Abstract
We consider Bayesian nonparametric inference in the right-censoring survival model, where modeling is made at the level of the hazard rate. We derive posterior limiting distributions for linear functionals of the hazard, and then for ‘many’ functionals simultaneously in appropriate multiscale spaces. As an application, we derive Bernstein–von Mises theorems for the cumulative hazard and survival functions, which lead to asymptotically efficient confidence bands for these quantities. Further, we show optimal posterior contraction rates for the hazard in terms of the supremum norm. In medical studies, a popular approach is to model hazards a priori as random histograms with possibly dependent heights. This and more general classes of arbitrarily smooth prior distributions are considered as applications of our theory. A sampler is provided for possibly dependent histogram posteriors. Its finite sample properties are investigated on both simulated and real data experiments.
Funding Statement
The first author gratefully acknowledges support from the Institut Universitaire de France (IUF) and from the ANR grant ANR-17-CE40-0001 (BASICS). The second author is (partly) financed by the Dutch Research Council (NWO), under Veni grant 192.087.
Acknowledgments
I. C. would like to thank Richard Nickl for insightful discussions, in particular pertaining to low regularities treatment. S. P. would like to thank Leonhard Held for drawing our attention to the median survival as a quantity of interest, and Judith Rousseau for a question on lower smoothness levels. The authors would also like to thank the Associate Editor and referees, as well as Bo Ning, for insightful comments.
Funding Statement
The first author gratefully acknowledges support from the Institut Universitaire de France (IUF) and from the ANR grant ANR-17-CE40-0001 (BASICS). The second author is (partly) financed by the Dutch Research Council (NWO), under Veni grant 192.087.
Acknowledgments
I. C. would like to thank Richard Nickl for insightful discussions, in particular pertaining to low regularities treatment. S. P. would like to thank Leonhard Held for drawing our attention to the median survival as a quantity of interest, and Judith Rousseau for a question on lower smoothness levels. The authors would also like to thank the Associate Editor and referees, as well as Bo Ning, for insightful comments.
Citation
Ismaël Castillo. Stéphanie van der Pas. "Multiscale Bayesian survival analysis." Ann. Statist. 49 (6) 3559 - 3582, December 2021. https://doi.org/10.1214/21-AOS2097
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