Temporal analysis of airborne particulate matter reveals a dose-rate effect on mortality in El Paso: indications of differential toxicity for different particle mixtures

One of two topics explored is the limitations of the daily average in summarizing pollutant hourly profiles. The daily average of hourly measurements of air pollutant constituents provides continuity with previous studies using monitoring technology that only provided the daily average. However, other summary statistics are needed that make better use of all available information in 24-hr profiles. The daily average reflects the total daily dose, obscuring hourly resolution of the dose rate. Air pollutant exposures with comparable total daily doses may have very different effects when occurring at high levels over a few hours as opposed to low levels over a longer time. Alternative data-based choices for summary statistics are provided using principal component analysis to capture the exposure dose rate, while preserving ease of interpretation. This is demonstrated using the earliest hourly particle concentration data available for El Paso from archived records of particulate matter (PM)10. In this way, a significant association between evening PM10 exposures and nonaccidental daily mortality is found in El Paso from 1992 to 1995, otherwise missed using the daily average. Secondly, the nature and, hence, effects of particles in the ambient aerosol during El Paso sandstorms is believed different from that of particles present during stillair conditions resulting from atmospheric temperature inversions. To investigate this, wind speed (ws) is used as a surrogate variable to label PM10 exposures as Low-ws (primarily fine particles), High-ws (primarily coarse particles), or Mid-ws (a mixture of fine and coarse particles). A High-ws evening is significantly associated with a 10% lower risk of mortality on the succeeding third day, as compared with comparable exposures at Low- or Mid-ws. Although this analysis cannot be used to form firm conclusions because it uses a very small data set, it demonstrates the limitations of the daily average and suggests differential toxicity for different particle compositions

Wavelet-based functional mixed models

Increasingly, scientific studies yield functional data, in which the ideal units of observation are curves and the observed data consist of sets of curves that are sampled on a fine grid. We present new methodology that generalizes the linear mixed model to the functional mixed model framework, with model fitting done by using a Bayesian wavelet-based approach. This method is flexible, allowing functions of arbitrary form and the full range of fixed effects structures and between-curve covariance structures that are available in the mixed model framework. It yields nonparametric estimates of the fixed and random-effects functions as well as the various between-curve and within-curve covariance matrices. The functional fixed effects are adaptively regularized as a result of the non-linear shrinkage prior that is imposed on the fixed effects' wavelet coefficients, and the random-effect functions experience a form of adaptive regularization because of the separately estimated variance components for each wavelet coefficient. Because we have posterior samples for all model quantities, we can perform pointwise or joint Bayesian inference or prediction on the quantities of the model. The adaptiveness of the method makes it especially appropriate for modelling irregular functional data that are characterized by numerous local features like peaks. Copyright 2006 Royal Statistical Society.