  Our work was motivated by a recent study on birth defects of infants born to
pregnant women exposed to a certain medication for treating chronic diseases.
Outcomes such as birth defects are rare events in the general population, which
often translate to very small numbers of events in the unexposed group. As drug
safety studies in pregnancy are typically observational in nature, we control
for confounding in this rare events setting using propensity scores (PS). Using
our empirical data, we noticed that the estimated odds ratio for birth defects
due to exposure varied drastically depending on the specific approach used. The
commonly used approaches with PS are matching, stratification, inverse
probability weighting (IPW) and regression adjustment. The extremely rare
events setting renders the matching or stratification infeasible. In addition,
the PS itself may be formed via different approaches to select confounders from
a relatively long list of potential confounders. We carried out simulation
experiments to compare different combinations of approaches: IPW or regression
adjustment, with 1) including all potential confounders without selection, 2)
selection based on univariate association between the candidate variable and
the outcome, 3) selection based on change in effects (CIE). The simulation
showed that IPW without selection leads to extremely large variances in the
estimated odds ratio, which help to explain the empirical data analysis results
that we had observed. The simulation also showed that IPW with selection based
on univariate association with the outcome is preferred over IPW with CIE.
Regression adjustment has small variances of the estimated odds ratio
regardless of the selection methods used.
