Selecting an exposure lag period

In epidemiology, there is an inclination to consider more credible the larger estimates of exposure effect. For example, higher relative risks or rate ratios are often emphasized as a criterion for choosing among various hypothesized exposure-lag values. An alternative criterion for this choice might be based on a goodness-of-fit measure. We present examples, based on hypothetical data, in which an exposure-lag parameter is estimated by trial and error fitting: we compare the behavior of the likelihood-ratio goodness-of-fit statistic obtained over the assigned values of the parameter with that of the relative risk. We show that there can be inconsistencies between the highest-estimate and likelihood-based goodness-of-fit criteria. Concern about the validity of the highest-estimate criterion prompts us to recommend that this criterion not be used for the estimation of exposure-weighting parameters, which should preferably be based on a priori biological knowledge or on goodness-of-fit criteria.