Limits...
Bias and sensitivity analysis when estimating treatment effects from the cox model with omitted covariates.

Lin NX, Logan S, Henley WE - Biometrics (2013)

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.

View Article: PubMed Central - PubMed

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.

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Comparison of simulated biases, asymptotic biases and first-order Taylor series approximations for different types of omitted covariate and censorship. Since  is the asymptotic value of the MLE  and the sample size=10,000 is large, we calculated the simulated bias by . The asymptotic biases and Taylor series approximations were obtained from 2004 and 2001, respectively. Monte Carlo integration was used to approximate the expectations in formulae. (a) Binary confounder c: (), censored; (b) Normal confounder c: (), censored; (c) Binary confounder c: (), censored; (d) Normal confounder c: (), censored; (e) Binary balanced c: (), uncensored; (f) Normal balanced c: (), uncensored.
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fig01: Comparison of simulated biases, asymptotic biases and first-order Taylor series approximations for different types of omitted covariate and censorship. Since is the asymptotic value of the MLE and the sample size=10,000 is large, we calculated the simulated bias by . The asymptotic biases and Taylor series approximations were obtained from 2004 and 2001, respectively. Monte Carlo integration was used to approximate the expectations in formulae. (a) Binary confounder c: (), censored; (b) Normal confounder c: (), censored; (c) Binary confounder c: (), censored; (d) Normal confounder c: (), censored; (e) Binary balanced c: (), uncensored; (f) Normal balanced c: (), uncensored.

Mentions: Figure 1 shows a comparison of the asymptotic and simulated biases and Taylor series approximation under the influence of different sources of bias. We generated 10,000 x from . The confounder C was generated from for the binary confounder, and from for the normal confounder. The event times t were generated from model (1) with , and taking 100 sequence values from to 10. For the censoring cases, we let with . The observed times were given by .


Bias and sensitivity analysis when estimating treatment effects from the cox model with omitted covariates.

Lin NX, Logan S, Henley WE - Biometrics (2013)

Comparison of simulated biases, asymptotic biases and first-order Taylor series approximations for different types of omitted covariate and censorship. Since  is the asymptotic value of the MLE  and the sample size=10,000 is large, we calculated the simulated bias by . The asymptotic biases and Taylor series approximations were obtained from 2004 and 2001, respectively. Monte Carlo integration was used to approximate the expectations in formulae. (a) Binary confounder c: (), censored; (b) Normal confounder c: (), censored; (c) Binary confounder c: (), censored; (d) Normal confounder c: (), censored; (e) Binary balanced c: (), uncensored; (f) Normal balanced c: (), uncensored.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4230475&req=5

fig01: Comparison of simulated biases, asymptotic biases and first-order Taylor series approximations for different types of omitted covariate and censorship. Since is the asymptotic value of the MLE and the sample size=10,000 is large, we calculated the simulated bias by . The asymptotic biases and Taylor series approximations were obtained from 2004 and 2001, respectively. Monte Carlo integration was used to approximate the expectations in formulae. (a) Binary confounder c: (), censored; (b) Normal confounder c: (), censored; (c) Binary confounder c: (), censored; (d) Normal confounder c: (), censored; (e) Binary balanced c: (), uncensored; (f) Normal balanced c: (), uncensored.
Mentions: Figure 1 shows a comparison of the asymptotic and simulated biases and Taylor series approximation under the influence of different sources of bias. We generated 10,000 x from . The confounder C was generated from for the binary confounder, and from for the normal confounder. The event times t were generated from model (1) with , and taking 100 sequence values from to 10. For the censoring cases, we let with . The observed times were given by .

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.

View Article: PubMed Central - PubMed

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