Analyzing Potential Non-Ignorable Selection Bias in an Off-Wave Mail Survey Implemented in a Long-Standing Panel Study.

Typical design-based methods for weighting probability samples rely on several assumptions, including the random selection of sampled units according to known probabilities of selection and ignorable unit nonresponse. If any of these assumptions are not met, weighting methods that account for the probabilities of selection, nonresponse, and calibration may not fully account for the potential selection bias in a given sample, which could produce misleading population estimates. This analysis investigates possible selection bias in the 2019 Health Survey Mailer (HSM), a sub-study of the longitudinal Health and Retirement Study (HRS). The primary HRS data collection has occurred in "even" years since 1992, but additional survey data collections take place in the "off-wave" odd years via mailed invitations sent to selected participants. While the HSM achieved a high response rate (83 percent), the assumption of ignorable probability-based selection of HRS panel members may not hold due to the eligibility criteria that were imposed. To investigate this possible non-ignorable selection bias, our analysis utilizes a novel analysis method for estimating measures of unadjusted bias for proportions (MUBP), introduced by Andridge et al. in 2019. This method incorporates aggregate information from the larger HRS target population, including means, variances, and covariances for key covariates related to the HSM variables, to inform estimates of proportions. We explore potential non-ignorable selection bias by comparing proportions calculated from the HSM under three conditions: ignoring HRS weights, weighting based on the usual design-based approach for HRS "off-wave" mail surveys, and using the MUBP adjustment. We find examples of differences between the weighted and MUBP-adjusted estimates in four out of ten outcomes we analyzed. However, these differences are modest, and while this result gives some evidence of non-ignorable selection bias, typical design-based weighting methods are sufficient for correcting for it and their use is appropriate in this case.