Models for the relationship between ambient temperature and daily mortality

Ambient temperature is an important determinant of daily mortality that is of interest both in its own right and as a confounder of other determinants investigated using time-series regressions, in particular, air pollution. The temperature-mortality relationship is often found to be substantially nonlinear and to persist (but change shape) with increasing lag. We review and extend models for such nonlinear multilag forms.

Popular models for mortality by temperature at given lag include polynomial and natural cubic spline curves, and the simple but more easily interpreted linear thresholds model, comprising linear relationships for temperatures below and above thresholds and a flat middle section. Most published analyses that have allowed the relationship to persist over multiple lags have done so by assuming that spline or threshold models apply to mean temperature in several lag strata (e.g., lags 0-1, 2-6, and 7-13). However, more flexible models are possible, and a modeling framework using products of basis functions ("cross-basis" functions) suggests a wide range, some used previously and some new. These allow for stepped or smooth changes in the model coefficients as lags increase. Applying a range of models to data from London suggest evidence for relationships up to at least 2 weeks' lag, with smooth models fitting best but lag-stratified threshold models allowing the most direct interpretation.

A wide range of multilag nonlinear temperature-mortality relationships can be modeled. More awareness of options should improve investigation of these relationships and help control for confounding by them.