Methodological Issues In Time Series Studies Of Changes In Environmental Exposure Between Successive Days And Health

Abstract

Introduction: There is growing interest in evaluating the association of changes or rate of changes in exposure between successive days and health outcomes in time series studies. This is because physiological systems may respond to changes in environmental stimuli as well as absolute exposure concentrations. Several studies have investigated this for temperature exposure and few for air pollution exposure. However, statistical issues related to modelling changes (delta) together with absolute concentrations in time series context have yet to be discussed and our study aims to fill this gap for particulate matter with aero-dynamic diameter < 10 μg/m3 (PM10) pollution. Methods: The change metrics (delta = lag0 PM10 - lag1 PM10) and proposed alternative metrics for delta were defined, which included relative delta=delta/lag1 PM10, absolute value of delta and the maximum of delta and zero. The mathematical equivalence of potential identifiable models for delta with the unconstrained distributed lag (UDL) model for lags 0 and 1 was shown and the problem of potential collinearity discussed. Using simulation studies we 1) assessed the impact of measurement error and missing data on analysis using the delta and absolute metrics 2) compared the relative model fit and properties of the alternative and the original change metrics. Conclusions: Our results showed that 1) measurement error could have more severe impact on the delta metrics than the absolute metrics as reflected by larger variance of the former with increasing measurement error 2) the relative efficiency of the approach imputing missing data was much larger than analysis excluding them particularly as the missing rate increased. Thus handling of missing data should be an important first step for models using the delta metrics. 3) the relative delta (proportional change) had the strongest correlation with delta, reasonably similar model fit to the standard UDL model and arguably greater biological plausibility.