9th International symposium on epidemiology in occupational health: book of abstracts. Cincinnati, OH: U.S. Department of Health and Human Services, Public Health Service, Centers for Disease Control and Prevention, National Institute for Occupational Safety and Health, 1992 Sep; :50
As epidemiologists, we are generally inclined to consider more credible those associations showing a stronger exposure-response relation, such as higher relative risks or rate ratios. Higher parameter estimates look particularly credible, because one usually exercises care to avoid sources of upward bias, such as bias from selection or misclassification or confounding. Whereas the "higher estimate" approach may often work in practice, such a criterion for credibility may, however, not have general validity and it may actually be in contradiction with a likelihood-based approach. There is a potential conflict between a "naive" approach based on the magnitude of parameter estimates and a "statistical" criterion based on maximization of the likelihood function. It is likely that most epidemiologists believe that the two approaches are equivalent or that they may at the most show trivial differences of no practical relevance. The goal of this presentation is to illustrate, by way of examples, situations in which there may be inconsistencies between the two approaches. In the examples, based on regression models with both published and artificial data, the maximum likelihood estimate for exposure-lag parameters was obtained by fitting models to lagged exposure with different values of the lag. In this way, it was possible to compare the behavior of the lag-likelihood statistics with that of the relative risk. The examples show that a higher estimate of the relative risk may be accompanied by an increase in the degree of its uncertainty, in which case the "higher estimate" criterion may not agree with the likelihood. The results of this exercise suggest that the "estimate" criterion may not be valid and that, once we can exclude sources of bias, epidemiologic inference should be based on the likelihood function.