A recent multigenerational study of diethylstilbestrol and attention deficit hyperactivity disorder exhibited signs of both informative cluster size—the outcome was more prevalent in small families—and exposure misclassification—self‐report of familial diethylstilbestrol exposure was substantially mismeasured. Motivated by this, we study the effect of exposure misclassification when cluster size is potentially informative and, in particular, when misclassification is differential by cluster size. We find that: misclassification in an exposure that is related to cluster size induces informativeness when cluster size would otherwise be non‐informative; and misclassification that is differential by informative cluster size may attenuate, inflate or possibly reverse the sign of estimates. To mitigate these issues, we propose an observed likelihood correction for joint models of cluster size and outcomes, and an expected estimating equations correction. We evaluate these approaches in simulations and in application to the motivating data from the second Nurses Health Study, NHS II.

中文翻译：

---

关于暴露度分类错误和信息量大的相互作用

近期对己烯雌酚和注意缺陷多动障碍的多代研究显示，既有信息量大的迹象，也有小群体的结果，还有暴露分类错误，对家族己烯雌酚暴露的自我报告严重错误。因此，我们研究了当簇大小可能提供信息时，尤其是当错误分类因簇大小而异时，暴露分类错误的影响。我们发现：与簇大小相关的暴露的错误分类会在簇大小不具有信息性的情况下引起信息性；且由于信息类聚类大小不同而导致的错误分类可能会削弱，夸大或颠倒估计的符号。为了减轻这些问题，我们提出了针对集群大小和结果的联合模型的观测似然校正，以及预期的估计方程校正。我们在模拟中以及在第二次护士健康研究NHS II的激励数据应用中评估了这些方法。