Testing Linear and Nonlinear Hypotheses in a Cox Proportional Hazards Model with Errors in Covariates
Articles
Oksana Chernova
Taras Shevchenko National University of Kyiv, Ukraine
Alexander Kukush
Taras Shevchenko National University of Kyiv, Ukraine
Published 2019-12-20
https://doi.org/10.15388/LJS.2019.16669
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Keywords

Cox proportional hazards model
hypothesis testing
right censoring
simultaneous estimator of baseline hazard rate and regression parameter

How to Cite

Chernova O. and Kukush A. (2019) “Testing Linear and Nonlinear Hypotheses in a Cox Proportional Hazards Model with Errors in Covariates”, Lithuanian Journal of Statistics, 58(1), pp. 39-47. doi: 10.15388/LJS.2019.16669.

Abstract

We investigate linear and nonlinear hypotheses testing in a Cox proportional hazards model for right-censored survival data when the covariates are subject to measurement errors. In Kukush and Chernova (2018) [Theor. Probability and Math. Statist. 96, 101–110], a consistent simultaneous estimator is introduced for the baseline hazard rate and the vector of regression parameters. Therein the baseline hazard rate belongs to an unbounded set of nonnegative Lipschitz functions, with fixed constant, and the vector of regression parameters belongs to a compact parameter set. Based on the estimator, we develop two procedures to test nonlinear and linear hypotheses about the vector of regression parameters: Wald-type and score-type tests. The latter is based on an unbiased estimating equation. The consistency of the tests is shown.

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