Sensitivity Analyses for Nonignorable Selection Bias When Estimating Subgroup Parameters in Nonprobability Samples: A Weighting Approach
Selection bias in survey estimates is a major concern, affecting both nonprobability samples and probability samples with low response rates. The proxy-pattern mixture model (PPMM) offers a method for conducting a sensitivity that assumes a nonignorable selection mechanism, where selection depends on survey outcomes of interest. This approach requires summary-level auxiliary information for the target population of interest from a reference data source. While PPMM methods have been successfully applied to derive overall population-level estimates, extension to domain-level estimates is challenging when population-level summaries for the specific subgroup are unavailable. This occurs when the domain indicator is observed only in the survey, or for complex intersectional subgroups where stable/reliable population-level auxiliary variable estimates are unavailable. To combat this issue, we propose a novel approach: creating nonignorable selection weights based on the PPMM based on a re-expression of the PPMM as a selection model. These weights can be directly applied to calculate domain-level estimates, circumventing the need for domain-specific population-level summaries of auxiliary variables. They rely on a single sensitivity parameter (ranging from 0 to 1) that captures a spectrum of nonresponse assumptions, ranging from an ignorable mechanism to an extreme nonignorable mechanism. We discuss differences in weight construction for continuous versus binary outcomes, describe the necessary assumptions for these weights to produce informative domain-level estimates, and illustrate properties through simulation. We then apply the approach to the Census Household Pulse Survey to estimate various subgroup quantities under a range of assumptions on the selection mechanism.
Rebecca R. Andridge, PhD
The Ohio State University
College of Public Health, Division of Biostatistics
Associate Dean for Undergraduate Studies
Professor of Biostatistics
Dr. Andridge's research is focused on imputation methods for missing data, primarily when missingness is driven by the missing values themselves (missing not at random), and on measures of selection bias for nonprobability samples. She also works on statistical challenges that arise in analysis of data from group-randomized trials. She collaborates with researchers across campus, including the Institute for Behavioral Medicine Research, the Nisonger Center for Excellence in Developmental Disabilities, and The OSU Comprehensive Cancer Center, and serves as Lead Methodologist for several state-sponsored population-based surveys. She is an Elected Fellow of the American Statistical Association (2020).