Studies of the health effects of air pollution such as the National Morbidity and Mortality Air Pollution Study (NMMAPS) relate changes in daily pollution to daily deaths in a sample of cities and calendar years. Generally, city-specific estimates are combined into regional and national estimates using two-stage models. Our two-stage analysis identifies effect modifiers of the relation between single-day lagged PM10 and daily mortality in people age 65 and older from the 50 largest NMMAPS cities. We build on the standard approach by "fractionating" city-specific analyses to produce month-year-city specific estimated air pollution effects (slopes) in Stage I. In Stage II, we identify potential effect modifiers via weighted regression and weighted regression trees with the estimated slopes as dependent variables and predictors such as temperature, relative humidity, CO, NO2, O3, SO2, season, year, and other city-specific characteristics.
Eckel, Sandrah P. and Louis, Thomas A., "IDENTIFYING EFFECT MODIFIERS IN AIR POLLUTION TIME-SERIES STUDIES USING A TWO-STAGE ANALYSIS" (June 2007). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 148.