Giovanni Poli, Elena Fountzilas, Apostolia-Maria Tsimeridou, Peter Müller
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A multivariate Polya tree model for meta-analysis with event-time distributions.
We develop a nonparametric Bayesian prior for a family of random probability measures by extending the Polya tree ($\mbox{PT}$) prior to a joint prior for a set of probability measures $G_1,\dots ,G_n$, suitable for meta-analysis with event-time outcomes. In the application to meta-analysis, $G_i$ is the event-time distribution specific to study $i$. The proposed model defines a regression on study-specific covariates by introducing increased correlation for any pair of studies with similar characteristics. The desired multivariate $\mbox{PT}$ model is constructed by introducing a hierarchical prior on the conditional splitting probabilities in the $\mbox{PT}$ construction for each of the $G_i$. The hierarchical prior replaces the independent beta priors for the splitting probability in the PT construction with a Gaussian process prior for corresponding (logit) splitting probabilities across all studies. The Gaussian process is indexed by study-specific covariates, introducing the desired dependence with increased correlation for similar studies. The main feature of the proposed construction is (conditionally) conjugate posterior updating with commonly reported inference summaries for event-time data. The construction is motivated by a meta-analysis over cancer immunotherapy studies.
期刊介绍:
The International Biometric Society is an international society promoting the development and application of statistical and mathematical theory and methods in the biosciences, including agriculture, biomedical science and public health, ecology, environmental sciences, forestry, and allied disciplines. The Society welcomes as members statisticians, mathematicians, biological scientists, and others devoted to interdisciplinary efforts in advancing the collection and interpretation of information in the biosciences. The Society sponsors the biennial International Biometric Conference, held in sites throughout the world; through its National Groups and Regions, it also Society sponsors regional and local meetings.