Daniela Cocchi

Multiple testing on standardized mortality ratios: a Bayesian hierarchical model for FDR estimation

The analysis of large data sets of standardized mortality ratios (SMRs), obtained by collecting observed and expected disease counts in a map of contiguous regions, is a first step in descriptive epidemiology to detect potential environmental risk factors. A common situation arises when counts are collected in small areas, that is, where the expected count is very low, and disease risks underlying the map are spatially correlated. Traditional p-value-based methods, which control the false discovery rate (FDR) by means of Poisson p-values, might achieve small sensitivity in identifying risk in small areas. This problem is the focus of the present work, where a Bayesian approach which performs a test to evaluate the null hypothesis of no risk over each SMR and controls the posterior FDR is proposed. A Bayesian hierarchical model including spatial random effects to allow for extra-Poisson variability is implemented providing estimates of the posterior probabilities that the null hypothesis of absence of risk is true. By means of such posterior probabilities, an estimate of the posterior FDR conditional on the data can be computed. A conservative estimation is needed to achieve the control which is checked by simulation. The availability of this estimate allows the practitioner to determine nonarbitrary FDR-based selection rules to identify high-risk areas according to a preset FDR level. Sensitivity and specificity of FDR-based rules are studied via simulation and a comparison with p-value-based rules is also shown. A real data set is analyzed using rules based on several FDR levels.

A stratified model for the assessment of meteorologically adjusted trends of surface ozone

We consider the problem of assessing long-term trends of ozone concentrations measured on a single site located in an urban area. Among the many methods proposed in the literature to eliminate the confounding effect of changing weather conditions, we employ a stratification of daily maxima based on regression trees. Within each stratum conditional independence and Weilbull distribution are assumed for maxima. Long-term trend is defined non-parametrically by the sequence of yearly medians. Models are estimated following the Bayesian approach. The alternative assumptions of common and stratum specific trends are compared and a model with common trend for all strata is selected for the analyzed real dataset. The conditional independence assumption is checked by the comparison with a model including an autoregressive component.