Time-lag bias induced by unobserved heterogeneity: comparing treated patients to controls with a different start of follow-up

In comparative effectiveness research, treated and control patients might have a different start of follow-up as treatment is often started later in the disease trajectory. This typically occurs when data from treated and controls are not collected within the same source. Only patients who did not yet experience the event of interest whilst in the control condition end up in the treatment data source. In case of unobserved heterogeneity, these treated patients will have a lower average risk than the controls. We illustrate how failing to account for this time-lag between treated and controls leads to bias in the estimated treatment effect. We define estimands and time axes, then explore five methods to adjust for this time-lag bias by utilising the time between diagnosis and treatment initiation in different ways. We conducted a simulation study to evaluate whether these methods reduce the bias and then applied the methods to a comparison between fertility patients treated with insemination and similar but untreated patients. We conclude that time-lag bias can be vast and that the time between diagnosis and treatment initiation should be taken into account in the analysis to respect the chronology of the disease and treatment trajectory.