Haiming Zhou

MODELLING COUNTY LEVEL BREAST CANCER SURVIVAL DATA USING A COVARIATE-ADJUSTED FRAILTY PROPORTIONAL HAZARDS MODEL.

Understanding the factors that explain differences in survival times is an important issue for establishing policies to improve national health systems. Motivated by breast cancer data arising from the Surveillance Epidemiology and End Results program, we propose a covariate-adjusted proportional hazards frailty model for the analysis of clustered right-censored data. Rather than incorporating exchangeable frailties in the linear predictor of commonly-used survival models, we allow the frailty distribution to flexibly change with both continuous and categorical cluster-level covariates and model them using a dependent Bayesian nonparametric model. The resulting process is flexible and easy to fit using an existing R package. The application of the model to our motivating example showed that, contrary to intuition, those diagnosed during a period of time in the 1990s in more rural and less affluent Iowan counties survived breast cancer better. Additional analyses showed the opposite trend for earlier time windows. We conjecture that this anomaly has to be due to increased hormone replacement therapy treatments prescribed to more urban and affluent subpopulations.

Bayesian Spatial Survival Models

Survival analysis has received a great deal of attention as a subfield of Bayesian nonparametrics over the last 50 years. In particular, the fitting of survival models that allow for sophisticated correlation structures has become common due to computational advances in the 1990s, in particular Markov chain Monte Carlo techniques. Very large, complex spatial datasets can now be analyzed accurately including the quantification of spatiotemporal trends and risk factors. This chapter reviews four nonparametric priors on baseline survival distributions in common use, followed by a catalogue of semiparametric and nonparametric models for survival data. Generalizations of these models allowing for spatial dependence are then discussed and broadly illustrated. Throughout, practical implementation through existing software is emphasized.

Generalized accelerated failure time spatial frailty model for arbitrarily censored data

Flexible incorporation of both geographical patterning and risk effects in cancer survival models is becoming increasingly important, due in part to the recent availability of large cancer registries. Most spatial survival models stochastically order survival curves from different subpopulations. However, it is common for survival curves from two subpopulations to cross in epidemiological cancer studies and thus interpretable standard survival models can not be used without some modification. Common fixes are the inclusion of time-varying regression effects in the proportional hazards model or fully nonparametric modeling, either of which destroys any easy interpretability from the fitted model. To address this issue, we develop a generalized accelerated failure time model which allows stratification on continuous or categorical covariates, as well as providing per-variable tests for whether stratification is necessary via novel approximate Bayes factors. The model is interpretable in terms of how median survival changes and is able to capture crossing survival curves in the presence of spatial correlation. A detailed Markov chain Monte Carlo algorithm is presented for posterior inference and a freely available function frailtyGAFT is provided to fit the model in the R package spBayesSurv. We apply our approach to a subset of the prostate cancer data gathered for Louisiana by the surveillance, epidemiology, and end results program of the National Cancer Institute.

Marginal Bayesian nonparametric model for time to disease arrival of threatened amphibian populations

The global emergence of Batrachochytrium dendrobatidis (Bd) has caused the extinction of hundreds of amphibian species worldwide. It has become increasingly important to be able to precisely predict time to Bd arrival in a population. The data analyzed herein present a unique challenge in terms of modeling because there is a strong spatial component to Bd arrival time and the traditional proportional hazards assumption is grossly violated. To address these concerns, we develop a novel marginal Bayesian nonparametric survival model for spatially correlated right-censored data. This class of models assumes that the logarithm of survival times marginally follow a mixture of normal densities with a linear-dependent Dirichlet process prior as the random mixing measure, and their joint distribution is induced by a Gaussian copula model with a spatial correlation structure. To invert high-dimensional spatial correlation matrices, we adopt a full-scale approximation that can capture both large- and small-scale spatial dependence. An efficient Markov chain Monte Carlo algorithm with delayed rejection is proposed for posterior computation, and an R package spBayesSurv is provided to fit the model. This approach is first evaluated through simulations, then applied to threatened frog populations in Sequoia-Kings Canyon National Park.

The Expanding Burden of Elevated Blood Pressure in China: Evidence From Jiangxi Province, 2007-2010.

AbstractElevated blood pressure (BP) as a risk factor accounts for the biggest burden of disease worldwide and in China. This study aimed to estimate attributed mortality and life expectancy (LE) to elevated BP in Jiangxi province between 2007 and 2010.BP and mortality data (2007 and 2010 inclusive) were obtained from the National Chronic Diseases and Risk Factors Surveillance Survey and Disease Surveillance Points system, respectively. Population-attributable fraction used in comparative risk assessment of the Global Burden of Disease study 2010 were followed to quantify the attributed mortality to elevated BP, subsequently life table methods were applied to estimate its effects on LE. Uncertainty analysis was conducted to get 95% uncertainty intervals (95% uncertainty interval [UI]) for each outcome.There are 35,482 (95% UI: 31,389–39,928) and 47,842 (42,323–53,837) deaths in Jiangxi province were caused by elevated BP in 2007 and 2010, respectively. 2.24 (1.87–2.65) years of LE would be gained if all the attributed deaths were eliminated in 2007, and increased to 3.04 (2.52–3.48) in 2010. If the mean value of elevated BP in 2010 was decreased by 5 and 10 mm Hg, 5324 (4710–5991) and 11,422 (10,104–12,853) deaths would be avoided, with 0.41 (0.37–0.48) and 0.85 (0.71–1.09) years of LE gained, respectively.The deaths attributable to elevated BP in Jiangxi province has increased by 35% from 2007 to 2010, with 0.8 years of LE loss, suggesting the necessity to take actions to control BP in Chinese population.

Bayes factors for choosing among six common survival models

A super model that includes proportional hazards, proportional odds, accelerated failure time, accelerated hazards, and extended hazards models, as well as the model proposed in Diao et al. (Biometrics 69(4):840–849, 2013) accounting for crossed survival as special cases is proposed for the purpose of testing and choosing among these popular semiparametric models. Efficient methods for fitting and computing fast, approximate Bayes factors are developed using a nonparametric baseline survival function based on a transformed Bernstein polynomial. All manner of censoring is accommodated including right, left, and interval censoring, as well as data that are observed exactly and mixtures of all of these; current status data are included as a special case. The method is tested on simulated data and two real data examples. The approach is easily carried out via a new function in the spBayesSurv R package.

A unified framework for fitting Bayesian semiparametric models to arbitrarily censored survival data, including spatially-referenced data

ABSTRACT A comprehensive, unified approach to modeling arbitrarily censored spatial survival data is presented for the three most commonly used semiparametric models: proportional hazards, proportional odds, and accelerated failure time. Unlike many other approaches, all manner of censored survival times are simultaneously accommodated including uncensored, interval censored, current-status, left and right censored, and mixtures of these. Left-truncated data are also accommodated leading to models for time-dependent covariates. Both georeferenced (location exactly observed) and areally observed (location known up to a geographic unit such as a county) spatial locations are handled; formal variable selection makes model selection especially easy. Model fit is assessed with conditional Cox–Snell residual plots, and model choice is carried out via log pseudo marginal likelihood (LPML) and deviance information criterion (DIC). Baseline survival is modeled with a novel transformed Bernstein polynomial prior. All models are fit via a new function which calls efficient compiled C++ in the R package spBayesSurv. The methodology is broadly illustrated with simulations and real data applications. An important finding is that proportional odds and accelerated failure time models often fit significantly better than the commonly used proportional hazards model. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.