ABSTRACT
The time-varying coefficient models discussed in Chapters 6 to 9 present a simple and flexible structured nonparametric approach for modeling the timevarying covariate effects on the outcome variable of interest. Despite their success in many longitudinal studies, these models have a number of restrictions which limit their practical values. For example, the time-varying coefficient models, as shown in (7.1), require that the linear coefficients to be functions of time only and the values of the time-dependent covariates do not depend on the values of the outcome variable at the previous time points. To broaden the scope of applications, we present generalizations of the time-varying coefficient models in three areas: (a) structured modeling for the effects outcome-adaptive covariates; (b) mixed-effects extension to incorporate subject-specific effects; (c) incorporating time-lagging effects using the conditional distributions. In this chapter, we consider the extension in (a) with concomitant interventions. The results of this chapter demonstrate that, because the initiation of concomitant interventions often depends on the outcome variable, the usual approach of mixed-effects models or nonparametric models may lead to biased inferences for the effects of a concomitant intervention. The extensions in (b) and (c) are discussed in Chapters 11 to 14.
