Fig. 1

Causal diagram using VanderWeele’s et al.65 approach for confounding control in a three-wave panel design (solid lines denote assumed causality, dashed lines denote confounding path). By including baseline measures of the outcome, as well as including the baseline treatment, and a rich array of covariates, we assume back door paths between the treatment and outcome will be blocked. However, because of possible unmeasured confounding, we also perform sensitivity analyses with E-values.