Error Augmentation for a Kind of Differential Measurement Error

Abstract

When a covariate was measured with error, it may happen that the times of repeat measurements depends on the variable of interest. Such as in a joint model of time-to-event and longitudinal data, the longitudinal data is available only before the time-to-event. Thus, those who have longer studying time should have more measurements. Or in a capture-recapture experiment, the covariate of an animal can be measured only when it was captured. Hence the number of measurements equals the times of being captured. In these situations, the measurement error is differential since it has distribution depending on the response variable. In this talk, we will introduce an error augmentation to modify existent analyses to incorporate such differential measurement error. We also found that the modification is easy, consistent and can result more efficient estimations.