Bias and sensitivity analysis when estimating treatment effects from the cox model with omitted covariates.
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.
['Lin|Nan Xuan|NX|', 'Logan|Stuart|S|', 'Henley|William Edward|WE|']
D015982:Bias D003627:Data Interpretation, Statistical D004314:Down Syndrome D006801:Humans D016013:Likelihood Functions D017063:Outcome Assessment, Health Care D015995:Prevalence D016016:Proportional Hazards Models D015203:Reproducibility of Results D012307:Risk Factors D018401:Sample Size D012680:Sensitivity and Specificity D016019:Survival Analysis D016896:Treatment Outcome D014481:United States
Sensitivity analysis Cox model Omitted covariates Unmeasured confounding Bias analysis Survival analysis