Bias and Sensitivity Analysis When Estimating Treatment Effects from the Cox Model with Omitted Covariates
Article first published online: 13 NOV 2013
© 2013 The Authors. Biometrics published by The International Biometric Society.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Volume 69, Issue 4, pages 850–860, December 2013
How to Cite
Lin, N. X., Logan, S. and Henley, W. E. (2013), Bias and Sensitivity Analysis When Estimating Treatment Effects from the Cox Model with Omitted Covariates. Biometrics, 69: 850–860. doi: 10.1111/biom.12096
- Issue published online: 12 DEC 2013
- Article first published online: 13 NOV 2013
- Manuscript Accepted: 1 JUN 2013
- Manuscript Revised: 1 MAY 2013
- Manuscript Received: 1 DEC 2011
- National Institute for Health Research (NIHR)
- Collaboration for Leadership in Applied Health Research and Care (CLAHRC)
- Bias analysis;
- Cox model;
- Omitted covariates;
- Sensitivity analysis;
- Survival analysis;
- Unmeasured confounding
Omission of relevant covariates can lead to bias when estimating treatment or exposure effects from survival data in both randomized controlled trials and observational studies. This paper presents a general approach to assessing bias when covariates are omitted from the Cox model. The proposed method is applicable to both randomized and non-randomized studies. We distinguish between the effects of three possible sources of bias: omission of a balanced covariate, data censoring and unmeasured confounding. Asymptotic formulae for determining the bias are derived from the large sample properties of the maximum likelihood estimator. A simulation study is used to demonstrate the validity of the bias formulae and to characterize the influence of the different sources of bias. It is shown that the bias converges to fixed limits as the effect of the omitted covariate increases, irrespective of the degree of confounding. The bias formulae are used as the basis for developing a new method of sensitivity analysis to assess the impact of omitted covariates on estimates of treatment or exposure effects. In simulation studies, the proposed method gave unbiased treatment estimates and confidence intervals with good coverage when the true sensitivity parameters were known. We describe application of the method to a randomized controlled trial and a non-randomized study.