Statistical Model Proposed to Predict Survival Rate among Patients Performed Liver Transplantation Operation in Egypt

Abstract

Survival analysis is generally defined as a set of statistical methods for analyzing data where the outcome variable of interest is the time to the occurrence of an event. Survival data have some features that are difficult to handle with traditional statistical methods which are censoring and time-dependent covariates. Regression models for survival data have traditionally been based on the Cox regression model, which assumes that the underlying hazard function for any two levels of some covariates is proportional over the period of follow-up time. If the assumption of proportional hazards is not justified we need to use methods that do not assume proportionality, such as the Cox model with time-dependent covariates and Stratified Cox Regression model. In recent years several strategies have been developed to extend machine learning techniques especially NN methods to accommodate right-censored data. Neural networks may offer an interesting alternative because of their universal approximation property and the fact that no baseline hazard assumption is needed. The main objective of the current study is to construct statistical model that estimate the survival function of Egyptian patients performed liver transplantation operation due to liver diseases and to determine the risk factors affecting the outcome of liver transplantation operation by using different statistical methods represented in Non Parametric, Semi parametric and Parametric methods. Also the study aimed to construct feed-forward neural network and use it as a classifier to distinguish between censored and uncensored patients who had performed liver transplantation operation in Egypt. Nature of the Problem: End Stage Liver Disease has become a national health problem in Egypt, especially during the last two decades. The burden of liver disease in Egypt is exceptionally high, maintaining the highest prevalence of hepatitis C virus worldwide. The current era of severe liver disease lead to the rapidly increasing demands for liver transplantation, however, donor organ shortages underscore the need to optimize the outcome of liver transplantation. Such goals can be realized only with better understanding of the factors that influence patient survival . Objectives of the Study: The main objective of this study is to determine the factors affecting the survival rate of the patients performed liver transplantation operation due to end-stage liver disease and to construct statistical models that predict patient survival function by: Using the Kaplan-Meier survival estimate and Nelson - Aalen estimator to estimate the survival and hazard function. Using the log-rank test to test the significance of the survival functions in two or more groups. Constructing the Cox PH Regression Model for examining the covariate effects on the hazard function. Using the Stratified Cox Regression Model for non proportional hazard to deal with the violation of the PH assumption. Constructing the Parametric AFT models including (the exponential AFT model, Weibull AFT model, log-logistic AFT model, log-normal AFT model) and compare its results to measure the direct effect of the covariate on the survival time. Constructing the Piecewise-Constant Exponential (PCE) model to describe both the effects of the covariates and the underlying hazard function, where the hazard is assumed constant within pre-specified survival time intervals but differ from interval to interval. Also the study aimed to construct to construct Feed Forward Neural Network by using MS Excel to classify the survival data into censored and non-censored patients. Source of the Data &the variables of the model: This study included 302 patients who had undergone liver transplantation operation due to liver disease during the period from January 2007 till end of June 2013. They were followed up for 24 months after transplantation at the Specialized Hospital of Ain Shams University and Egypt Air hospital. Variables of the model Dependent variable: Survival time Independent variables (Risk Factors): Recipient age Recipient sex Donor age Donor Sex Body Mass Index ( BMI ) HCC Model for End Stage Liver Disease (MELD) score Child Turcotte Pough ( CTP ) score Past Hepatic History:{ Ascites, Encephalopathy} Coagulation profile { I.N.R } Liver function tests {Total bilirubin (mg/dl), Albumin (g/dl)} Kidney function tests {Creatinine (mg/dl), Na (mg/dl), K (mg/dl), Ca (mg/dl), } Graft-Recipient Body weight Ratio (GRWR)

Results of the Study: The results of the Kaplan-Meier estimate The Kaplan-Meier survival estimate showed that the probability of 1 year survival after LDLT was 85.76% with mean survival time 10.504 months however the probability of 2 year survival after LDLT was 81.45% with mean survival time 20.584 months. The results of the Cox PH regression model The Cox PH regression model showed that: the variables Recipient age, 〖MELD〗_3 , Ln_Creatinine, and GRWR are statistically significant and selected as significant factors for risk of death after liver transplantation operation. The final multivariate Cox PH model is given by: h_i (t)=h_0 (t) Exp (0.604 Recipient Age+1.160 〖MELD〗_3+0.518 Ln .creatinine -1.423 GRWR)

Also the scaled Schoenfeld residual displayed non-proportionality for variable Recipient Age and this variable needed to be stratified.