# The Impact of Confounder Selection in Propensity Scores for Rare Events Data - with Applications to Birth Defects

## TL;DR

This study examines how different confounder selection methods affect propensity score analyses in rare event settings, such as birth defects, revealing that certain approaches lead to more stable and reliable estimates.

## Contribution

It compares various confounder selection strategies in propensity score methods for rare events, highlighting the impact on variance and estimate stability through simulation and empirical data.

## Key findings

- IPW without confounder selection yields high variance in estimates.
- Selection based on univariate association improves IPW performance.
- Regression adjustment remains stable regardless of confounder selection method.

## Abstract

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.