Reducing survivorship bias due to heterogeneity when comparing treated and controls with a different start of follow up

In comparative effectiveness research, treated and control patients might have a different start of follow up, e.g. when treatment is started later in the disease trajectory. When the follow up period of control patients starts earlier in the disease trajectory than follow up of the treated, estimation of the treatment effect suffers from different types of survival/survivorship bias. We study unobserved heterogeneity and illustrate how failing to account for the time difference in recruitment between treated and controls leads to bias in the estimated treatment effect. We explore five methods to adjust for this survivorship bias by including the time between diagnosis and treatment initiation (wait time) in the analysis in different ways. We first conducted a simulation study on whether these methods reduce survivorship bias, then applied our methods to fertility data on insemination. The five methods were: first, to regress on wait time as an additional covariate in the analysis model. Second, to match on wait time. Third, to select treated who started treatment immediately. Fourth, to select controls who survived up to the median time of treatment initiation. Fifth, to consider the wait time as the time of left truncation. All methods reduced survivorship bias in the simulation. In the application to fertility data, failing to adjust for survivorship bias led to a hazard ratio (HR) of 1.63 (95%CI: 1.13-1.65) whereas a HR of 2.15 (1.71-2.69) was expected when using a time-varying covariate for treatment, which in this prospective cohort coincided with the left truncation approach. In agreement with our simulations, the method in which adjustment corrected the HR upwards the most was left truncation. We conclude that the wait time between diagnosis and treatment initiation should be taken into account in the analysis to respect the chronology of the disease and treatment trajectory.