In Bayesian semi-parametric analyses of time-to-event data, non-parametric process priors are adopted for the baseline hazard function or the cumulative baseline hazard function for a given finite partition of the time axis. However, it would be controversial to suggest a general guideline to construct an optimal time partition. While a great deal of research has been done to relax the assumption of the fixed split times for other non-parametric processes, to our knowledge, no methods have been developed for a gamma process prior, which is one of the most widely used in Bayesian survival analysis. In this paper, we propose a new Bayesian framework for proportional hazards models where the cumulative baseline hazard function is modeled a priori by a gamma process. A key feature of the proposed framework is that the number and position of interval cutpoints are treated as random and estimated based on their posterior distributions.
Survival models are used to analyze time-to-event data in a variety of disciplines. Proportional hazard models provide interpretable parameter estimates, but proportional hazards assumptions are not always appropriate. Non-parametric models are more flexible but often lack a clear inferential framework. We propose a Bayesian tree partition model which is both flexible and inferential. Inference is obtained through the posterior tree structure and flexibility is preserved by modeling the the hazard function in each partition using a latent exponentiated Gaussian process. An efficient reversible…
A Bayesian Gamma-power-mixture survival regression model: predicting the recurrence of prostate cancer post-prostatectomy
University of Oxford（牛津大学）；Trinity College, Cambridge（剑桥大学三一学院）；Medical Research Council Laboratory of Molecular Biology（英国医学研究分子生物学实验室）；Medical University of Vienna（维也纳医科大学）
The stratified proportional hazards model represents a simple solution to account for heterogeneity within the data while keeping the multiplicative effect on the hazard function. Strata are typically defined a priori by resorting to the values taken by a categorical covariate. A general framework is proposed, which allows for the stratification of a generic accelerated life time model, including as a special case the Weibull proportional hazard model. The stratification is determined a posteriori by taking into account that strata might be characterized by different baseline survivals as well…
Cost-effectiveness analyses (CEAs) are at the center of health economic decision making. While these analyses help policy analysts and economists determine coverage, inform policy, and guide resource allocation, they are statistically challenging for several reasons. Cost and effectiveness are correlated and follow complex joint distributions which are difficult to capture parametrically. Effectiveness (often measured as increased survival time) and accumulated cost tends to be right-censored in many applications. Moreover, CEAs are often conducted using observational data with non-random trea…
Bayesian Semiparametric Model for Sequential Treatment Decisions with Informative Timing
Brown University（布朗大学）；University of Pennsylvania（宾夕法尼亚大学）；University of Southern California（南加州大学）；Children’s Hospital of Philadelphia（费城儿童医院）；Rutgers University（罗格斯大学）
In this paper, we propose a flexible cure rate model with frailty term in latent risk, which is obtained by incorporating a frailty term in risk function of latent competing causes. The number of competing causes of the event of interest follows negative binomial distribution and the frailty variable follows power variance function distribution, in which includes other frailty models such as gamma, positive stable and inverse Gaussian frailty models as special cases. The proposed model takes into account the presence of covariates and right-censored survival data suitable for populations with …
A bivariate cure copula model with zero-inflated gamma frailty for right-censored data
Graduate Institute for Advanced Studies, SOKENDAI（SOKENDAI 高级研究研究生院）；Institute of Statistical Mathematics（统计数学研究所）；School of Informatics and Data Science, Hiroshima University（广岛大学信息科学与数据科学学院）
Tree-based methods are popular nonparametric tools in studying time-to-event outcomes. In this article, we introduce a novel framework for survival trees and ensembles, where the trees partition the dynamic survivor population and can handle time-dependent covariates. Using the idea of randomized tests, we develop generalized time-dependent Receiver Operating Characteristic (ROC) curves for evaluating the performance of survival trees. The tree-building algorithm is guided by decision-theoretic criteria based on ROC, targeting specifically for prediction accuracy. To address the instability is…
Health economic evaluations often require predictions of survival rates beyond the follow-up period. Parametric survival models can be more convenient for economic modelling than the Cox model. The generalized gamma (GG) and generalized F (GF) distributions are extensive families that contain almost all commonly used distributions with various hazard shapes and arbitrary complexity. In this study, we present a new SAS macro for implementing a wide variety of flexible parametric models including the GG and GF distributions and their special cases, as well as the Gompertz distribution. Proper cu…
Survival models incorporating random effects to account for unmeasured heterogeneity are being increasingly used in biostatistical and applied research. Specifically, unmeasured covariates whose lack of inclusion in the model would lead to biased, inefficient results are commonly modelled by including a subject-specific (or cluster-specific) frailty term that follows a given distribution (e.g. Gamma or log-Normal). Despite that, in the context of parametric frailty models little is known about the impact of misspecifying the baseline hazard, the frailty distribution, or both. Therefore, our ai…
As cancer patient survival improves, late effects from treatment are becoming the next clinical challenge. Chemotherapy and radiotherapy, for example, potentially increase the risk of both morbidity and mortality from second malignancies and cardiovascular disease. To provide clinically relevant population-level measures of late effects, it is of importance to (1) simultaneously estimate the risks of both morbidity and mortality, (2) partition these risks into the component expected in the absence of cancer and the component due to the cancer and its treatment, and (3) incorporate the multiple…
A new class of survival frailty models based on the Generalized Inverse-Gaussian (GIG) distributions is proposed. We show that the GIG frailty models are flexible and mathematically convenient like the popular gamma frailty model. Furthermore, our proposed class is robust and does not present some computational issues experienced by the gamma model. By assuming a piecewise-exponential baseline hazard function, which gives a semiparametric flavour for our frailty class, we propose an EM-algorithm for estimating the model parameters and provide an explicit expression for the information matrix. …
Laplacian-P-splines for shared Gamma frailty models applied to clustered right-censored time-to-event data
Department of Neurodegeneration Diagnostics, University Hospital Bialystok, Poland（比亚韦斯托克医院神经退行性疾病诊断系）；Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat), Data Science Institute, Hasselt University, Belgium（哈瑟尔特大学生物统计与统计生物信息学跨大学研究所（I-BioStat））；Global Health Institute, Family Medicine and Population Health, University of Antwerp, Belgium（安特卫普大学全球健康学院）
