For a study, researchers sought to present Bias Reduction through Analysis of Competing Events (BRACE), a method for reducing bias in the presence of residual confounding. BRACE was a novel method for adjusting for bias in proportional hazards models caused by residual confounding. Using standard simulation methods, they compared BRACE to Cox proportional hazards regression in the presence of an unmeasured confounder. Estimator distributions, bias, mean squared error (MSE), and coverage probability were investigated. Using the Veterans Affairs database, investigators then estimated the treatment effects of high versus low-intensity treatments in 36,630 prostate cancer, 4,069 lung cancer, and 7,117 head/neck cancer patients. They compared conventional multivariable Cox and propensity score (adjusted using inverse probability weighting) models to BRACE-adjusted estimates for cancer-specific mortality (CSM), noncancer mortality (NCM), and overall survival (OS). BRACE uniformly reduced bias and MSE in simulations with residual confounding. BRACE introduced a bias toward the null without bias, albeit with a lower MSE. BRACE significantly increased coverage probability but tended to overcorrect for effective but nontoxic treatments. More intensive treatments were associated with significantly lower CSM, NCM, and OS risks in each clinical cohort. BRACE reduced OS estimates, yielding more consistent results with randomized trials and meta-analyses. When residual confounding existed, BRACE reduced bias and MSE and represented a novel approach to improving treatment effect estimation in nonrandomized studies.
