Bias Reduction through Analysis of Competing Events (BRACE): A Novel Method to Mitigate Bias from Residual Confounding in Observational Data

ABSTRACT Purpose To introduce a method to mitigate bias from residual confounding in non-randomized data and examine its performance under varying conditions using simulated data. Methods We developed a method called Bias Reduction through Analysis of Competing Events (BRACE) based on a proportional relative hazards model. We followed recommended guidelines (ADEMP) established for the conduct of simulation studies. The primary estimand of interest was the treatment effect on the composite hazard for a primary or competing event. We compared the BRACE method to a standard Cox proportional hazards regression model in the presence of an unmeasured confounder, using a parametric (Weibull) simulation model. We examined estimator distributions, bias, mean squared error (MSE), and coverage probability for both methods using ridge, box-and-whisker, forest, and zip plots, respectively. Comparisons with a hypothetical validation estimate treating the confounder as measurable were also performed. Results We presented 16 simulation scenarios under varying parameters. In simulations where residual confounding was present, the BRACE method uniformly reduced both bias and MSE compared to standard Cox models. In the scenario of moderate bias with an effective but non-toxic treatment, MSE was 3.51×10 −2 with the standard model vs. 0.259×10 −2 with the BRACE method. In the absence of bias, the BRACE method introduced bias toward the null (2.90 x10 −2 ) compared to the standard method (0.331×10 −2 ), albeit with lower MSE (0.341 x10 −2 vs. 0.484 x10 −2 , respectively). Relative to the standard approach, the BRACE method markedly improved coverage probability, but with a tendency toward overcorrection in the case of the effective but non-toxic treatment. Conclusions were similar under different parameter assumptions. Conclusion The BRACE method can reduce bias and MSE in the setting of residual confounding.