ABSTRACT

We address a problem in inference from retrospective studies where the value of a variable is measured at the date of the survey but is used as covariate to events that have occurred long before the survey. This causes problem because the value of the current-date (anticipatory) covariate does not follow the temporal order of events. We propose a dynamic Bayesian approach for modelling jointly the anticipatory covariate and the event of interest, and allowing the effects of the anticipatory covariate to vary over time. The issues are illustrated with data on the effects of education attained by the survey-time on divorce risks among Swedish men. The overall results show that failure to adjust for the anticipatory nature of education leads to elevated relative risks of divorce across educational levels. The results are partially in accordance with previous findings based on analyses of the same data set. More importantly, our findings provide new insights in that the bias due to anticipatory covariates varies over marriage duration.

摘要

我们从回顾性研究中解决了一个推断问题，其中变量的值是在调查日期测量的，但被用作调查之前很久发生的事件的协变量。这会导致问题，因为当前日期（预期）协变量的值不遵循事件的时间顺序。我们提出了一种动态贝叶斯方法，用于联合建模预期协变量和感兴趣的事件，并允许预期协变量的影响随时间变化。这些问题通过调查时间获得的教育对瑞典男性离婚风险的影响的数据进行了说明。总体结果表明，未能根据教育的预期性质进行调整会导致不同教育水平的离婚相对风险升高。结果部分符合先前基于对同一数据集的分析的发现。更重要的是，我们的研究结果提供了新的见解，即由于预期协变量导致的偏差随婚姻持续时间而变化。