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Abstract:
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Truncation is a well-known phenomenon that may be present in observational studies of time-to-event data. While methods exist for applying the Cox regresson model for either left or right truncated data, no method exists for adjusting the model for simultaneous left and right truncation. We propose a weighted Cox regression model to adjust for this double truncation, where the weights are estimated from the data and are inversely proportional to the probability that a subject is observed. The resulting weighted estimator of the hazard ratio is consistent. The proposed estimator is asymptotically normal when the weights are estimated parametrically, and a consistent estimator of the asymptotic variance is provided. We obtain a consistent estimate of the variance using a bootstrap when the weights are estimated nonparametrically. We demonstrate through extensive simulations that the proposed estimator is unbiased, while the estimator resulting from the unweighted Cox regression model which ignores truncation is biased. We illustrate our approach in an analysis of autopsy confirmed Alzheimer's disease patients to assess the effect of depression on survival.
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