Multilevel Poisson sample selection models and alternative methods for estimating hospital effects on long-term outcomes

Hospital care focuses on improving patients' long-term quality of life, yet hospital quality metrics typically focus on short-term processes. Attempting to understand a patient's long-term process introduces sample selection bias since patients must survive the hospitalization in order to observe post-hospitalization outcomes. As a result, proper analysis of long-term outcomes should account for clustering, due to the hierarchical structure of hospital data, as well as sample selection bias. The objective of this paper was to evaluate random effect parameter estimation and higher-level ranking of long-term count outcomes and short-term selection processes in the presence of cluster and selection bias by comparing multilevel Poisson models, multilevel zero-inflated Poisson models, and multilevel Poisson sample selection models (MPSSMs) in a series of simulations. We simulated an outcome resembling a post-discharge Poisson count with a pre-specified selection process determining a patient's hospitalization survival with each hospital having a unique effect on both processes. In order to clarify the methodology, we also analyzed a real-world hospital dataset involving a count outcome conditioned on the selection process of hospital survival. Across all simulations, the random effect parameter estimates were directly compared and the empirical Bayes estimates were extracted, ranked, and compared using the Spearman rank correlation. Results show that the MPSSM produces more accurate random effect parameter estimates and higher-level empirical Bayes ranks. When modeling multilevel effects on long-term count outcomes observed after a short-term selection process, higher-level effects are more reliably measured using MPSSMs.