A Case Study for Modelling Cancer Incidence Using Bayesian Spatio‐Temporal Models

Researchers familiar with spatial models are aware of the challenge of choosing the level of spatial aggregation. Few studies have been published on the investigation of temporal aggregation and its impact on inferences regarding disease outcome in space–time analyses. We perform a case study for modelling individual disease outcomes using several Bayesian hierarchical spatio‐temporal models, while taking into account the possible impact of spatial and temporal aggregation. Using longitudinal breast cancer data from South East Queensland, Australia, we consider both parametric and non‐parametric formulations for temporal effects at various levels of aggregation. Two temporal smoothness priors are considered separately; each is modelled with fixed effects for the covariates and an intrinsic conditional autoregressive prior for the spatial random effects. Our case study reveals that different model formulations produce considerably different model performances. For this particular dataset, a classical parametric formulation that assumes a linear time trend produces the best fit among the five models considered. Different aggregation levels of temporal random effects were found to have little impact on model goodness‐of‐fit and estimation of fixed effects.     

Producing ratio measures of effect with quantitative microbial risk assessment

Estimating the risk of infections or other outcomes incident to pathogen exposure is a primary goal of quantitative microbial risk assessment (QMRA). Such estimates are useful to predict population-level risks, to evaluate exposures based on normative or tolerable risk guidelines, and to interpret the likely public health relevance of microbial measurements in environmental media. To evaluate alternative control measures (interventions), ratio estimates of effect (e.g., odds and risk ratios) are needed that are more broadly interpretable in the health sciences and consistent with convention in epidemiology. In this paper, we propose a general method for estimating widely used ratio measures of effect derived from stochastic QMRA approaches, including the generation of appropriate confidence intervals. Such QMRA-derived ratios can be used as a basis for evaluating interventions via hypothesis testing and for inclusion in systematic reviews and meta-analyses in a form consistent with risk estimation approaches commonly used in epidemiology.     

Statistical inference for Cox proportional hazards models with a diverging number of covariates

For statistical inference on regression models with a diverging number of covariates, the existing literature typically makes sparsity assumptions on the inverse of the Fisher information matrix. Such assumptions, however, are often violated under Cox proportion hazards models, leading to biased estimates with under-coverage confidence intervals. We propose a modified debiased lasso method, which solves a series of quadratic programming problems to approximate the inverse information matrix without posing sparse matrix assumptions. We establish asymptotic results for the estimated regression coefficients when the dimension of covariates diverges with the sample size. As demonstrated by extensive simulations, our proposed method provides consistent estimates and confidence intervals with nominal coverage probabilities. The utility of the method is further demonstrated by assessing the effects of genetic markers on patients' overall survival with the Boston Lung Cancer Survival Cohort, a large-scale epidemiology study investigating mechanisms underlying the lung cancer.