We then compute the share of FHBC cases within each of the 20 groups, which we denote as [P.sub.BC, j].
Our approach results in a (weighted) usual care comparison sample that is very similar to the FHBC sample on all observable characteristics (see Table 1).
With FHBC and weighted usual care samples that are nearly identical on the dimensions accounted for by matching variables, the comparison of outcome measures between the two samples is straightforward.
To address the concern that unobserved differences in risk could still bias the estimated effects of FHBC care using the propensity score approach, we also conduct an instrumental variable (IV) analysis.
An instrumental variable should (1) have a strong effect on FHBC use; and (2) only influence the outcome measures through its effect on FHBC use (after other covariates are held fixed).
In a simple linear probability model of being in the birth center as a function of the instrument and controls, the instrument is a strong predictor of FHBC use with an F-statistic of 321.5.
For smoking, lung disease, and herpes, however, we find statistically significant evidence that a lower prevalence of these risk factors is associated with greater distance from the FHBC. If such a relationship holds for unobserved risk factors as well (i.e., unobserved risk is higher near the FHBC), the IV estimates would be biased in the direction of unfavorable birth center effects.
For continuous outcome measures, we use two-stage least squares (2SLS) with logit-predicted birth center status as the instrument, where the logit equation contains all control variables and distance to the FHBC.
In turn, some cases that had been dropped for perfectly predicting FHBC status in the propensity score analysis were retained in the IV analysis.