Shared parameter and copula models for analysis of semicontinuous longitudinal data with nonrandom dropout and informative censoring

Analysis of longitudinal semicontinuous data characterized by subjects’ attrition triggered by nonrandom dropout is complex and requires accounting for the within-subject correlation, and modeling of the dropout process. While methods that address the within-subject correlation and missing data are available, approaches that incorporate the nonrandom dropout, also referred to informative right censoring, in the modeling step are scarce due to the computational intensity and possible intractable integration needed for its implementation. Appreciating the complexity of this problem and the need for a new methodology that is feasible for implementation, we propose to extend a framework of likelihood-based marginalized two-part models to account for informative right censoring. The censoring process is modeled using two approaches: (1) Poisson censoring for the count of visits before dropout and (2) survival time to dropout. Novel consideration was given to the proposed joint modeling approaches for the semicontinuous and censoring components of the likelihood function which included (1) shared parameter, and (2) Clayton copula. The cross-part and within-part correlations were accounted for through a complex random effect structure that models correlated random intercepts and slopes. Feasibility of implementation, and accuracy of these approaches were investigated using extensive simulation studies and clinical application.

A marginalized two-part model with heterogeneous variance for semicontinuous data

Semicontinuous data, characterized by a point mass at zero followed by a positive, continuous distribution, arise frequently in medical research. These data are typically analyzed using two-part mixtures that separately model the probability of incurring a positive outcome and the distribution of positive values among those who incur them. In such a conditional specification, however, standard two-part models do not provide a marginal interpretation of covariate effects on the overall population. We have previously proposed a marginalized two-part model that yields more interpretable effect estimates by parameterizing the model in terms of the marginal mean. In the original formulation, a constant variance was assumed for the positive values. We now extend this model to a more general framework by allowing non-constant variance to be explicitly modeled as a function of covariates, and incorporate this variance into two flexible distributional assumptions, log-skew-normal and generalized gamma, both of which take the log-normal distribution as a special case. Using simulation studies, we compare the performance of each of these models with respect to bias, coverage, and efficiency. We illustrate the proposed modeling framework by evaluating the effect of a behavioral weight loss intervention on health care expenditures in the Veterans Affairs health system.