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: Figure 4a shows the sensitivity of the lower limit of the confidence interval for the hazard ratio of folinic acid to adjustment for an unmeasured binary covariate of specified properties, where we set . For , the difference in probabilities must be for the treatment effect to become significant. The same conclusion can be obtained from the contour plot in Web Figure 3 which shows results of a similar sensitivity analysis for the P-value of the treatment estimate. The results for antioxidant supplementation in Web Table 3 show that the treatment effect is significant only when and . Given the nature of the study design, the conditions required for the treatment effects to be significant are implausible, suggesting that the original findings of non-significance are robust to the presence of realistic levels of unmeasured confounding.
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.