A semi-parametric generalization of the Cox proportional hazards regression model: Inference and Applications

ArticleinComputational Statistics & Data Analysis 55(1):667-676 · September 2011with37 Reads
DOI: 10.1016/j.csda.2010.06.010 · Source: RePEc
The assumption of proportional hazards (PH) fundamental to the Cox PH model sometimes may not hold in practice. In this paper, we propose a generalization of the Cox PH model in terms of the cumulative hazard function taking a form similar to the Cox PH model, with the extension that the baseline cumulative hazard function is raised to a power function. Our model allows for interaction between covariates and the baseline hazard and it also includes, for the two sample problem, the case of two Weibull distributions and two extreme value distributions differing in both scale and shape parameters. The partial likelihood approach can not be applied here to estimate the model parameters. We use the full likelihood approach via a cubic B-spline approximation for the baseline hazard to estimate the model parameters. A semi-automatic procedure for knot selection based on Akaike's information criterion is developed. We illustrate the applicability of our approach using real-life data.
    • "L iver transplantation is the treatment of choice for end-stage liver disease (ESLD) and acute fulminant hepatitis [1,2]. In most cases, a liver transplant from a brain-dead person is performed with the consent of their relatives. "
    [Show abstract] [Hide abstract] ABSTRACT: Background: Identification of the prognostic factors for survival in patients with liver transplantation is challengeable. Various methods of survival analysis have provided different, sometimes contradictory, results from the same data. Objective: To compare Cox’s regression model with parametric models for determining the independent factors for predicting adults’ and pediatrics’ survival after liver transplantation. Methods: This study was conducted on 183 pediatric patients and 346 adults underwent liver transplantation in Namazi Hospital, Shiraz, southern Iran. The study population included all patients undergoing liver transplantation from 2000 to 2012. The prognostic factors sex, age, Child class, initial diagnosis of the liver disease, PELD/MELD score, and pre-operative laboratory markers were selected for survival analysis. Results: Among 529 patients, 346 (64.5%) were adult and 183 (34.6%) were pediatric cases. Overall, the lognormal distribution was the best-fitting model for adult and pediatric patients. Age in adults (HR=1.16, p<0.05) and weight (HR=2.68, p<0.01) and Child class B (HR=2.12, p<0.05) in pediatric patients were the most important factors for prediction of survival after liver transplantation. Adult patients younger than the mean age and pediatric patients weighing above the mean and Child class A (compared to those with classes B or C) had better survival. Conclusion: Parametric regression model is a good alternative for the Cox’s regression model.
    Full-text · Article · Jul 2015
    • "This model allows hazard and survival curves to cross. Finally, several interesting " super models " have been proposed in the literature, including non-proportional hazard regression models that include PH as a special case (Devarajan and Ebrahimi, 2011 ), generalized odds-rate hazards models that include PH and PO as special cases (Dabrowska and Doksum, 1988; Scharfstein et al., 1998), Box-Cox transformation regression models that include PH and AH as spe-cial cases (Yin and Ibrahim, 2005; Martinussen and Scheike, 2006), and extended hazard regression models that include both PH and AFT as special cases (Chen and Jewell, 2001; Li et al., 2015b). "
    [Show abstract] [Hide abstract] ABSTRACT: Survival analysis has received a great deal of attention as a subfield of Bayesian nonparametrics over the last 50 years. In particular, the fitting of survival models that allow for sophisticated correlation structures has become common due to computational advances in the 1990s, in particular Markov chain Monte Carlo techniques. Very large, complex spatial datasets can now be analyzed accurately including the quantification of spatiotemporal trends and risk factors. This chapter reviews four nonparametric priors on baseline survival distributions in common use, followed by a catalogue of semiparametric and nonparametric models for survival data. Generalizations of these models allowing for spatial dependence are then discussed and broadly illustrated. Throughout, practical implementation through existing software is emphasized.
    Chapter · Jan 2015 · PLoS ONE
    • "Gene expression and survival data available for 55 ccRCC patients in the TCGA database (https://tcga-data.nci.nih.gov/ tcga/) was used for survival analyses using univariate Cox proportional hazards (PH) and Accelerated Failure Time (AFT) models [26]. A goodness-of-fit (GOF) test of the Cox PH model was performed [27]. "
    [Show abstract] [Hide abstract] ABSTRACT: To determine the expression patterns of NF-κB regulators and target genes in clear cell renal cell carcinoma (ccRCC), their correlation with von Hippel Lindau (VHL) mutational status, and their association with survival outcomes. Meta-analyses were carried out on published ccRCC gene expression datasets by RankProd, a non-parametric statistical method. DEGs with a False Discovery Rate of < 0.05 by this method were considered significant, and intersected with a curated list of NF-κB regulators and targets to determine the nature and extent of NF-κB deregulation in ccRCC. A highly-disproportionate fraction (~40%; p < 0.001) of NF-κB regulators and target genes were found to be up-regulated in ccRCC, indicative of elevated NF-κB activity in this cancer. A subset of these genes, comprising a key NF-κB regulator (IKBKB) and established mediators of the NF-κB cell-survival and pro-inflammatory responses (MMP9, PSMB9, and SOD2), correlated with higher relative risk, poorer prognosis, and reduced overall patient survival. Surprisingly, levels of several interferon regulatory factors (IRFs) and interferon target genes were also elevated in ccRCC, indicating that an 'interferon signature' may represent a novel feature of this disease. Loss of VHL gene expression correlated strongly with the appearance of NF-κB- and interferon gene signatures in both familial and sporadic cases of ccRCC. As NF-κB controls expression of key interferon signaling nodes, our results suggest a causal link between VHL loss, elevated NF-κB activity, and the appearance of an interferon signature during ccRCC tumorigenesis. These findings identify NF-κB and interferon signatures as clinical features of ccRCC, provide strong rationale for the incorporation of NF-κB inhibitors and/or and the exploitation of interferon signaling in the treatment of ccRCC, and supply new NF-κB targets for potential therapeutic intervention in this currently-incurable malignancy.
    Full-text · Article · Oct 2013
Show more