Balancing versus modelling in weighted analysis of non-randomised studies with survival outcomes: A simulation study

Weighting methods are widely used for causal effect estimation in non-randomised studies. In general, these methods use the propensity score (PS), the probability of receiving the treatment given the covariates, to arrive at the respective weights. All of these "modelling" methods actually optimize prediction of the respective outcome, which is, in the PS model, treatment assignment. However, this does not match with the actual aim of weighting, which is eliminating the association between covariates and treatment assignment. In the "balancing" approach, covariates are thus balanced directly by solving systems of numerical equations, explicitly without fitting a PS model. To compare modelling, balancing and hybrid approaches to weighting we performed a large simulation study for a binary treatment and a survival outcome. For maximal practical relevance all simulation parameters were selected after a systematic review of medical studies that used PS methods for analysis. We also introduce a new hybrid method that uses the idea of the covariate balancing propensity score and matching weights, thus avoiding extreme weights. In addition, we present a corrected robust variance estimator for some of the methods. Overall, our simulations results indicate that balancing approach methods work worse than expected. However, among the considered balancing methods, entropy balancing consistently outperforms the variance balancing approach. All methods estimating the average treatment effect in the overlap population perform well with very little bias and small standard errors even in settings with misspecified propensity score models. Finally, the coverage using the standard robust variance estimator was too high for all methods, with the proposed corrected robust variance estimator improving coverage in a variety of settings.