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Truncation is a statistical phenomenon that occurs in many time to eventstudies. For example, autopsy-confirmed studies of neurodegenerative diseasesare subject to an inherent left and right truncation, also known as doubletruncation. When the goal is to study the effect of risk factors on survival,the standard Cox regression model cannot be used when the data is subject totruncation. Existing methods which adjust for both left and right truncation inthe Cox regression model require independence between the survival times andtruncation times, which may not be a reasonable assumption in practice. Wepropose an expectation-maximization algorithm to relax the independenceassumption in the Cox regression model under left, right, or double truncation,to an assumption of conditional independence. The resulting regressioncoefficient estimators are consistent and asymptotically normal. We demonstratethrough extensive simulations that the proposed estimators have little biasand, in most practical situations, have a lower mean-squared error compared toexisting estimators. We implement our approach to assess the effect ofoccupation on survival in subjects with autopsy-confirmed Alzheimer's disease.

Cox Regression Model Under Dependent Truncation