A practical approach to estimating the true effect of exposure despite imprecise exposure classification

Abstract

Accurate information on actual exposure to some possibly toxic agent usually is not available in long-term occupational studies. Any strategy for assigning exposure levels or categories necessarily results in misclassification, where some individuals classified as exposed have no real exposure and some individuals classified as not exposed have some exposure to the agent. Both misclassification errors serve to reduce the estimate of risk associated with exposure. The question arises, "How much does the true risk depart from the observed estimate given an assumed level of misclassification?" This paper quantifies the effect of such misclassification on several forms of standardized risk ratios. Our results express the true risk as a function of the apparent risk based on imprecise exposure classification and parameters representing the proportion of each of the groups that are correctly classified. In any practical situation, the apparent risk can be computed based on whatever classification scheme is being used. On the other hand, the proportions of the imprecisely classified groups actually exposed cannot. However, the investigator may have information or may make assumptions for likely ranges of values for these proportions. Given the apparent risk, estimated true risks can be calculated and plotted or represented in tabular form as a function of the proportions of actual exposure. The resulting graph or table enables the investigator to read off the range of possible true risk values based on what he is prepared to believe or what other information indicates about the range of proportions of misclassified subjects. For instance, results for a typical value of apparent risk of 1.8 show that the true risk may be twice the apparent risk with only 23% misclassification in each exposure group. The value of the true risk that would be necessary to be consistent with a given apparent risk increases rapidly as the extent of misclassification increases. We also show that, if the extent of misclassification is large, the apparent relative risk is close to 1.0 regardless of the actual value of the true risk. Therefore, a small apparent risk does not necessarily indicate that there is no occupational hazard.