Health disparity research often evaluates health outcomes across subgroups. Multilevel regression and poststratification (MRP) is a popular approach for small subgroup estimation due to its ability to stabilize estimates by fitting multilevel models and to adjust for selection bias by poststratifying on auxiliary variables, which are population characteristics predictive of the analytic outcome. However, the granularity and quality of the estimates produced by MRP are limited by the availability of the auxiliary variables' joint distribution; data analysts often only have access to the marginal distributions. To overcome this limitation, we develop an integrative inference framework that embeds the estimation of population cell counts needed for poststratification into the MRP workflow: embedded MRP (EMRP). Under EMRP, we generate synthetic populations of the auxiliary variables before implementing MRP. All sources of estimation uncertainty are propagated with a fully Bayesian framework. Through simulation studies, we compare different methods and demonstrate EMRP's improvements over classical MRP on the bias-variance tradeoff to yield valid subpopulation inferences of interest. As an illustration, we estimate food insecurity prevalence among vulnerable groups in New York City by applying EMRP to the Longitudinal Survey of Wellbeing. We find that the improvement is primarily on subgroup estimation with efficiency gains.

翻译：多层次回归和后处理(MRP)是小分组估算的流行方法,因为它有能力通过安装多层次模型来稳定估计数,并适应辅助变数的附加变数的选择偏向,这些变数是预测分析结果的人口特征,但是,由MRP得出的估计数的颗粒性和质量受到辅助变数联合分布的可用性的限制;数据分析员往往只能取得边际分布;为了克服这一限制,我们制定了一个综合推论框架,将批准后所需人口单位数目的估算纳入MRP工作流程:嵌入的MRP(EMRP) 。根据EMRP,我们在实施MRP之前产生辅助变数的合成人口。所有估计不确定性的来源都通过完全的Bayesian框架加以传播。通过模拟研究,我们比较不同的方法,并显示EMRP在经典的偏差交易中比传统MRP的改进,从而产生有效的子群增益。我们估计的弱势群体粮食无保障程度,主要通过应用IMRP对长期收益的分组进行我们发现。