The hazard of using the Poisson model to cope with immortal time bias in the case of time-varying hazard.

Background: A time-dependent analysis, usually by means of Poisson and Cox regression models, can be applied to prevent immortal time bias. However, the use of the Poisson model requires the assumption that the event rate is constant over time. This study aims to assess the potential consequences of using the Poisson model to cope with immortal time bias on estimating the exposure-outcome relationship in the case of time-varying risks.

Methods: A simulation study was carried out. Survival times were assumed to follow a Weibull distribution, and the Weibull parameters were chosen to identify three different scenarios: the hazard of the event is constant, decreases, or increases over time. A dichotomous time-varying exposure in which patients can change at most once from unexposed to exposed was considered. The Poisson model was fitted to estimate the exposure-outcome association.

Results: Small changes in the outcome risk over time (as denoted by the shape parameter of the Weibull distribution) strongly affected the exposure-outcome association estimate. The estimated effect of exposure was always lower and greater than the true exposure effect when the event risk decreases or increases over time, and this was the case irrespective of the true exposure effect. The bias magnitude was positively associated with the prevalence of and time to exposure.

Conclusions: Biased estimates were obtained from the Poisson model to cope with immortal time. In settings with a time-varying outcome risk, the model should adjust for the trend in outcome risk. Otherwise, other models should be considered.