  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.
