Fixed factors that modify the effects of time-varying factors: applying the case-only approach

The effects of air pollution or weather on mortality may be stronger in susceptible groups. Conventional investigation of such effect modification through interaction terms in time-series regression analysis depends on hard-to-verify modeling assumptions, and can be computationally unwieldy. As an alternative, we investigate the use of case-only approaches originally proposed for studying gene-environment interactions.

We consider an investigation of whether persons of low socio-economic status (SES) are more susceptible to the effect of high outside temperatures on mortality. If low SES persons are more prevalent among deaths on hot days than on days with more moderate temperatures, then this suggests the group is more susceptible. Extending the case-only theory developed for gene-environment interactions allows this to be described more quantitatively.

Conventionally based analysis estimated that mortality in the Sao Paulo rose by 2.3% (SE 0.3%) for each degree of increase in outside temperature above 20 degrees C. This effect was greater by 1.11% (SE 0.72) in the lowest compared with highest quartile of SES. Case-only analysis estimated the difference in effect to be 1.14% (SE 0.72).

The simplicity and reduced assumptions of the case-only approach provide an advantage over conventional analysis, although the approach gives information only on modification, not main effects.