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

Tweedie Compound Poisson Models with Covariate-Dependent Random Effects for Multilevel Semicontinuous Data

Multilevel semicontinuous data occur frequently in medical, environmental, insurance and financial studies. Such data are often measured with covariates at different levels; however, these data have traditionally been modelled with covariate-independent random effects. Ignoring dependence of cluster-specific random effects and cluster-specific covariates in these traditional approaches may lead to ecological fallacy and result in misleading results. In this paper, we propose Tweedie compound Poisson model with covariate-dependent random effects to analyze multilevel semicontinuous data where covariates at different levels are incorporated at relevant levels. The estimation of our models has been developed based on the orthodox best linear unbiased predictor of random effect. Explicit expressions of random effects predictors facilitate computation and interpretation of our models. Our approach is illustrated through the analysis of the basic symptoms inventory study data where 409 adolescents from 269 families were observed at varying number of times from 1 to 17 times. The performance of the proposed methodology was also examined through the simulation studies.

Bayesian variable selection for the Cox regression model with spatially varying coefficients with applications to Louisiana respiratory cancer data

The Cox regression model is a commonly used model in survival analysis. In public health studies, clinical data are often collected from medical service providers of different locations. There are large geographical variations in the covariate effects on survival rates from particular diseases. In this paper, we focus on the variable selection issue for the Cox regression model with spatially varying coefficients. We propose a Bayesian hierarchical model which incorporates a horseshoe prior for sparsity and a point mass mixture prior to determine whether a regression coefficient is spatially varying. An efficient two-stage computational method is used for posterior inference and variable selection. It essentially applies the existing method for maximizing the partial likelihood for the Cox model by site independently first and then applying an Markov chain Monte Carlo algorithm for variable selection based on results of the first stage. Extensive simulation studies are carried out to examine the empirical performance of the proposed method. Finally, we apply the proposed methodology to analyzing a real dataset on respiratory cancer in Louisiana from the Surveillance, Epidemiology, and End Results (SEER) program.

Bayesian and Frequentist Analytical Approaches Using Log-Normal and Gamma Frailty Parametric Models for Breast Cancer Mortality

One of the major causes of death among females in Saudi Arabia is breast cancer. Newly diagnosed cases of breast cancer among the female population in Saudi Arabia is 19.5%. With this high incidence, it is crucial that we explore the determinants associated with breast cancer among the Saudi Arabia populace—the focus of this current study. The total sample size for this study is 8312 (8172 females and about 140 representing 1.68% males) patients that were diagnosed with advanced breast cancer. These are facility-based cross-sectional data collected over a 9-year period (2004 to 2013) from a routine health information system database. The data were obtained from the Saudi Cancer Registry (SCR). Both descriptive and inferential (Cox with log-normal and gamma frailties) statistics were conducted. The deviance information criterion (DIC), Watanabe–Akaike information criterion (WAIC), Bayesian information criterion (BIC), and Akaike information criterion were used to evaluate or discriminate between models. For all the six models fitted, the models which combined the fixed and random effects performed better than those with only the fixed effects. This is so because those models had smaller AIC and BIC values. The analyses were done using R and the INLA statistical software. There are evident disparities by regions with Riyadh, Makkah, and Eastern Province having the highest number of cancer patients at 28%, 26%, and 20% respectively. Grade II (46%) and Grade III (45%) are the most common cancer grades. Left paired site laterality (51%) and regional extent (52%) were also most common characteristics. Overall marital status, grade, and cancer extent increased the risk of a cancer patient dying. Those that were married had a hazard ratio of 1.36 (95% CI: 1.03–1.80) while widowed had a hazard ratio of 1.57 (95% CI: 1.14–2.18). Both the married and widowed were at higher risk of dying with cancer relative to respondents who had divorced. For grade, the risk was higher for all the levels, that is, Grade I (Well diff) (HR = 7.11, 95% CI: 3.32–15.23), Grade II (Mod diff) (HR = 7.89, 95% CI: 3.88–16.06), Grade III (Poor diff) (HR = 5.90, 95% CI (2.91–11.96), and Grade IV (Undiff) (HR = 5.44, 95% (2.48–11.9), relative to B-cell. These findings provide empirical evidence that information about individual patients and their region of residence is an important contributor in understanding the inequalities in cancer mortalities and that the application of robust statistical methodologies is also needed to better understand these issues well.

Bayesian proportional hazards model with latent variables

We consider a joint modeling approach that incorporates latent variables into a proportional hazards model to examine the observed and latent risk factors of the failure time of interest. An exploratory factor analysis model is used to characterize the latent risk factors through multiple observed variables. In commonly used confirmatory factor analysis, the number of latent variables and their observed indicators are specified prior to analysis. By contrast, the exploratory factor analysis model allows such information to be fully determined by the data. A Bayesian approach coupled with efficient sampling methods is developed to conduct statistical inference, and the performance of the proposed methodology is confirmed through simulations. The model is applied to a study on the risk factors of chronic kidney disease for patients with type 2 diabetes.

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.

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.