Adjusting for Time-Varying Confounding in Survival Analysis

1. Adjusting for Time-Varying Confounding in Survival Analysis Jennifer S. Barber Susan A. Murphy Natalya Verbitsky University of Michigan

2. Outline • Introduction/motivation • Weighting method • Empirical example • Simulation • Conclusions

3. Introduction/Motivation • Causal questions • Experimental setting • Social science = observational data • Confounders • Standard statistical method • Biased if confounders affected by exposure (i.e., endogenous) • Time-varying confounders

4. Research Question “If more children in poor countries attend school, would more couples limit their total family size via sterilization?” Children’s school attendance º Sterilization

5. Weighting Method • Developed by Robins and colleagues • Marginal Structural Models (MSMs) • Uses sample weights (inverse-probability-of-exposure weights) • Clear research question/hypothesis

6. Two pie chart slides here.

8. Empirical Example • Chitwan Valley Family Study • Representative sample of 171 neighborhoods • Each adult in neighborhood interviewed (also spouses) • 97% response rate • Retrospective histories of change in each neighborhood • Retrospective histories of individual behavior using life history calendar

9. Two important measured time-varying variables that are likely confounders: • Availability of schools near neighborhood • Total number of children born to couple • Both are potentially endogenous to children’s education º sterilization • Also multiple time-invariant confounders • Parents’ education • Parents’ exposure to schools during childhood • Religious/ethnic/racial group • Distance to nearest town

10. Comparison of three methods • Naïve (ignores time-varying confounding) if exposure had been randomized, we would fit the model: logit (pij) = $0 + $1exposij + $2subpopj • Standard (includes time-varying confounders as covariates in the model) logit (pij) = $0 + $1exposij + $2subpopj + $3 confoundersij • Weighted (MSM) logit (pij) = $0 + $1exposij + $2subpopj

11. Table 5. Logistic regression estimates (with robust standard errors) of hazard of sterilization on children’s education

12. Primary Assumptions of the Weighting Method • Assumption 1: • No direct unmeasured confounders (sequential ignorability) • Note: same as the first assumption underlying the standard method • Assumption 2: • No past confounder patterns exclude particular levels of exposure • e.g., even if the couple does not live near a school, it is still possible that they have sent a child to school (a distant school)

13. Simulated Data • 1,000 datasets of 1,000 cases • constructed so that expos does not affect resp

14. Simulated Data • Comparison of same three methods: • Naïve (ignores time-varying confounding) • Standard (includes time-varying confounders as covariates in the model) • Weighted (MSM) • Assign a substantive meaning to each variable

15. Note: this page is for figure 5

16. Results of Simulation • Naïve method produces biased estimators • Standard method produces biased estimators • Weighted method reduces bias (even when there is unmeasured confounding) • The Unexpected Finding

17. Conclusions • Clear research question, clear hypotheses • Collect your own data • Weighting method “does no harm” • Look out for confounder/exposure patterns that are near impossible