To extend the ps-BART model for time-varying treatments and outcomes in a longitudinal setting, several modifications can be implemented. First, the model can incorporate a time index into the treatment and outcome variables, allowing for the modeling of treatment effects that change over time. This can be achieved by defining the treatment variable ( D(t) ) and the outcome variable ( Y(t) ) as functions of time, where ( t ) represents discrete time points in the longitudinal data.
Additionally, the model can utilize a hierarchical structure to account for the repeated measures on the same subjects. This involves specifying a random effects component that captures individual-level variability in treatment responses over time. By integrating a random effects structure, the ps-BART model can better accommodate the correlation of outcomes within individuals across different time points.
Moreover, the inclusion of lagged treatment effects can enhance the model's ability to capture the dynamic nature of treatment impacts. This can be done by incorporating past treatment values ( D(t-1), D(t-2), \\ldots ) as predictors in the model, allowing for the exploration of how previous treatment levels influence current outcomes.
Finally, the estimation of the propensity score can be adapted to account for time-varying covariates, ensuring that the model appropriately adjusts for confounding factors that may also change over time. This comprehensive approach would enable the ps-BART model to effectively estimate causal effects in longitudinal studies with time-varying treatments and outcomes.