Statistical analysis
The analytical methods were developed and adopted by all four teams in a common protocol. The protocol includes the specifications for selection of monitoring stations, as well as quality assurance and quality control procedures for data collection and for health outcomes and air pollutants to be included in the analysis. Generalized linear modeling was used to model daily health outcomes, with natural spline smoothers (Burnett et al. 2004; Wood 2006) for filtering out seasonal patterns and long-term trends in daily mortality, as well as temperature and relative humidity. We also included an adjustment for the day of the week and dichotomous variables relevant to individual cities if available, such as public holidays (Hong Kong) and extreme weather conditions (Wuhan). In an attempt to minimize autocorrelation, which would bias the standard errors, the aim of the core model was for partial autocorrelation function plots to have coefficients in absolute values < 0.1 for the first 2 lag days. Randomness of residuals was also considered in selecting the most appropriate models. If these criteria were not met, other methods were used to reduce autocorrelation, such as the inclusion of explanatory variables to model influenza epidemics and the addition of autoregression terms. If there were special periods with extra variations for which the core model could not account, an additional spline smoother was included. Air pollutant concentrations were entered into the core model to assess the health effects of specific pollutants. Exposure at the current day (lag 0), a 2-day average of lag 0 and lag 1 days (lag 0–1), and a 5-day average of lag 0 to lag 4 days (lag 0–4) were examined. For each pollutant, the excess risk of mortality with the 95% confidence interval (CI) per 10-μg/m3 increase in average concentration at lag 0–1 was calculated. However, for brevity’s sake, point estimates with p-values could be used to describe sets of effects.