Abstract
In survival analysis under the proportional hazards model, covariates may be subject to both measurement error and detection limits. Most existing approaches only address one of these two complications and can lead to substantial bias and erroneous inference when dealing with both simultaneously. There is very limited research that addresses both these problems at the same time. These approaches are exclusively based on likelihood and require distribution assumptions on the underlying true covariates, as well as restricted independence assumptions on the censoring time. We propose a novel corrected score approach that relieves such stringent assumptions and is simpler in computation. The estimator is shown to be consistent and asymptotically normal. The finite sample performance of the proposed estimator is assessed through simulation studies and illustrated by application to data from an AIDS clinical trial. The approach can be used in the case of replicate data or instrumental data. It can also be extended to more general models and outcomes.