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

Abstract

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

Comparison of Cox Proportional Hazards Model and Lognormal Accelerated Failure Time Model: Application in Time to Event Analysis of Acute Liver Failure Patients in India

“…The maximum likelihood estimates of the parameters for both the models are estimated by using iterative Newton-Raphson procedure (Collett, 2003;Hosmer & Lemeshow, 1999). The details about the model specification, goodness of fit of the model, assessment of proportionality of hazards assumption, residuals analysis for CPH model for this data has already been explained (Khanal et al, 2018), and the required tests for selection of Lognormal AFT model, goodness of fit of the model, residual analysis, etc has also been already described for this ALF data (Khanal et al, 2014). Both the considered models have satisfied the goodness of fit of the model for this ALF data 2014, 2018.…”

“…The formula used to compute CS residuals, R 2 type statistic, etc in the analysis of ALF data were discussed elsewhere 2014, 2018. The mathematical expression for computation of survival probability in different risk strata and PI for CPH model had been explained by Khanal et al(2018). The mathematical expression for computation of survival probability in different risk strata and PI in Lognormal AFT model has been provided as follows.…”

“………………………………… 4The PI values computed from the model are ranked and divided into number of strata in such a way that there are approximately equal numbers of events in each stratum in a similar manner as done in the case of Cox regression model (Khanal et al, 2018). Curves of model predicted survival probability and observed survival probability (by K-M method) for each risk stratum can be compared for visual assessment of good fit of the model.…”

“…Till date, in most of the studies related to survival of Acute Liver Failure (ALF) patients has been analyzed by using K-M method, logistic regression model and CPH model. Khanal, Sreenivas, and Acharya (2018) has also applied CPH model to identify the prognostic factors of ALF patients in India. With the best of our knowledge, for the first time, the survival analysis of ALF data had been found analyzed by applying AFT models and their comparison was also reported by Khanal, Sreenivas, and Acharya (2014).…”