Left-censored recurrent event analysis in epidemiological studies: a proposal for when the number of previous episodes is unknown.

Background: When dealing with recurrent events in observational studies it is common to include subjects who became at risk before follow-up. This phenomenon is known as left censoring, and simply ignoring these prior episodes can lead to biased and inefficient estimates. We aimed to propose a statistical method that performs well in this setting.

Methods: Our proposal was based on the use of models with specific baseline hazards. In this, the number of prior episodes were imputed when unknown and stratified according to whether the subject had been at risk of presenting the event before t = 0. A frailty term was also used. Two formulations were used for this "Specific Hazard Frailty Model Imputed" based on the "counting process" and "gap time." Performance was then examined in different scenarios through a comprehensive simulation study.

Results: The proposed method performed well even when the percentage of subjects at risk before follow-up was very high. Biases were often below 10% and coverages were around 95%, being somewhat conservative. The gap time approach performed better with constant baseline hazards, whereas the counting process performed better with non-constant baseline hazards.

Conclusions: The use of common baseline methods is not advised when knowledge of prior episodes experienced by a participant is lacking. The approach in this study performed acceptably in most scenarios in which it was evaluated and should be considered an alternative in this context. It has been made freely available to interested researchers as R package miRecSurv.