A semiparametric Bayesian model for multiple monotonically increasing count sequences

In longitudinal clinical trials, subjects may be evaluated many times over the course of the study. This article is motivated by a medical study conducted in the U.S. Veterans Administration Cooperative Urological Research Group to assess the effectiveness of a treatment in preventing recurrence on subjects affected by bladder cancer. The data consist of the accumulated tumor counts over a sequence of regular checkups, with many missing observations. We propose a hierarchical nonparametric Bayesian model for sequences of monotonically increasing counts. Unlike some of the previous analyses for these data, we avoid interpolation by explicitly incorporating the missing observations under the assumption of these being missing completely at random. Our formulation involves a generalized linear mixed effects model, using a dependent Dirichlet process prior for the random effects, with an autoregressive component to include serial correlation along patients. This provides great flexibility in the desired inference, that is, assessing the treatment effect. We discuss posterior computations and the corresponding results obtained for the motivating dataset, including a comparison with parametric alternatives.