Estimation and Model Misspecification for Recurrent Event Data with Covariates Under Measurement Errors

For subject i, we monitor an event that can occur multiple times over a random observation window [0, τi). At each recurrence, p concomitant variables, xi, associated to the event recurrence are recorded—a subset (q≤p) of which is measured with errors. To circumvent the problem of bias and consistency associated with parameter estimation in the presence of measurement errors, we propose inference for corrected estimating equations with well-behaved roots under an additive measurement errors model. We show that estimation is essentially unbiased under the corrected profile likelihood for recurrent events, in comparison to biased estimations under a likelihood function that ignores correction. We propose methods for obtaining estimators of error variance and discuss the properties of the estimators. We further investigate the case of misspecified error models and show that the resulting estimators under misspecification converge to a value different from that of the true parameter—thereby providing a basis for bias assessment. We demonstrate the foregoing correction methods on an open-source rhDNase dataset gathered in a clinical setting.