThe second problem with conditioning on X2. spurious non-causal path Y3 U Motivation, social support,... QOL A1 A2 Weight at 4 weeks Weight at 8 weeks X2 exer4-8, comply4-8,... Time Interval 1 Time Interval 2 End of Study

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

  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. • 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. • Bray, Almirall, Zimmerman, Lynam & Murphy(2006). Assessing the Total Effect of Time-varying Predictors in Prevention Research. Prevention Science 7(1):1-17.

  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.

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