Keywords: missing data, non-ignorable missingness; non-monotone missingness; Bayesain nonparametric analysis
In longitudinal studies, outcomes are measured repeatedly over time. It is common that not all the patients can be measured throughout the study, e.g. patients lost to follow-up (monotone missingness) or missing one or more visits (non-monotone missingness), so that there are missing outcomes. In the longitudinal settings, we often assume the missingness is related to the unobserved data so that it is non-ignorable. Pattern-mixture models (PMM) analyze the joint distribution of outcome and missingness patterns in longitudinal data with non-ignorable non-monotone missingness. Then the unobserved outcomes are imputed using the distribution of observed outcomes, conditioned on missing patterns. However, the existing methods suffer from model identification issues if data is sparse in specific missing patterns, which is very likely to happen with a small sample size or a large number of repetitions. 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 among latent classes when fitting a model. A novel imputation method is also developed using the distribution of observed data conditioned on latent classes. Our model performs better than existing methods for data with small sample size. The method is applied to dataset from a phase II clinical trial that studies the quality of life for patients with prostate cancer receiving radiation therapy.