The Role of Sample Size to Attain Statistically Comparable Groups – A Required Data Preprocessing Step to Estimate Causal Effects With Observational Data

Background: Propensity score methods provide data preprocessing tools to remove selection bias and attain statistically comparable groups - the first requirement when attempting to estimate causal effects with observational data. Although guidelines exist on how to remove selection bias when groups in comparison are large, not much is known on how to proceed when one of the groups in comparison, for example, a treated group, is particularly small, or when the study also includes lots of observed covariates (relative to the treated group's sample size). Objectives: This article investigates whether propensity score methods can help us to remove selection bias in studies with small treated groups and large amount of observed covariates. Measures: We perform a series of simulation studies to study factors such as sample size ratio of control to treated units, number of observed covariates and initial imbalances in observed covariates between the groups of units in comparison, that is, selection bias. Results: The results demonstrate that selection bias can be removed with small treated samples, but under different conditions than in studies with large treated samples. For example, a study design with 10 observed covariates and eight treated units will require the control group to be at least 10 times larger than the treated group, whereas a study with 500 treated units will require at least, only, two times bigger control group. Conclusions: To confirm the usefulness of simulation study results for practice, we carry out an empirical evaluation with real data. The study provides insights for practice and directions for future research.