A likelihood-based two-part marginal model for longitudinal semicontinuous data.

Two-part models are an attractive approach for analysing longitudinal semicontinuous data consisting of a mixture of true zeros and continuously distributed positive values. When the population-averaged (marginal) covariate effects are of interest, two-part models that provide straightforward interpretation of the marginal effects are desirable. Presently, the only available approaches for fitting two-part marginal models to longitudinal semicontinuous data are computationally difficult to implement. Therefore, there exists a need to develop two-part marginal models that can be easily implemented in practice. We propose a fully likelihood-based two-part marginal model that satisfies this need by using the bridge distribution for the random effect in the binary part of an underlying two-part mixed model; and its maximum likelihood estimation can be routinely implemented via standard statistical software such as the SAS NLMIXED procedure. We illustrate the usage of this new model by investigating the marginal effects of pre-specified genetic markers on physical functioning, as measured by the Health Assessment Questionnaire, in a cohort of psoriatic arthritis patients from the University of Toronto Psoriatic Arthritis Clinic. An added benefit of our proposed marginal model when compared to a two-part mixed model is the robustness in regression parameter estimation when departure from the true random effects structure occurs. This is demonstrated through simulation.