Bayesian nonparametric models for spatially indexed data of mixed type

We develop Bayesian nonparametric models for spatially indexed data of mixed type. Our work is motivated by challenges that occur in environmental epidemiology, where the usual presence of several confounding variables that exhibit complex interactions and high correlations makes it difficult to estimate and understand the effects of risk factors on health outcomes of interest. The modeling approach we adopt assumes that responses and confounding variables are manifestations of continuous latent variables, and uses multivariate Gaussians to jointly model these. Responses and confounding variables are not treated equally as relevant parameters of the distributions of the responses only are modeled in terms of explanatory variables or risk factors. Spatial dependence is introduced by allowing the weights of the nonparametric process priors to be location specific, obtained as probit transformations of Gaussian Markov random fields. Confounding variables and spatial configuration have a similar role in the model, in that they only influence, along with the responses, the allocation probabilities of the areas into the mixture components, thereby allowing for flexible adjustment of the effects of observed confounders, while allowing for the possibility of residual spatial structure, possibly occurring due to unmeasured or undiscovered spatially varying factors. Aspects of the model are illustrated in simulation studies and an application to a real data set

Health Information and Health Outcomes: An Application of the Regression Discontinuity Design to the 1995 UK Contraceptive Pill Scare Case

This paper provides a general formulation of the regression discontinuity (RD) design and shows its general applicability to many epidemiological problems. It then applies the RD method to estimate the effects of the 1995 pill scare in the UK, using individual birth records and aggregate monthly statistics. The results show that, following the announce- ment of the health warning on the þird generation" pill, conception rates increased by about 7%, with a 9% increase in abortion rates and a 6-7% rise in birth rates. No e®ect was found on still births, very low birth weight, sex ratios, or average birth weight. There is evidence of a slight increase in the rates of low birth weight births and multiple births and of a considerable reduction in the rate of births with congenital anomalies. Hetero- geneity by mother's age and social class is very pronounced, with most of the e®ects being experienced by women aged less than 25 and of lower socioeconomic status

Classification Loss Function for Parameter Ensembles in Bayesian Hierarchical Models

Parameter ensembles or sets of point estimates constitute one of the cornerstones of modern statistical practice. This is especially the case in Bayesian hierarchical models, where different decision-theoretic frameworks can be deployed to summarize such parameter ensembles. The estimation of these parameter ensembles may thus substantially vary depending on which inferential goals are prioritised by the modeller. In this note, we consider the problem of classifying the elements of a parameter ensemble above or below a given threshold. Two threshold classification losses (TCLs) --weighted and unweighted-- are formulated. The weighted TCL can be used to emphasize the estimation of false positives over false negatives or the converse. We prove that the weighted and unweighted TCLs are optimized by the ensembles of unit-specific posterior quantiles and posterior medians, respectively. In addition, we relate these classification loss functions on parameter ensembles to the concepts of posterior sensitivity and specificity. Finally, we find some relationships between the unweighted TCL and the absolute value loss, which explain why both functions are minimized by posterior medians.Comment: Submitted to Probability and Statistics Letter

Quantile regression with aggregated data

Administrative data can contain a wealth of information for empirical research. Just to cite two examples, administrative data on schools can be used to study pupils’ educational attainments while hospital data can be useful for health research. However, access to administrative information is often restricted to aggregated data and this can lead to biased results. The estimation bias caused by using aggregated rather than individual data is known as the ecological bias. In this paper we consider for the first time this issue in the context of quantile regressions. We show how data can be aggregated to obtain unbiased estimation of quantile regressions with categorical covariates and how the bias can be reduced when researchers are interested to estimate quantile regression where some of the covariates are continuous

Diagram-based Analysis of Causal Systems (DACS): elucidating inter-relationships between determinants of acute lower respiratory infections among children in sub-Saharan Africa.

Effective interventions require evidence on how individual causal pathways jointly determine disease. Based on the concept of systems epidemiology, this paper develops Diagram-based Analysis of Causal Systems (DACS) as an approach to analyze complex systems, and applies it by examining the contributions of proximal and distal determinants of childhood acute lower respiratory infections (ALRI) in sub-Saharan Africa