Determination of the functional form of the relationship of covariates to the log hazard ratio in a Cox model
In this paper, we review available methods for determination of the functional form of the relation between a covariate and the log hazard ratio for a Cox model. We pay special attention to the detection of influential observations to the extent that they influence the estimated functional
form of the relation between a covariate and the log hazard ratio. Our paper is motivated by a data set from a cohort study of lung cancer and silica exposure, where the nonlinear shape of the estimated log hazard ratio for silica exposure plotted against cumulative exposure and hereafter
referred to as the exposure–response curve was greatly affected by whether or not two individuals with the highest exposures were included in the analysis. Formal influence diagnostics did not identify these two individuals but did identify the three highest exposed cases. Removal of
these three cases resulted in a biologically plausible exposure–response curve.
Keywords: Cox models; dfbeta residuals; influence; martingale residuals; natural and penalized splines
Document Type: Research Article
Affiliations: 1: Department of Statistics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata, 700019, India 2: Central Inland Fisheries Research Institute, ICAR, Kolkata, 700120, India 3: Department of Mathematics and Statistics, American University, Washington, USA 4: Department of Public Health, University of California, Berkeley, CA, USA
Publication date: 04 May 2015
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