Abstract
Distributed lag models, either for linear (DLM) or non-linear (DLNM) associations, represent an established methodological tool in time series analysis of environmental factors. Recent developments of this modelling framework allows extensions beyond time series data, for instance in study designs based on individual data. In this contribution, we illustrate an example of application in a case-crossover study of the effect of air pollution and temperature on respiratory mortality. Data include 410,728 deaths for respiratory causes occurring in England and Wales in 2001-2006. Control days were selected following a time-stratified design. Daily measures of ozone and mean temperature were assigned individually to each subject using modelled data on a 5-km grid. Odds ratios (OR) for the two exposures were estimated by conditional logistic regression including a DLM and a DLNM based on spline functions with lag periods up to 10 and 21 days, respectively. We also tested interactions with individual variables such as sex or socio-economic status. All analyses was performed in R with the package dlnm. The lag-response for ozone showed significant effects up to 8 days, with an overall cumulative linear OR of 1.010 (95%CI:1.005-1.014) for 10 ug/m3. The overall cumulative exposure-response of temperature displayed the classical U-shape, with OR of 1.94 (95%CI: 1.81-2.07) for 0°C and 7.80 (95%CI:3.65-16.67) for 28°C, compared to the minimum mortality temperature of 19°C. Neither sex nor socio-economic status show significant effect modifications. Information at the individual level, now more readily available for environmental studies, provides the opportunity to extend and improve epidemiological investigations. In this application we illustrate how the flexibility of DLM-DLNM can be extended to study designs based on individual data. Advantages and limitations if compared to the standard time series approach are discussed, together with statistical and computational aspects.
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