Class of Hazard Rate Mixtures for Combining Survival Data From Different Experiments

• Published in: Journal of the American Statistical Association Vol. 109; no. 506; pp. 802 - 814
• Main Authors: Lijoi, Antonio, Nipoti, Bernardo
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 01.06.2014; Taylor & Francis Group, LLC; Taylor & Francis Ltd
• Subjects: Analytical estimating; Bayesian nonparametrics; Censored data; Completely random measures; data analysis; data collection; Datasets; Dependent processes; Estimators; Experiments; Extended gamma processes; Hazards; Kaplan Meier estimator; Markov analysis; Markov chain; Mathematical vectors; Mixtures; Monte Carlo method; Monte Carlo simulation; Nonparametric models; Partial exchangeability; Random variables; Reliability functions; Sample size; Statistical analysis; Statistics; Survival analysis; Theory and Methods
• ISSN: 1537-274X; 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2013.869499

Mixture models for hazard rate functions are widely used tools for addressing the statistical analysis of survival data subject to a censoring mechanism. The present article introduced a new class of vectors of random hazard rate functions that are expressed as kernel mixtures of dependent completely random measures. This leads to define dependent nonparametric prior processes that are suitably tailored to draw inferences in the presence of heterogenous observations. Besides its flexibility, an important appealing feature of our proposal is analytical tractability: we are, indeed, able to determine some relevant distributional properties and a posterior characterization that is also the key for devising an efficient Markov chain Monte Carlo sampler. For illustrative purposes, we specialize our general results to a class of dependent extended gamma processes. We finally display a few numerical examples, including both simulated and real two-sample datasets: these allow us to identify the effect of a borrowing strength phenomenon and provide evidence of the effectiveness of the prior to deal with datasets for which the proportional hazards assumption does not hold true. Supplementary materials for this article are available online.