Statistical methods for computing causal effect in single-arm trial with External Control Arm (ECA) assume no difference in outcome measurement between both arms. However, when the ECA is derived from routinely collected data, only proxy outcomes may be available, leading to potential misclassification and biased estimates. This study aimed to quantify the bias from ignoring binary outcome misclassification and propose a likelihood-based method to correct this bias

The proposed model relies on a validation study in which both proxy and reference outcomes are measured, to overcome the misclassification problem, and a joint likelihood estimation for the validation, ECA, and the prospective single-arm data. In addition to standard assumptions in indirect treatment comparisons, the proposed model requires a correctly specified outcome measurement error model that accounts for all variables contributing to non-differential measurement error. Simulations were performed to evaluate different performance metrics of usual approaches (i.e. uncorrected methods) and the proposed approach. Various scenarios were defined by varying sample sizes, specificity and sensitivity for the non-differential misclassification model. Five thousand simulations per scenario were performed. The performance metrics included both absolute and relative bias, empirical Standard Error (SE) and root mean square error, along with coverage probability of the 95% Confidence Interval (CI). In an applied example, we compared sorafenib with a proxy outcome (PRODIGE-11 trial) versus placebo with the reference outcome (SHARP trial), using the SHARP trial's gold standard treatment effect estimate.

The simulations showed that ignoring misclassification in binary outcomes leads to substantial bias in the estimation of indirect treatment effects. Even with a specificity and sensitivity at 0.9, the uncorrected method had a relative bias of 67%. The proposed model reduced bias in all simulation sets, with a relative bias below 5% and a 95%CI coverage between 95% and 96.5%. Across varying levels of specificity and sensitivity, the proposed method achieved approximately half the RMSE of the uncorrected method. Additionally, increasing the ECA sample size had a greater impact on reducing the proposed method's RMSE than enlarging the validation study sample size. The gold standard effect of sorafenib compared with placebo was OR=0.52 (SHARP). Ignoring outcome misclassification resulted in an overestimation of the indirect treatment effect (OR=0.36), using the proposed model the estimation was OR=0.55. However, with only 161 patients in the sorafenib arm of the PRODIGE-11 trial, the 95%CI estimated by the proposed model was wide. This is conservative, as it transfers the uncertainty in measurement to the uncertainty in the decision. These findings align with simulation results, where the empirical SE of the proposed model was twice that of the reference outcome regression for a sample size of 200 patients

The findings underscore the importance of addressing outcome misclassification in indirect comparisons. The proposed correction method may improve reliability in unanchored indirect treatment comparisons