Summary
This paper develops a Bayesian semiparametric approach to the extended hazard model, with generalization to high-dimensional spatially-grouped data. County-level spatial correlation is accommodated marginally through the normal transformation model of Li and Lin (2006), using a correlation structure implied by an intrinsic conditionally autoregressive prior. Efficient Markov chain Monte Carlo algorithms are developed, especially applicable to fitting very large, highly-censored areal survival data sets. Per-variable tests for proportional hazards, accelerated failure time, and accelerated hazards are efficiently carried out with and without spatial correlation through Bayes factors. The resulting reduced, interpretable spatial models can fit significantly better than a standard additive Cox model with spatial frailties.
The article develops a Bayesian nonparametric reliability model for recurrent events where failure and truncated time-to-failure density shape is regressed on past maintenance decisions: perfect repair and minimal repair. By comparing the system interfailure lifetime distributions after minimal and perfect repair, we are able to test the minimal repair assumption of "good as old." Interfailure hazard functions after perfect and minimal repairs are estimated, shedding light on departures from minimal repair. The method is illustrated both on simulated data as well as failure time data from air-conditioning units at the South Texas Nuclear Operating Company near Bay City, Texas. This article has supplementary material online.
Motivated by data gathered in an oral health study, we propose a Bayesian nonparametric approach for population-averaged modeling of correlated time-to-event data, when the responses can only be determined to lie in an interval obtained from a sequence of examination times and the determination of the occurrence of the event is subject to misclassification. The joint model for the true, unobserved time-to-event data is defined semiparametrically; proportional hazards, proportional odds, and accelerated failure time (proportional quantiles) are all fit and compared. The baseline distribution is modeled as a flexible tailfree prior. The joint model is completed by considering a parametric copula function. A general misclassification model is discussed in detail, considering the possibility that different examiners were involved in the assessment of the occurrence of the events for a given subject across time. We provide empirical evidence that the model can be used to estimate the underlying time-to-event distribution and the misclassification parameters without any external information about the latter parameters. We also illustrate the effect on the statistical inferences of neglecting the presence of misclassification.
Summary
The paper extends the latent promotion time cure rate marker model of Kim, Xi and Chen for right‐censored survival data. Instead of modelling the cure rate parameter as a deterministic function of risk factors, they assumed that the cure rate parameter of a targeted population is distributed over a number of ordinal levels according to the probabilities governed by the risk factors. We propose to use a mixture of linear dependent tail‐free processes as the prior for the distribution of the cure rate parameter, resulting in a latent promotion time cure rate model. This approach provides an immediate answer to perhaps one of the most pressing questions ‘what is the probability that a targeted population has high proportions (e.g. greater than 70%) of being cured?’. The approach proposed can accommodate a rich class of distributions for the cure rate parameter, while centred at gamma densities. The algorithms that are developed in this work allow the fitting of latent promotion time cure rate models with several survival models for metastatic tumour cells.
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