Supplementary Table from Bias Reduction through Analysis of Competing Events (BRACE) Correction to Address Cancer Treatment Selection Bias in Observational Data
ARTICLE ABSTRACTCancer treatments can paradoxically appear to reduce the risk of noncancer mortality in observational studies, due to residual confounding. Here we introduce a method, Bias Reduction through Analysis of Competing Events (BRACE), to reduce bias in the presence of residual confounding.
BRACE is a novel method for adjusting for bias from residual confounding in proportional hazards models. Using standard simulation methods, we compared BRACE with Cox proportional hazards regression in the presence of an unmeasured confounder. We examined estimator distributions, bias, mean squared error (MSE), and coverage probability. We then estimated treatment effects of high versus low intensity treatments in 36,630 prostate cancer, 4,069 lung cancer, and 7,117 head/neck cancer patients, using the Veterans Affairs database. We analyzed treatment effects on cancer-specific mortality (CSM), noncancer mortality (NCM), and overall survival (OS), using conventional multivariable Cox and propensity score (adjusted using inverse probability weighting) models, versus BRACE-adjusted estimates.
In simulations with residual confounding, BRACE uniformly reduced both bias and MSE. In the absence of bias, BRACE introduced bias toward the null, albeit with lower MSE. BRACE markedly improved coverage probability, but with a tendency toward overcorrection for effective but nontoxic treatments. For each clinical cohort, more intensive treatments were associated with significantly reduced hazards for CSM, NCM, and OS. BRACE attenuated OS estimates, yielding results more consistent with findings from randomized trials and meta-analyses.
BRACE reduces bias and MSE when residual confounding is present and represents a novel approach to improve treatment effect estimation in nonrandomized studies.