A factor mixture model for multivariate survival data: an application to the analysis of lifetime mental disorders

Developmental considerations in survival models as applied to substance use research

Survival analysis is a class of models that are ideal for evaluating questions of timing of events, which makes them well-suited for modeling the development of a process such as initiation of substance use, development of addiction, or post-treatment recovery. The focus of this review paper is to demonstrate how survival models operate in a broader developmental framework and to offer guidance on selecting the appropriate model on the basis of the research question at hand. We provide a basic overview of survival models and then identify several key issues, explain how they pertain to research in the addiction field, and describe studies that utilize survival models to address questions about timing. We discuss the importance of carefully selecting the metric and origin of the time scale that corresponds to developmental process under investigation and we describe types of censoring/truncation. We describe the value of modeling covariates as time-invariant versus time-varying, and make the distinction between time-varying covariates and time-varying effects of covariates. We also explain how to test for substantive differences due to the timing of the assessment of the predictor. We finish the paper with a presentation of relatively novel extensions of survival models, including models that integrate standard statistical mediational analysis with discrete-time survival analysis, models that simultaneously consider order and timing of multiple events, and models that involve joint modeling of longitudinal and survival data. We also present our own substantive examples of various models in an Appendix containing annotated syntax and output.