Adjusting for unmeasured confounding in survival causal effect using validation data

Unmeasured confounding is an important problem in observational studies, which brings a great challenge to eliminate or reduce bias. A large main data set with unmeasured confounders and a smaller validation data set with detailed information on these confounders are combined to estimate the survival causal effect. The initial estimator based on the small validation data set under the ignorable treatment assignment and the error-prone estimator based on the large main data set are both obtained by the doubly robust method. Then, the proposed estimator is obtained by leveraging the correlation between the initial estimator and the error-prone estimator. The large sample theory of the proposed estimator is established. Simulation studies are conducted to show the good performance of the proposed method. A real data of breast cancer from the cBio Cancer Genomics Portal is analyzed to illustrate the proposed method.(c) 2022 Elsevier B.V. All rights reserved.