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

Gilma Hernández-Herrera,David Moriña,Albert Navarro

doi:10.1186/s12874-022-01503-1

Abstract

BackgroundWhen 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.MethodsOur 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.ResultsThe 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.ConclusionsThe 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.

Highlights

When dealing with recurrent events in observational studies it is common to include subjects who became at risk before follow-up
Baseline hazard models, known as conditional models or Prentice, Williams, and Peterson (PWP) models [12], are used to consider the existence of event dependence. These models assume that the baseline hazard of an episode differs as a function of episodes that have already occurred, stratifying by how many there have been. This allows general or specific effects to be calculated for each episode, with all at-risk individuals included in the first strata, but only those with an episode in the previous strata subsequently considered at risk
For the first three populations, SPECIFIC.Gap time (GT) shows equal or less bias than SPECIFIC.Counting process (CP), whereas the converse is true for the second three populations, provided that risk starts during follow-up for at least 50% of the cohort

Summary

Introduction

When dealing with recurrent events in observational studies it is common to include subjects who became at risk before follow-up. There is a need to clarify how data are handled when the prior history is unknown in a cohort and the outcome of interest is a recurrent event with event dependence This concerns situations where we know the moment from when individuals become at risk, but we do know the number of prior episodes. Concerning the risk of sick leave in a work force, we will likely know the start date for employment; especially for people with ample trajectory, we may not know how many sick leaves they had prior to this employment Another example can be seen in cohorts where the outcome is the incidence of infection with the human papilloma virus in adult women. It would be relatively simple to know how long they have been at risk (first sexual intercourse), but we will not know the true number of infections because they are typically asymptomatic

Objectives

Methods

Results

Discussion

Conclusion