OBJECTIVES: Unmeasured confounding presents a key challenge when performing treatment comparisons using real world data. Quantitative bias analysis (QBA) is an important tool for assessing the robustness of treatment effect estimates obtained from such studies, but no published method is applicable to time-to-event (TTE) outcomes when the proportional hazards (PH) assumption is violated – a common circumstance when therapies with different molecular mechanisms are compared. This study developed, and assessed (with a simulation study), a method for QBA which used the accelerated failure time (AFT) model in order to relax the PH assumption.

METHODS: A two-step method was developed in which, firstly, the expectation-maximisation (EM) algorithm was used to impute an unmeasured binary confounder, U, with a known association with treatment assignment and the outcome. An AFT model was used for the TTE outcome, and a probit model for U. In the second step, an AFT model was fitted to the imputed data and a treatment effect obtained which was consequently adjusted for U. The method was assessed for accuracy using simulated data from a Weibull distribution over two data generating mechanisms which violated the PH assumption: delayed and waning treatment effect.

RESULTS: When using this two-step approach bias was small, particularly for the delayed treatment effect. Relative bias was 0.01% for delayed treatment effect and -0.10% for waning. Coverage achieved the expected level of 95% for both scenarios.

CONCLUSIONS: This study demonstrates a valid QBA framework which can be applied to TTE outcomes, without assuming PH. The framework can be readily applied, given the widespread use of both AFT models and the EM algorithm in statistical software; as well as being straightforward to interpret. This method could be applied to, for example, external control arm studies to formally demonstrate the robustness of results to unmeasured confounding.