Sensitivity Analyses for Nonignorable Selection Bias When Estimating Subgroup Parameters in Nonprobability Samples

Music City Center 

Selection bias in survey estimates is a major concern, for both non-probability samples and probability samples with low response rates. The proxy-pattern mixture model (PPMM) has been proposed as a method for conducting a sensitivity analysis that allows selection to depend on survey outcomes of interest, i.e., assuming a nonignorable selection mechanism. Indices based on the PPMM have been proposed and used to quantify the potential for non-ignorable nonresponse or selection bias, including the SMUB for means and the MUBP for proportions. These methods require information from a reference data source, such as a large probability-based survey, with summary-level auxiliary information for the target population of interest (means, variances, and covariances of the auxiliary variables). To this point, the SMUB/MUBP measures have exclusively been used to estimate bias in overall population-level estimates. Extension to domain-level estimates is straightforward if the reference data source contains the domain indicator so that population-level margins within the domain of interest can be calculated.

However, interest may often lie in subgroups for which population-level summaries are not available. This will happen in cases where the domain indicator is observed on the survey only (not in the reference data source) and can also happen when the goal is estimation within intersectional subgroups for which stable/reliable population-level estimates of auxiliary variables may not be available. To combat this issue, we propose creating nonignorable selection weights based on the PPMM and using these weights for domain estimation and subsequent calculation of the SMUB/MUBP within subgroups.

These PPMM selection weights rely on a single sensitivity parameter that ranges from 0 to 1 and captures a range of selection mechanisms, from ignorable to an "extreme" non-ignorable mechanism where selection depends only on the outcome of interest. The PPMM selection weights are based on the re-expression of the PPMM as a selection model, using the known equivalence between pattern-mixture models and selection models. In this talk, we briefly describe the re-expression of the PPMM as a selection model and illustrate the use of the novel non-ignorable selection weights to estimate various subgroup quantities using the Census Household Pulse Survey under a range of assumptions on the selection mechanism.

proxy pattern-mixture model

domain estimation