Cox regression analysis for distorted covariates with an unknown distortion function

Abstract

We study inference for censored survival data where some covariates are distorted by some unknown functions of an observable confounding variable in a multiplicative form. An example of this kind of data in medical studies is normalizing some important observed exposure variables by patients' body mass index , weight, or age. Such a phenomenon also appears frequently in environmental studies where an ambient measure is used for normalization and in genomic studies where the library size needs to be normalized for the next generation sequencing of data. We propose a new covariate‐adjusted Cox proportional hazards regression model and utilize the kernel smoothing method to estimate the distorting function, then employ an estimated maximum likelihood method to derive the estimator for the regression parameters. We establish the large sample properties of the proposed estimator. Extensive simulation studies demonstrate that the proposed estimator performs well in correcting the bias arising from distortion. A real dataset from the National Wilms' Tumor Study is used to illustrate the proposed approach.

NKAIN1, as an oncogene, promotes the proliferation and metastasis of breast cancer, affecting its prognosis

“…This may explain superior OS and RFS in the high NKAIN1 expression group compared to that in the low‐expression group. Cox regression analysis 26 also identified NKAIN1 overexpression as a prognostic protective factor. Interestingly, when the cohort was subdivided according to hormone receptor status, the difference in OS was no longer significant.…”

The geochemical characteristics of Cretaceous volcanics in southern Hainan Island and implications for tectonic evolution in the South China Sea

“…There were high-Mg andesites-adakitic rocks in the mid-Cretaceous assemblage on Hainan Island. This mid-Cretaceous assemblage is also found in Guangxi and Guangdong, to the north of Hainan Island (Sun et al, 2017;Zhang et al, 2017;Liu et al, 2020;Liu et al, 2021). In the modern subduction zones, this Frontiers in Earth Science frontiersin.org type of assemblage is often related to the subduction of the ocean ridge (Sajona et al, 2000;Bourdon et al, 2003;Castillo, 2008).…”

“…The narrow ranges of La/Yb and U/Th ratios, combined with the significantly elevated Th/Ta and Th/Nb ratios (Figures 6A, B), suggest that the magmas originated from the EM-II type source with inputs of continental crust material, as in the Andes Arc. Liu et al (2020Liu et al ( , 2021 showed that the andesites in Guangdong and Guangxi, north of Hainan Island, also had similar Frontiers in Earth Science frontiersin.org geochemical characteristics, and the mid-Cretaceous magmatic sources were altered by the melt of continental sediments. In addition, zircon ε Hf (t) data range from −9.73 to +0.47 (Zhou et al, 2015a), which is the result of the addition of continental crust materials to the magmatic source.…”

“…Guangdong and southern Vietnam, surrounding Hainan Island (Jiang et al, 2015;Liu et al, 2020;Liu et al, 2021). Besides, there are contemporaneous diorites reported in Hainan Island (Dilek and Tang, 2020).…”