# Blending of Probability and Non-Probability Samples: Applications to a Survey of Military Caregivers

## TL;DR

This paper develops novel statistical methods to combine probability and non-probability samples, improving inference accuracy for small subpopulations, demonstrated through a survey of military caregivers with enhanced insights and reduced bias.

## Contribution

The paper introduces new weighting techniques for blending probability and non-probability samples, addressing bias and variance issues in small subpopulation surveys.

## Key findings

- Blended samples yield stronger conclusions about caregiver hardships.
- Proposed methods improve estimate precision while controlling bias.
- Simulation studies validate the effectiveness of the blending techniques.

## Abstract

Probability samples are the preferred method for providing inferences that are generalizable to a larger population. However, when a small (or rare) subpopulation is the group of interest, this approach is unlikely to yield a sample size large enough to produce precise inferences. Non-probability (or convenience) sampling often provides the necessary sample size to yield efficient estimates, but selection bias may compromise the generalizability of results to the broader population. Motivating the exposition is a survey of military caregivers; our interest is focused on unpaid caregivers of wounded, ill, or injured servicemembers and veterans who served in the US armed forces following September 11, 2001. An extensive probability sampling effort yielded only 72 caregivers from this subpopulation. Therefore, we consider supplementing the probability sample with a convenience sample from the same subpopulation, and we develop novel methods of statistical weighting that may be used to combine (or blend) the samples. Our analyses show that the subpopulation of interest endures greater hardships than caregivers of veterans with earlier dates of service, and these conclusions are discernably stronger when blended samples with the proposed weighting schemes are used. We conclude with simulation studies that illustrate the efficacy of the proposed techniques, examine the bias-variance trade-off encountered when using inadequately blended data, and show that the gain in precision provided by the convenience sample is lower in circumstances where the outcome is strongly related to the auxiliary variables used for blending.