LAUSR

There are important challenges to the estimation and identification of average causal effects in longitudinal data with time-varying exposures. Here, we discuss the difficulty in meeting the positivity condition. Our motivating example is the per-protocol analysis of the Effects of Aspirin in Gestation and Reproduction trial. We estimated the average causal effect comparing incidence of pregnancy by 26 weeks had all women been assigned to aspirin and complied versus been assigned to placebo and complied. Using flexible targeted minimum loss-based estimation, we estimated a risk difference of 1.27% (95% CI: -9.83%, 12.38%). Using a less flexible inverse probability weighting approach, the risk difference was 5.77% (95% CI: -1.13%, 13.05%). However, the cumulative probability of compliance conditional on covariates approached zero as follow-up accrued, indicating a practical violation of the positivity assumption, which limited our ability to make causal interpretations. The effects of non-positivity were more apparent when using a more flexible estimator, as indicated by the greater imprecision. When faced with non-positivity, one can use a flexible approach and be transparent about the uncertainty, use a parametric approach and smooth over gaps in the data, or target a different estimand which will be less vulnerable to positivity violations.