Triggering Myocardial Infarction by Marijuana

Breslow (1981, Biometrika 68, 73-84) has shown that the Mantel-Haenszel odds ratio is a consistent estimator of a common odds ratio in sparse stratifications. For cohort studies, however, estimation of a common risk ratio or risk difference can be of greater interest. Under a binomial sparse-data model, the Mantel-Haenszel risk ratio and risk difference estimators are consistent in sparse stratifications, while the maximum likelihood and weighted least squares estimators are biased. Under Poisson sparse-data models, the Mantel-Haenszel and maximum likelihood rate ratio estimators have equal asymptotic variances under the null hypothesis and are consistent, while the weighted least squares estimators are again biased; similarly, of the common rate difference estimators the weighted least squares estimators are biased, while the estimator employing "Mantel-Haenszel" weights is consistent in sparse data. Variance estimators that are consistent in both sparse data and large strata can be derived for all the Mantel-Haenszel estimators.

The case-crossover study design is a method to assess the effect of transient exposures on the risk of onset of acute events. Control information for each case is based on his/her past exposure experience, and a self-matched analysis is conducted. Empiric evaluation of five approaches to the analysis of case-crossover data from a study of heavy physical exertion and acute myocardial infarction onset is shown. The data presented are from the Onset Study, a case-crossover study of the determinants of myocardial infarction onset conducted in 45 centers from August 1989 to October 1992. In model 1, exactly one control period (matched on clock-time) was sampled per case. In models 2-4, up to 25 control periods were sampled, and the effect of clock-time on the baseline hazard of infarction was modeled. In model 5, a census of the person-time experienced by each subject over the year preceding the infarction was sampled. The 95% confidence interval for model 1 was 2.7 times wider, and the relative efficiency, defined as v infinity/vM, where vM represents the asymptotic variance estimate of the estimated log relative risk with M control periods sampled per case, was only about 14% of model 5. In models 2-4, the efficiency increased with the number of control periods, regardless of the modeling assumptions. Even with many control periods sampled, models 2-4 achieved only half the efficiency of model 5. The control sampling strategy in any given case-crossover study should be selected with the trade-offs between precision and potential biases of the estimates in mind.