Statistical Modeling of Longitudinal Data with Non-Ignorable Non-Monotone Missingness with Semiparametric Bayesian and Machine Learning Components

In longitudinal studies, outcomes are measured repeatedly over time and it is common that not all the patients will be measured throughout the study. For example patients can be lost to follow-up (monotone missingness) or miss one or more visits (non-monotone missingness); hence there are missing outcomes. In the longitudinal setting, we often assume the missingness is related to the unobserved data, which is non-ignorable. Pattern-mixture models (PMM) analyze the joint distribution of outcome and patterns of missingness in longitudinal data with non-ignorable non-monotone missingness. Existing methods employ PMM and impute the unobserved outcomes using the distribution of observed outcomes, conditioned on missing patterns. We extend the existing methods using latent class analysis (LCA) and a shared-parameter PMM. The LCA groups patterns of missingness with similar features and the shared-parameter PMM allows a subset of parameters to be different between latent classes when fitting a model. We also propose a method for imputation using distribution of observed data conditioning on latent class. Our model improves existing methods by accommodating data with small sample size. In a simulation study our estimator had smaller mean squared error than existing methods. Our methodology is applied to data from a phase II clinical trial that studies quality of life of patients with prostate cancer receiving radiation therapy.