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

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

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?

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?

Data Structure

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

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

Data Structure: More Outcomes?Outcome May be Time-Varying, But...

A1 A2

Y3Y1 Y2

Time Interval 1 Time Interval 2 End of Study

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

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,...

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,...

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,...

Formalizing Scientific Questions

• What are ways we can operationalize this?

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?

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?

Data AnalysisThe challenge of time-varying confounders

• Will ordinary regression work?

Motivating Example 1: Weight Loss

Unadjusted Linear Effect = -2.623

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

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,...

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,...

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,...

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,...

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? ...

Data AnalysisThe first problem with conditioning on X2.

X2

A1 A2

Y3

Time Interval 1 Time Interval 2 End of Study

Xcut o

ff

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,...

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

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,...

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.

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?

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.

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

Thank you.