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

Outline Introduction/motivation Weighting method Empirical example Simulation Conclusions

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

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

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

Two pie chart slides here.

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

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

Comparison of three methods Naïve (ignores time-varying confounding) if exposure had been randomized, we would fit the model: logit (p ij ) = $ 0 + $ 1 expos ij + $ 2 subpop j Standard (includes time-varying confounders as covariates in the model) logit (p ij ) = $ 0 + $ 1 expos ij + $ 2 subpop j + $ 3 confounders ij Weighted (MSM) logit (p ij ) = $ 0 + $ 1 expos ij + $ 2 subpop j

Table 5. Logistic regression estimates (with robust standard errors) of hazard of sterilization on children’s education Naïve (1) Standard (2) Weighted (3) Any child has ever attended school.93*** (.10).74*** (.11).68*** (.11) School is present within 5 minute walk.17* (.08) Family size: Couple has 1 child -.68*** (.11) Couple has 4 or more children.49*** (.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)

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

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

Note: this page is for figure 5

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

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