Bias and sensitivity analysis when estimating treatment effects from the cox model with omitted covariates.
Bottom Line: 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.
Affiliation: Institute of Health Research, University of Exeter Medical School, Exeter, U.K.; Centre for Health and Environmental Statistics, University of Plymouth, Plymouth, U.K.Show MeSH
Related in: MedlinePlus
Mentions: Under the approach of Lin et al. (1998), an additional covariate Z does not affect the bias if the mean of C conditional on x and z is additive in x and z, that is (VanderWeele, 2008). However, our simulation results in Figure 3a–c show that an additional covariate may introduce a small degree of bias when is large. We generated 100,000 and . The additional covariate Z was simulated from , and for Figure 3a–c, respectively. Under these data-generating processes, and the additivity assumption is satisfied.
Affiliation: Institute of Health Research, University of Exeter Medical School, Exeter, U.K.; Centre for Health and Environmental Statistics, University of Plymouth, Plymouth, U.K.