Is the sequence ratio an unbiased estimate of the incidence rate ratio? A simulation study

Purpose: We aimed to evaluate the conditions under which the sequence ratio (SR) obtained from a sequence symmetry analysis is an unbiased estimate of the true incidence rate ratio (IRR). Methods: We simulated cohorts of 1 million individuals who could initiate an exposure drug and experience a very rare, rare, common, or frequent outcome of interest. The outcome rate among exposed individuals was modified by a true incidence rate ratio of 0.2, 0.5, 1.0, 2.0, and 5.0. We further evaluated scenarios where the outcome was fatal and led to immediate censoring or the outcome reduced the rate of initiation of the exposure drug. Results: We found the SR to be close to unbiased for rare, common, and frequent events, except when the true IRR was 5.0 (mean SR 4.94 and 3.74 for common and frequent events). The SR was slightly biased when the outcome was very rare. When the outcome was potentially fatal, the SR was increasingly biased with an increasing probability of death. Likewise, when the outcome reduced the probability of future exposure, the SR was upwards biased. Conclusion: The SR is a biased estimate of the incidence rate ratio, when the true IRR is high, the outcome has a high mortality, or when the outcome reduces the probability of future exposure.