Methodological approaches to the analysis of hierarchical studies of air pollution and respiratory health - examples from the CESAR study

Objectives: Many studies of air pollution and health are carried out over s everal geographical areas, and sometimes over several countries. This paper explores three approaches to analysis in such studies: a non hierarchical model, a two-stage analysis, and multilevel modelling. Illustrations are gi ven using a preliminary subset of data from the CESAR study. Design: The Ce ntral European Study on Air pollution and Respiratory Health (CESAR) was co nducted in 25 areas within six Central European countries, enrolling 20,271 schoolchildren. Pollution averages were calculated for each area. Associat ions between pollution and health outcomes were estimated under different m odels. Main results: A regression analysis of log FVC (forced vital capacit y) on PM10, ignoring the geographical hierarchy, estimated a significant me an drop in FVC (adjusted for confounders) of 2.2% (95% CI 0.5% to 1.3%), p= 0.007, from the area with the lowest PM10 to that with the highest. A multi level model (m/m),using data for all children, but with random effects at a rea and country level, estimated a drop of 2.8% (-0.6% to 6.1%), p=0.110. A two-stage analysis (mean log FVC, adjusted for confounders, was estimated for each area using regression, and these means then regressed on PM10) est imated a drop of 2.6% (-0.5% to 5.5%), p=0.101. Simulation exercises showed the non hierarchical method to be very inadequate in the context of the CE SAR study, with only half of all 95% confidence intervals for the estimated PM10 slope containing the true value (i.e., that used to create the simula ted data). The two-stage and multilevel modelling methods gave results whic h were substantially better, though both underperformed slightly All three methods appeared to give unbiased slope estimates. Conclusions: Acknowledge ment of hierarchical structures is essential in statistical inference - sta ndard errors can be substantially incorrect when they are ignored. Multilev el, random-effects models correctly address hierarchical structures, though having few units at higher levels can cause problems in convergence, espec ially where complex modelling is required. Two-stage analyses, acknowledgin g hierarchy, provide simple alternatives to random-effects models.