Models and Software Development For Interval-Censored Data

Interval-censored time-to-event data occur naturally in studies of diseases where the symptoms are not directly observable, and periodic clinical examinations are required for detection. Due to the lack of well-established procedures, interval-censored data have been conventionally treated as right-censored data, however, this introduces bias at the first place. This dissertation focuses on methodological research and software development for interval-censored data. Specifically, it consists of three projects. The first project is to create an R package for regression analysis and survival curve estimation of interval-censored data based on several published papers by our research team. In the second project, a Bayesian semiparametric proportional hazards model with spatial random effect is developed for spatially correlated interval-censored data. In the third project, we propose a multivariate frailty model for clustered interval-censored failure times, which is analogous to a mixed model in regression analysis

A mixed model approach for structured hazard regression

The classical Cox proportional hazards model is a benchmark approach to analyze continuous survival times in the presence of covariate information. In a number of applications, there is a need to relax one or more of its inherent assumptions, such as linearity of the predictor or the proportional hazards property. Also, one is often interested in jointly estimating the baseline hazard together with covariate effects or one may wish to add a spatial component for spatially correlated survival data. We propose an extended Cox model, where the (log-)baseline hazard is weakly parameterized using penalized splines and the usual linear predictor is replaced by a structured additive predictor incorporating nonlinear effects of continuous covariates and further time scales, spatial effects, frailty components, and more complex interactions. Inclusion of time-varying coefficients leads to models that relax the proportional hazards assumption. Nonlinear and time-varying effects are modelled through penalized splines, and spatial components are treated as correlated random effects following either a Markov random field or a stationary Gaussian random field. All model components, including smoothing parameters, are specified within a unified framework and are estimated simultaneously based on mixed model methodology. The estimation procedure for such general mixed hazard regression models is derived using penalized likelihood for regression coefficients and (approximate) marginal likelihood for smoothing parameters. Performance of the proposed method is studied through simulation and an application to leukemia survival data in Northwest England

Bayesian modeling of clustered competing risks survival times with spatial random effects

n some studies, survival data are arranged spatially such as geographical regions. Incorporating spatial associationin these data not only can increase the accuracy and efficiency of the parameter estimation, but it also investigatesthe spatial patterns of survivorship. In this paper, we considered a Bayesian hierarchical survival model in thesetting of competing risks for the spatially clustered HIV/AIDS data. In this model, a Weibull Parametric distributionwith the spatial random effects in the form of county-failure type-level was used. A multivariate intrinsic conditionalautoregressive (MCAR) distribution was employed to model the areal spatial random effects. Comparison amongcompeting models was performed by the deviance information criterion and log pseudo-marginal likelihood. Weillustrated the gains of our model through the simulation studies and application to the HIV/AIDS data

spBayesSurv: Fitting Bayesian Spatial Survival Models Using R

Spatial survival analysis has received a great deal of attention over the last 20 years due to the important role that geographical information can play in predicting survival. This paper provides an introduction to a set of programs for implementing some Bayesian spatial survival models in R using the package spBayesSurv. The function survregbayes includes the three most commonly-used semiparametric models: proportional hazards, proportional odds, and accelerated failure time. 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. Time-dependent covariates are allowed under the piecewise constant assumption. Both georeferenced and areally observed spatial locations are handled via frailties. Model fit is assessed with conditional Cox-Snell residual plots, and model choice is carried out via the log pseudo marginal likelihood, the deviance information criterion and the WatanabeAkaike information criterion. The accelerated failure time frailty model with a covariatedependent baseline is included in the function frailtyGAFT. In addition, the package also provides two marginal survival models: proportional hazards and linear dependent Dirichlet process mixtures, where the spatial dependence is modeled via spatial copulas. Note that the package can also handle non-spatial data using non-spatial versions of the aforementioned models

Geoadditive hazard regression for interval censored survival times

The Cox proportional hazards model is the most commonly used method when analyzing the impact of covariates on continuous survival times. In its classical form, the Cox model was introduced in the setting of right-censored observations. However, in practice other sampling schemes are frequently encountered and therefore extensions allowing for interval and left censoring or left truncation are clearly desired. Furthermore, many applications require a more flexible modeling of covariate information than the usual linear predictor. For example, effects of continuous covariates are likely to be of nonlinear form or spatial information is to be included appropriately. Further extensions should allow for time-varying effects of covariates or covariates that are themselves time-varying. Such models relax the assumption of proportional hazards. We propose a regression model for the hazard rate that combines and extends the above-mentioned features on the basis of a unifying Bayesian model formulation. Nonlinear and time-varying effects as well as the baseline hazard rate are modeled by penalized splines. Spatial effects can be included based on either Markov random fields or stationary Gaussian random fields. The model allows for arbitrary combinations of left, right and interval censoring as well as left truncation. Estimation is based on a reparameterisation of the model as a variance components mixed model. The variance parameters corresponding to inverse smoothing parameters can then be estimated based on an approximate marginal likelihood approach. As an application we present an analysis on childhood mortality in Nigeria, where the interval censoring framework also allows to deal with the problem of heaped survival times caused by memory effects. In a simulation study we investigate the effect of ignoring the impact of interval censored observations

Bayesian Semi- and Non-parametric Analysis for Spatially Correlated Survival 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. The analysis of spatial survival data is challenged by the presence of spatial dependence and censoring for survival times. Accurately modeling the risk factors and geographical pattern that explain the differences in survival is particularly of interest. Within this dissertation, the first chapter reviews commonlyused baseline priors, semiparametric and nonparametric Bayesian survival models and recent approaches for accommodating spatial dependence, both conditional and marginal. The last three chapters contribute three flexible survival models: (1) a proportional hazards model with areal-level covariate-adjusted frailties with application to county-level breast cancer survival data, (2) a marginal Bayesian nonparametric model for time to disease arrival of threatened amphibian populations, and (3) a generalized accelerated failure time model with spatial intrinsic conditionally autoregressive frailties with application to county-level prostate cancer data. An R package spBayesSurv is developed to examine all the proposed models along with some traditional spatial survival models

Childhood mortality in sub-Saharan Africa : cross-sectional insight into small-scale geographical inequalities from Census data

Objectives To estimate and quantify childhood mortality, its spatial correlates and the impact of potential correlates using recent census data from three sub-Saharan African countries (Rwanda, Senegal and Uganda), where evidence is lacking. Design Cross-sectional. Setting Nation-wide census samples from three African countries participating in the 2010 African Census round. All three countries have conducted recent censuses and have information on mortality of children under 5 years. Participants 111 288 children under the age of 5 years in three countries. Primary and secondary outcome measures Under-five mortality was assessed alongside potential correlates including geographical location (where children live), and environmental, bio-demographic and socioeconomic variables. Results Multivariate analysis indicates that in all three countries the overall risk of child death in the first 5 years of life has decreased in recent years (Rwanda: HR=0.04, 95% CI 0.02 to 0.09; Senegal: HR=0.02 (95% CI 0.02 to 0.05); Uganda: HR=0.011 (95% CI 0.006 to 0.018). In Rwanda, lower deaths were associated with living in urban areas (0.79, 0.73, 0.83), children with living mother (HR=0.16, 95% CI 0.15 to 0.17) or living father (HR=0.38, 95% CI 0.36 to 0.39). Higher death was associated with male children (HR=1.06, 95% CI 1.02 to 1.08) and Christian children (HR=1.14, 95% CI 1.05 to 1.27). Children less than 1 year were associated with higher risk of death compared to older children in the three countries. Also, there were significant spatial variations showing inequalities in children mortality by geographic location. In Uganda, for example, areas of high risk are in the south-west and north-west and Kampala district showed a significantly reduced risk. Conclusions We provide clear evidence of considerable geographical variation of under-five mortality which is unexplained by factors considered in the data. The resulting under-five mortality maps can be used as a practical tool for monitoring progress within countries for the Millennium Development Goal 4 to reduce under-five mortality in half by 2015

BayesSPsurv: An R Package to Estimate Bayesian (Spatial) Split-Population Survival Models

Survival data often include a fraction of units that are susceptible to an event of interest as well as a fraction of “immune” units. In many applications, spatial clustering in unobserved risk factors across nearby units can also affect their survival rates and odds of becoming immune. To address these methodological challenges, this article introduces our BayesSPsurv R-package, which fits parametric Bayesian Spatial split-population survival (cure) models that can account for spatial autocorrelation in both subpopulations of the user \u27s time-to-event data. Spatial autocorrelation is modeled with spatially weighted frailties, which are estimated using a conditionally autoregressive prior. The user can also fit parametric cure models with or without nonspatial i.i.d. frailties, and each model can incorporate time-varying covariates. BayesSPsurv also includes various functions to conduct pre-estimation spatial autocorrelation tests, visualize results, and assess model performance, all of which are illustrated using data on post-civil war peace survival