Methods for multivariate recurrent event data with measurement error and informative censoring

In multivariate recurrent event data regression, observation of recurrent events is usually terminated by other events that are associated with the recurrent event processes, resulting in informative censoring. Additionally, some covariates could be measured with errors. In some applications, an instrumental variable is observed in a subsample, namely a calibration sample, which can be applied for bias correction. In this article, we develop two non-parametric correction approaches to simultaneously correct for the informative censoring and measurement errors in the analysis of multivariate recurrent event data. A shared frailty model is adopted to characterize the informative censoring and dependence among different types of recurrent events. To adjust for measurement errors, a non-parametric correction method using the calibration sample only is proposed. In the second approach, the information from the whole cohort is incorporated by the generalized method of moments. The proposed methods do not require the Poisson-type assumption for the multivariate recurrent event process and the distributional assumption for the frailty. Moreover, we do not need to impose any distributional assumption on the underlying covariates and measurement error. Both methods perform well, but the second approach improves efficiency. The proposed methods are applied to the Nutritional Prevention of Cancer trial to assess the effect of selenium treatment on the recurrences of basal cell carcinoma and squamous cell carcinoma.