Estimating curvilinear time-varying treatment effects: combining g-estimation of structural nested mean models with time-varying effect models for longitudinal causal inference

Longitudinal designs can fortify causal inquiries of a focal predictor (i.e., treatment) on an outcome. But valid causal inferences are complicated by causal feedback between confounders and treatment over time. G-estimation of a structural nested mean model (SNMM) is designed to handle the complexities beset by measured time-varying or treatment-dependent confounding in longitudinal data. But valid inference requires correctly specifying the functional form of the SNMM, such as how the effects stay constant or change over time. In this article, we develop a g-estimation strategy for linear structural nested mean models whose causal parameters adopt the form of time-varying coefficient functions. These time-varying coefficient functions are smooth semiparametric functions of time that permit probing how the treatment effects may change curvilinearly. Further effect modification by time-invariant and time-varying covariates can be readily postulated in the SNMM to test fine-grained effect heterogeneity. We then describe a g-estimation strategy for estimating such an SNMM. We utilize the established time-varying effect model (TVEM) approach from the prevention and psychotherapy research literature for modeling flexible changes in covariate-outcome associations over time. Moreover, we exploit a known benefit of g-estimation over routine regression methods: its double robustness conferring protection against biases induced by certain forms of model misspecification. We encourage psychology researchers seeking correct causal conclusions from longitudinal data to use an SNMM with time-varying coefficient functions to assess curvilinear causal effects over time, and to use g-estimation with TVEM to resolve measured treatment-dependent confounding.