DECOMPOSITION OF REGRESSION ESTIMATORS TO EXPLORE THE INFLUENCE OF "UNMEASURED" TIME-VARYING CONFOUNDERS

In environmental epidemiology, exposure X and health outcome Y vary in space and time. We present a method to diagnose the possible influence of unmeasured confounders U on the estimated effect of X on Y and to propose several approaches to robust estimation. The idea is to use space and time as proxy measures for the unmeasured factors U. We start with the time series case where X and Y are continuous variables at equally-spaced times and assume a linear model. We define matching estimator b(u)s that correspond to pairs of observations with specific lag u. Controlling for a smooth function of time, St, using a kernel estimator is roughly equivalent to estimating the association with a linear combination of the b(u)s with weights that involve two components: the assumptions about the smoothness of St and the normalized variogram of the X process. When an unmeasured confounder U exists, but the model otherwise correctly controls for measured confounders, the excess variation in b(u)s is evidence of confounding by U. We use the plot of b(u)s versus lag u, lagged-estimator-plot (LEP), to diagnose the influence of U on the effect of X on Y. We use appropriate linear combination of b(u)s or extrapolate to b(0) to obtain novel estimators that are more robust to the influence of smooth U. The methods are extended to time series log-linear models and to spatial analyses. The LEP plot gives us a direct view of the magnitude of the estimators for each lag u and provides evidence when models did not adequately describe the data.

A Nonstationary Negative Binomial Time Series with Time-Dependent Covariates: Enterococcus Counts in Boston Harbor

Boston Harbor has had a history of poor water quality, including contamination by enteric pathogens. We conduct a statistical analysis of data collected by the Massachusetts Water Resources Authority (MWRA) between 1996 and 2002 to evaluate the effects of court-mandated improvements in sewage treatment. Motivated by the ineffectiveness of standard Poisson mixture models and their zero-inflated counterparts, we propose a new negative binomial model for time series of Enterococcus counts in Boston Harbor, where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predictor. Without further restrictions, this function is not identifiable in the presence of time-dependent covariates; consequently we use a basis orthogonal to the space spanned by the covariates and use penalized quasi-likelihood (PQL) for estimation. We conclude that Enterococcus counts were greatly reduced near the Nut Island Treatment Plant (NITP) outfalls following the transfer of wastewaters from NITP to the Deer Island Treatment Plant (DITP) and that the transfer of wastewaters from Boston Harbor to the offshore diffusers in Massachusetts Bay reduced the Enterococcus counts near the DITP outfalls.

Ozone and Mortality: A Meta-Analysis of Time-Series Studies and Comparison to a Multi-City Study (The National Morbidity, Mortality, and Air Pollution Study)

While many time-series studies of ozone and daily mortality identified positive associations,others yielded null or inconclusive results. We performed a meta-analysis of 144 effect estimates from 39 time-series studies, and estimated pooled effects by lags, age groups,cause-specific mortality, and concentration metrics. We compared results to estimates from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS), a time-series study of 95 large U.S. cities from 1987 to 2000. Both meta-analysis and NMMAPS results provided strong evidence of a short-term association between ozone and mortality, with larger effects for cardiovascular and respiratory mortality, the elderly, and current day ozone exposure as compared to other single day lags. In both analyses, results were not sensitive to adjustment for particulate matter and model specifications. In the meta-analysis we found that a 10 ppb increase in daily ozone is associated with a 0.83 (95% confidence interval: 0.53, 1.12%) increase in total mortality, whereas the corresponding NMMAPS estimate is 0.25%(0.12, 0.39%). Meta-analysis results were consistently larger than those from NMMAPS,indicating publication bias. Additional publication bias is evident regarding the choice of lags in time-series studies, and the larger heterogeneity in posterior city-specific estimates in the meta-analysis, as compared with NMAMPS.