Abstract
In this paper we use Cox’s regression model to fit failure time data with continuous informative auxiliary variables in the presence of a validation subsample. We first estimate the induced relative risk function by kernel smoothing based on the validation subsample, and then improve the estimation by utilizing the information on the incomplete observations from non-validation subsample and the auxiliary observations from the primary sample. Asymptotic normality of the proposed estimator is derived. The proposed method allows one to robustly model the failure time data with an informative multivariate auxiliary covariate. Comparison of the proposed approach with several existing methods is made via simulations. Two real datasets are analyzed to illustrate the proposed method.
Highlights
1 Introduction In epidemiologic studies, the exposure variable vector X is often too difficult or too expensive to measure on the full cohort, whereas an auxiliary variable vector W for X can be measured for all subjects in the study cohort
The methods we considered are the newly proposed estimated partial likehood estimationand its conterpart in Zhou and Wang (2000), the estimator which does not use the information on W in V, the complete-case Cox regression analysis
7 Conclusion We have introduced an estimated partial likelihood function (EPL) estimation method for Cox’s models with informative auxiliary covariates and established asymptotic normality of our estimator
Summary
The exposure variable vector X is often too difficult or too expensive to measure on the full cohort, whereas an auxiliary variable vector W for X can be measured for all subjects in the study cohort. Our method will be expected to improve the efficiency of the estimator of Zhou and Wang (2000) in various situations, for example, when auxiliary variable W is informative or not very informative about X (see the simulation results). The above estimation of the relative risk function was used in Zhou and Wang (2000) for a nonparametric smoothing problem on the estimation of E[γi(β, t)|Si ≥ t, Zi(t), Wi(t)], where the “curse of dimensionality” problem can happen if W is multivariate Note that this estimation method uses only the complete observations in V and neglects the important information on incomplete observations in V. It follows that this approach cannot be expected to be efficient in certain situations It is required in Zhou and Wang (2000) that, conditional on X, the auxiliary variable W provides no additional information on the the hazard of failure. In small validation ratio settings, βV is not expected to perform well, since it uses only the observations in the validation set for smoothing
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of statistical distributions and applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
