How to perform prespecified subgroup analyses when using propensity score methods in the case of imbalanced subgroups.

Background: Looking for treatment-by-subset interaction on a right-censored outcome based on observational data using propensity-score (PS) modeling is of interest. However, there are still issues regarding its implementation, notably when the subsets are very imbalanced in terms of prognostic features and treatment prevalence.

Methods: We conducted a simulation study to compare two main PS estimation strategies, performed either once on the whole sample ("across subset") or in each subset separately ("within subsets"). Several PS models and estimands are also investigated. We then illustrated those approaches on the motivating example, namely, evaluating the benefits of facial nerve resection in patients with parotid cancer in contact with the nerve, according to pretreatment facial palsy.

Results: Our simulation study demonstrated that both strategies provide close results in terms of bias and variance of the estimated treatment effect, with a slight advantage for the "across subsets" strategy in very small samples, provided that interaction terms between the subset variable and other covariates influencing the choice of treatment are incorporated. PS matching without replacement resulted in biased estimates and should be avoided in the case of very imbalanced subsets.

Conclusions: When assessing heterogeneity in the treatment effect in small samples, the "across subsets" strategy of PS estimation is preferred. Then, either a PS matching with replacement or a weighting method must be used to estimate the average treatment effect in the treated or in the overlap population. In contrast, PS matching without replacement should be avoided in this setting.