Adjustment of Anticipatory Covariates in Retrospective Surveys: An Expected Likelihood Approach

We address an inference issue where the value of a covariate is measured at the date of the survey but is used to explain behavior that has occurred long before the survey. This causes bias because the value of the covariate does not follow the temporal order of events. We propose an expected likelihood approach to adjust for such bias and illustrate it with data on the effects of educational level achieved by the time of marriage on risks of divorce. For individuals with anticipatory educational level (whose reported educational level was completed after marriage), conditional probabilities of having attained the reported level before marriage are computed. These are then used as weights in the expected likelihood to obtain adjusted estimates of relative risks. For our illustrative data set, the adjusted estimates of relative risks of divorce did not differ significantly from those obtained from anticipatory analysis that ignores the temporal order of events. Our results are slightly different from those in two other studies that analyzed the same data set in a Bayesian framework, though the studies are not fully comparable to each other.