Analysis of time‐to‐event data using Cox's proportional hazards (PH) model is ubiquitous in scientific research. A sample is taken from the population of interest and covariate information is collected on everyone. If the event of interest is rare and covariate information is difficult to collect, the nested case‐control (NCC) design reduces costs with minimal impact on inferential precision. Under PH, application of the Cox model to data from a NCC sample provides consistent estimation of the hazard ratio. However, under non‐PH, the finite‐sample estimates corresponding to the Cox estimator depend on the number of controls sampled and the censoring distribution. We propose two estimators based on a binary predictor of interest: one recovers the estimand corresponding to the Cox model under a simple random sample, while the other recovers an estimand that does not depend on the censoring distribution. We derive the asymptotic distribution and provide finite‐sample variance estimators.
Survival models are used to analyze time-to-event data in a variety of disciplines. Proportional hazard models provide interpretable parameter estimates, but proportional hazard assumptions are not always appropriate. Non-parametric models are more flexible but often lack a clear inferential framework. We propose a Bayesian treed hazards partition model that is both flexible and inferential. Inference is obtained through the posterior tree structure and flexibility is preserved by modeling the log-hazard function in each partition using a latent Gaussian process. An efficient reversible jump Markov chain Monte Carlo algorithm is accomplished by marginalizing the parameters in each partition element via a Laplace approximation. Consistency properties for the estimator are established. The method can be used to help determine subgroups as well as prognostic and/or predictive biomarkers in time-to-event data. The method is compared with some existing methods on simulated data and a liver cirrhosis dataset.
more » « less- NSF-PAR ID:
- 10491177
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 80
- Issue:
- 1
- ISSN:
- 0006-341X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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