Bayesian Adjustment of Anticipatory Covariates in Analyzing Retrospective Data

In retrospective surveys, records on important variables such as the respondent's educational level and social class refer to what is achieved by the date of the survey. Such variables are then used as covariates in investigations of behavior such as marriage and divorce in life segments that have occurred before the survey. To what extent can any change in the behavior be attributed to the misclassification of respondents across the various levels of the anticipatory variable? To what extent do they reflect real differences in the behavior across the levels? The connection is obtained by a Bayesian adjustment, by specifying a continuous-time Markov model for the incompletely observed time-varying anticipatory covariates, and by implementing standard Bayesian data augmentation techniques. The issues are illustrated by estimating effects of educational level on risks of divorce in a multiplicative piecewise-constant hazard model. Results show that ignoring the time-inconsistency of anticipatory variables may seriously plague the analyses because the relative risks across the anticipatory educational level are overestimated.