The interpretation of exposure effect estimates in chronic air pollution studies

In this article we consider the interpretation of regression parameters used to represent 'chronic' or 'long-term' air pollution exposure effects. Although scientific interest typically lies in understanding such effects at the level of the individual, studies have generally employed a semi-ecological design; outcomes and confounder information are collected on individuals while exposure is only available at the aggregate-or group-level. A precise interpretation of results from a semi-ecological design must take into account the aggregated nature, both spatial and temporal, of the exposure measure. The most common analysis approach for assessing chronic exposure effects has been within the Cox proportional hazards model framework; specific analyses are tailored to accommodate the shortcomings of the available exposure information. We revisit the underlying assumptions of the Cox model and discuss the implications of two common aspects of chronic effects studies: time-dependent exposures and time-varying effects. Focusing on the consequences of temporal aggregation of exposure, we show that an estimate obtained from a time-aggregated semi-ecological design can correspond to very different underlying time-varying exposure and risk scenarios. Further, distinguishing which of these is correct is not possible from the semi-ecological data alone. Our goal is to highlight some statistical issues faced by existing studies of chronic air pollution effects, and aid in the development and planning of future studies.