Abstract
BackgroundIn follow-up studies, the occurrence of the intermediate event may influence the risk of the outcome of interest. Existing methods estimate the effect of the intermediate event by including a time-varying covariate in the outcome model. However, the insusceptible fraction to the intermediate event in the study population has not been considered in the literature, leading to effect estimation bias due to the inaccurate dataset.MethodsIn this paper, we propose a new effect estimation method, in which the susceptible subpopulation is identified firstly so that the estimation could be conducted in the right population. Then, the effect is estimated via the extended Cox regression and landmark methods in the identified susceptible subpopulation. For susceptibility identification, patients with observed intermediate event time are classified as susceptible. Based on the mixture cure model fitted the incidence and time of the intermediate event, the susceptibility of the patient with censored intermediate event time is predicted by the residual intermediate event time imputation. The effect estimation performance of the new method was investigated in various scenarios via Monte-Carlo simulations with the performance of existing methods serving as the comparison. The application of the proposed method to mycosis fungoides data has been reported as an example.ResultsThe simulation results show that the estimation bias of the proposed method is smaller than that of the existing methods, especially in the case of a large insusceptible fraction. The results hold for small sample sizes. Besides, the estimation bias of the new method decreases with the increase of the covariates, especially continuous covariates, in the mixture cure model. The heterogeneity of the effect of covariates on the outcome in the insusceptible and susceptible subpopulation, as well as the landmark time, does not affect the estimation performance of the new method.ConclusionsBased on the pre-identification of the susceptible, the proposed new method could improve the effect estimation accuracy of the intermediate event on the outcome when there is an insusceptible fraction to the intermediate event in the study population.
Highlights
In follow-up studies, the occurrence of the intermediate event may influence the risk of the outcome of interest
Since the information of the incidence and time of the time-varying intermediate event is combined by the mixture cure models [29], we propose to predict the susceptibility of patients via the residual time distribution [30] of the intermediate event based on the mixture cure model
To estimate the effect of the time-varying intermediate event when there is an insusceptible fraction to it in the study population, we propose an improved method in which the susceptible subpopulation pre-identification is newly considered
Summary
In follow-up studies, the occurrence of the intermediate event may influence the risk of the outcome of interest. Existing methods estimate the effect of the intermediate event by including a time-varying covariate in the outcome model. In the context of follow-up studies, some patients may experience the intermediate event before the occurrence of the outcome of interest. Rather than being determined at entry as in randomized controlled trials, the group of each patient is based on the whole follow-up in studies of time-varying intermediate events. For patients who have experienced the intermediate event, there is a period of time during which the outcome, such as death, did not happen This period of time is classified into the event group in traditional survival analysis, which is in favor of the event. Bias in the effect estimation of the timevarying intermediate event is incurred using the traditional survival analysis, which is called guarantee time bias or immortal time bias [4, 5]
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