Mortality displacement and Distributed Lag Models

Numerous time-series studies have investigated the association between daily mortality and daily ambient particulate air pollution concentrations (PM). The consensus from these studies is that increases in PM are associated with increases in daily mortality. However, it may be that increases in PM only hasten the deaths of individuals in a small, frail subset of the population whose longevity is short even in the absence of particulate air pollution. This hypothesis has been termed mortality displacement or harvesting. Distributed lag models (DLM) have been used to explore mortality effects of air pollution that are spread over multiple days, and DLM coefficients have been proposed as indicators of mortality displacement. We investigate statistical properties of DLM coefficients in the context of mortality displacement using simulation studies with frail population models. Our simulations use actual PM time series, as well as actual weather time series included as confounders. Our simulations show that DLM coefficients can have large bias when the mean lifetime of individuals in the frail subset of the population is more than a few weeks, and that the magnitude of this bias increases as the mean lifetime of individuals in the frail subset of the population increases. We conclude that DLM coefficients may be misleading as an indicator of mortality displacement, in the context of the frail population models that we explored