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

Left censoring can occur with relative frequency when analysing recurrent events in epidemiological studies, especially observational ones. Concretely, the inclusion of individuals that were already at risk before the effective initiation in a cohort study, may cause the unawareness of prior episodes that have already been experienced, and this will easily lead to biased and inefficient estimates. The objective of this paper is to propose a statistical method that performs successfully in these circumstances. Our proposal is based on the use of models with specific baseline hazard, imputing the number of prior episodes when unknown, with a stratified model depending on whether the individual had or had not previously been at risk, and the use of a frailty term. The performance is examined in different scenarios through a comprehensive simulation study.The proposed method achieves notable performance even when the percentage of subjects at risk before the beginning of the follow-up is very elevated, with biases that are often under 10\% and coverages of around 95\%, sometimes somewhat conservative. If the baseline hazard is constant, it seems to be that the ``Gap Time'' approach is better; if it is not constant, the ``Counting Process'' seems to be a better choice. Because of the lack of knowledge of the prior episodes that have been experienced by a part (or all) of subjects, the use of common baseline methods is not advised. Our proposal seems to perform acceptably in the majority of the scenarios proposed, becoming an interesting alternative in this context.