Abstract: A repeatedly measured outcome in longitudinal studies allows researchers to monitor how the outcome changes over time. When an intervention affects the outcome and subjects initiate the intervention at different times during the course of a study, it is essential to account for the varying time to intervention (TTI) in models of such changes. In this study, we develop a piecewise polynomial regression model with TTI-varying coefficients that describes the population mean outcome over time. The TTI-varying coefficients in the model enable us to capture the population mean outcome trajectory, affected by both the intervention and the varying TTI. In observational studies, other covariates can confound these effects, leading to estimation bias if not properly accounted for. To mitigate this, we propose a double-weighted estimation procedure based on a kernel function and a generalized propensity score. The proposed estimation procedure effectively corrects the estimation bias of the TTI-varying coefficients and provides valid statistical inferences about the coefficients. We apply our approach to assess changes in the population mean of an inflammation biomarker for HIV-infected adults in Haiti who initiate antiretroviral therapy following the World Health Organization guideline.

Key words and phrases: Causal inference, generalized propensity score, kernel smoothing, longitudinal data, piecewise polynomial regression, varying coefficients model.