Assessing the Effects of Time-varying Predictors or Treatments: A Conceptual Discussion
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Assessing the Effects of Time-varying Predictors or
Treatments: A Conceptual Discussion
Daniel AlmirallVA Medical Center, HSRD
Duke Medical Center, Dept. of Biostatistics
September 25, 2007
In-house HSRD Research Meeting
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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
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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?
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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?
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Data Structure
• For simplicity, we consider only 2 time points for the majority of this talk.
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Data Structure: Main IngredientsTime, Time-varying treatments, Outcome
A1 A2
Y3
Time Interval 1 Time Interval 2 End of Study
Weight at 4 weeks Weight at 8 weeks
GIFT? at baseline MEDS? at 8 weeks
Ex1:
Ex2:
.........
.........
Ex1: QOL
Ex2: PTSDSymptoms
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Data Structure: More Outcomes?Outcome May be Time-Varying, But...
A1 A2
Y3Y1 Y2
Time Interval 1 Time Interval 2 End of Study
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Data Structure: Main IngredientsTime, Time-varying treatments, Outcome
A1 A2
Y3
Time Interval 1 Time Interval 2 End of Study
Weight at 4 weeks Weight at 8 weeks
GIFT? at baseline
Ex1:
Ex2:
.........
.........
Ex1: QOL
Ex2: PTSDSymptoms
MEDS? at 8 weeks
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Data Structure: Covariates?May have Baseline Covariates X1
X1
A1 A2
Y3
Time Interval 1 Time Interval 2 End of Study
Weight at 4 weeks Weight at 8 weeks
QOL
age, race, diet, exer0,...
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Data Structure: Covariates?Covariates May Be Time-Varying, As Well
X1 X2
A1 A2
Y3
Time Interval 1 Time Interval 2 End of Study
Weight at 4 weeks Weight at 8 weeks
QOL
exer4-8, comply4-8,...age, race, diet, exer0,...
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Data Structure: Covariates?Covariates May Be Time-Varying, As Well
X1 X2
A1 A2
Y3
Time Interval 1 Time Interval 2 End of Study
GIFT? MEDS?
PTSD Symptoms
severity at week 8,...race, baseline severity,...
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Formalizing Scientific Questions
• What are ways we can operationalize this?
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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(QOL24 (WEIGHT0,4,8,12,16,20,24) )
= β0 + β1 WTSLP
Why not just do regression QOL24 ~ WTSLP?
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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?
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Data AnalysisThe challenge of time-varying confounders
• Will ordinary regression work?
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Motivating Example 1: Weight Loss
Unadjusted Linear Effect = -2.623
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Data AnalysisWe want the effect of f(A1,A2) on Y3
A1 A2
Y3
Time Interval 1 Time Interval 2 End of Study
Note: This effect may occur in a multitude of ways.
Weight at 4 weeks Weight at 8 weeks
GIFT? at baseline Meds? at 8 weeks
Ex1:
Ex2:
.........
.........
Ex1: QOL
Ex2: PTSD
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Data AnalysisConfounders at baseline
X1
A1 A2
Y3
Time Interval 1 Time Interval 2 End of Study
Weight at 4 weeks Weight at 8 weeks
QOL
diet, exer0,...
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Data AnalysisConfounders at baseline
X1
A1 A2
Y3
Time Interval 1 Time Interval 2 End of Study
spurious
spurious
Adjusting for X1 in ordinary regression is a legitimate strategy in this case.
Weight at 4 weeks Weight at 8 weeks
QOL
diet, exer0,...
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Data AnalysisWhat about time-varying confounders? Ex1
X1 X2
A1 A2
Y3
Time Interval 1 Time Interval 2 End of Study
Weight at 4 weeks Weight at 8 weeks QOL
exer4-8, comply4-8,...diet, exer0,...
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Data AnalysisWhat about time-varying confounders? Ex2
X1 X2
A1 A2
Y3
Time Interval 1 Time Interval 2 End of Study
GIFT? MEDS? PTSD Symptoms
severity at week 8,...race, baseline severity,...
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Data AnalysisNeed to adjust for time-varying confounders
X1 X2
A1 A2
Y3
Time Interval 1 Time Interval 2 End of Study
spurious
spurious
Adjusting for X2 in ordinary regression may be problematic in this case.
Why? ...
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Data AnalysisThe first problem with conditioning on X2.
X2
A1 A2
Y3
Time Interval 1 Time Interval 2 End of Study
Xcut o
ff
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Data AnalysisThe first problem with conditioning on X2.
X2
A1 A2
Y3
Time Interval 1 Time Interval 2 End of Study
Xcut o
ffWeight at 4 weeks Weight at 8 weeks
QOL
exer4-8, comply4-8,...
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Data AnalysisThe second problem with conditioning on X2.
X2
A1 A2
Y3
Time Interval 1 Time Interval 2 End of Study
U
spurious non-causal path
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Data AnalysisThe second problem with conditioning on X2.
X2
A1 A2
Y3
Time Interval 1 Time Interval 2 End of Study
U
spurious non-causal path
Weight at 4 weeks Weight at 8 weeks
QOL
exer4-8, comply4-8,...
Motivation, social support,...
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Data Analysis: What do we do?There exist weighted regression methods...
X1 X2
A1 A2
Y3
Time Interval 1 Time Interval 2 End 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.
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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?
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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.
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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
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Thank you.