Goodness-of-fit test in the Cox proportional hazards model with measurement errors

2020 ◽  
Vol 99 ◽  
pp. 125-135
Author(s):  
A. G. Kukush ◽  
O. O. Chernova
Keyword(s):  
Measurement Errors ◽  
Goodness Of Fit ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Goodness Of Fit Test ◽  
Hazards Model

scholarly journals Testing Linear and Nonlinear Hypotheses in a Cox Proportional Hazards Model with Errors in Covariates

2019 ◽  
Vol 58 (1) ◽  
pp. 39-47
Author(s):  
Oksana Chernova ◽  
Alexander Kukush
Keyword(s):  
Measurement Errors ◽  
Hazard Rate ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Baseline Hazard ◽  
Hazards Model ◽  
Regression Parameters ◽  
Linear And Nonlinear

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.

scholarly journals Cox Proportional Hazards Model for Identification of the Prognostic Factors in the Survival of Acute Liver Failure Patients in India

2018 ◽  
Vol 2 ◽  
pp. 53-74
Author(s):  
Shankar Prasad Khanal ◽  
V. Sreenivas ◽  
S.K. Acharya
Keyword(s):  
Survival Analysis ◽  
Prognostic Factors ◽  
Liver Failure ◽  
Cerebral Edema ◽  
Goodness Of Fit ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Hazards Model

Background: Acute Liver Failure (ALF) is a kind of dangerous rare liver injury among all liver diseases. Different statistical methods such as Logistic regression, Kaplan-Meier estimate of survival function followed by Log-rank test and semi-parametric approaches of survival analysis has been applied in order to identify the significant risk factors of ALF patients. In most of the studies, regression models used in this setup has not been evaluated by model assumptions and their goodness of fit tests.Objective: To apply appropriate survival analysis technique to identify the prognostic factors in the survival of ALF patients, to develop prognostic index, and to predict survival probability for different scenario.Materials and Methods: The study is based on the retrospective cohort study design with altogether 1099 ALF patients taken from the liver clinic, All India Institute of Medical Sciences, New Delhi India. Cox regression has been considered as the suitable model for handling this time to event data, and the assumptions of the model, goodness of fit of the model was assessed and survival probabilities were predicted.Results: This study has identified six prognostic factors namely age, prothrombin time, cerebral edema, total serum bilirubin, serum creatinine and etiology for ALF patients. The hazards of mortality [HR: 2.38; 95% C.I.: (1.99, 2.85), p < 0.001] is the highest for cerebral edema among all these prognostic factors. Nearly 9%, 26%, 39%, 50%, 59% and 63% of ALF patients with a PI of 1, 3, 5, 7, 9 and 10 respectively die by 3 days of hospital stay.Conclusion: The developed Cox Proportional Hazards model with six prognostic factors has satisfied the model assumptions and goodness of fit tests. The risk score and the predicted survival probabilities will be immensely helpful to the hepatologists to make a quick decision regarding the likely prognosis of a patient at admission and helpful in triaging the ALF patients for liver transplant.Nepalese Journal of Statistics, Vol. 2, 53-74

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