Modeling Related Survival Samples via Dependent Nonparametric Mixtures

Studies comprising multiple related samples are ubiquitous in survival analysis. Clinical studies typically compare the effectiveness of different drugs or assess the efficacy of a new treatment compared to a placebo. Considering the dependence between samples is key to improving estimation and reducing uncertainty, especially when analyzing small samples. At the same time, an adequate model should be flexible enough to allow for the presence of heterogeneity both between and within groups. We formulate a nonparametric mixture of gamma kernels for possibly censored survival data, where the mixing measure is distributed as a thinned-dependent Dirichlet process. We apply the model to analyze two datasets of remission times, showing how the proposed model allows for borrowing information between groups while admitting heterogeneity across samples.