Abstract
Multilevel regression and poststratification (MRP) has surged in popularity for population inference using survey samples. The method consists of two stages: First, fitting a regularized model that regresses the outcome on poststratification variables; second, predicting the outcome using the regularized model and aggregating the predictions to make population inferences. Existing MRP methods mostly focus on settings where the joint distribution of the poststratifiers is known in the population. However, in practice, such data information is often not available; instead, we are provided with the margins of the poststratifiers. Motivated by this challenge, we propose an adapted MRP in which we model both the survey outcome that we would like to estimate in the population and the population sizes of subgroups formed by the poststratifiers. We consider Poisson and negative binomial models for the population sizes of subgroups when the number of poststratifiers is small and Bayesian additive regression trees when there are many poststratifying variables. We apply the adapted MRP to estimate the proportion of viral load suppression and means of mental and physical health scales among persons with HIV in New York City using the 2018-2021 wave of the Community Health Advisory and Information Network survey, in which sampling and in-person data collection were disrupted by the COVID-19 pandemic.