The case-crossover design via penalized regression

The case-crossover design is an attractive alternative to the classical case-control design which can be used to study the onset of acute events if the risk factors of interest vary in time. By comparing exposures within cases at different time periods, the case-crossover design does not rely on control subjects which can be difficult to acquire. However, using the standard method of maximum likelihood, resulting risk estimates can be heavily biased when the prevalence to risk factors is very low (or very high).

To overcome the problem of low risk factor prevalences, penalized conditional logistic regression via the lasso (least absolute shrinkage and selection operator) has been proposed in the literature as well as related methods such as the Firth correction. We apply and compare several penalized regression approaches in the context of a case-crossover analysis of the European Study of Severe Cutaneous Adverse Reactions (EuroSCAR; 1997-2001).

Out of 30 drugs, standard methods only correctly classified 17 drugs (including some highly implausible risk estimates), while penalized methods correctly classified 22 drugs.

Penalized methods generally yield better risk classifications and much more plausible risk estimates for the EuroSCAR study than standard methods. As these novel techniques can be easily implemented using available R packages, we encourage routine use of penalized conditional logistic regression for case-crossover data.