Search In this Thesis
   Search In this Thesis  
العنوان
Statistical Model Proposed to Predict Survival Rate among Patients Performed Liver Transplantation Operation in Egypt /
المؤلف
Zakria, Sally Hossam ElDin Ahmed.
هيئة الاعداد
باحث / Sally Hossam ElDin Ahmed Zakria
مشرف / Medhat Mohamed Ahmed Abdel Aal
مشرف / Mohamed Amin Sakr
مناقش / Mostafa Galal Mostafa
الموضوع
Statistics, Mathematics & Insurance Department.
تاريخ النشر
2016.
عدد الصفحات
P 241. :
اللغة
الإنجليزية
الدرجة
ماجستير
التخصص
الإحصاء والاحتمالات
تاريخ الإجازة
1/1/2016
مكان الإجازة
جامعة عين شمس - كلية التجارة - قسم الاحصاء و الرياضة والتامين
الفهرس
Only 14 pages are availabe for public view

from 32

from 32

Abstract

Statistical Model Proposed to Predict Survival Rate among Patients Performed Liver Transplantation Operation in Egypt
Introduction
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.
The results of the Stratified Cox regression model
The stratified Cox model with interaction and with no interaction were applied and showed that the no-interaction model is acceptable at 0.05 level of significance and the variables〖 MELD〗_3 Score, Ln_Creatinine are statistically significant and selected as significant factors for risk of death after liver transplantation operation at 0.05 level of significance.
Variables No interaction model Interaction model
Strata 1
Recipient Age <50 Strata 2
Recipient Age ≥50
Coef. H.R. p value Coef. H.R. pvalue Coef. H.R. p value
〖MELD〗_(3 ) 1.15 3.178 0.0001 0.970 2.63 0.034 1.271 3.567 0.0001
Ln.creat. 0.521 1.684 0.050 0.2846 1.329 0.0669 0.5606 1.751 0.045
GRWR -1.40 0.246 0.107 -1.497 0.223 0.274 -1.347 0.259 0.232
The Likelihood ratio statistics=512.6292-512.1457=0.48348
The results of parametric AFT models
The AFT models showed that the variables: Recipient age, 〖MELD〗_3 , and GRWR are statistically significant and selected as significant factors for risk of death after liver transplantation operation.
Then it is concluded that the lognormal AFT model is the best model fitting the data, since its AIC value was the least (AIC =487.08) compared with other AFT models.
The multivariate AFT model (lognormal AFT model) is given by:
log(t)=5.26 -1.86 Recipient Age-3.09 〖MELD〗_3+3.59 GRWR+ σε_i
The results of the Piecewise Constant Exponential model
The PCE model showed that the estimated hazard increases highly in the first interval [0,6┤[ , then decreases in the second interval [6,12┤[ and again increases in the third interval [12,18┤[, and showed that the pattern of the coefficient estimates is not monotonic.
The results of the Feed Forward Neural Network
The feed forward neural networks were developed and trained using Microsoft Excel it consists of an input layer with 8 nodes, one hidden layer with 9 nodes, and an output layer with a single output node. The number of neurons in the hidden layer was chosen by experimentation. The best network is achieved when the minimum mean square error for training data is 0.0378, and for testing data is 0.2233. It was concluded that for the training data set a 228 correct classification of the 240 training observations, and the overall hit ratio is 95.0%. Also for testing data set a 47 correct classification of the 62 testing observations, while the overall hit ratio is 75.80%.
The Outline of the Study:
This study is presented in 6 main chapters summarized as follows:
Chapter One: Introduction
This chapter starts with an overview on liver transplantation operation, its indication and causes, and then it presents the nature of the problem, the importance and the objective of the study.
Chapter Two: Non parametric & Semi parametric Methods for Survival Data
This chapter briefly introduces the basic concepts and terminology of survival analysis and how to construct likelihood functions for censored data. Then a detailed discussion of the non parametric methods for estimating survival function in the presence of censored survival times. Also the Cox PH regression model is introduced and discussed in details; moreover the stratified Cox regression model for non proportional hazard is presented.
Chapter Three: Parametric Models for Survival Data
This chapter discussed several parametric models including Parametric PH models, AFT models, the piecewise constant exponential model and the discrete time survival models.
Chapter Four: The Artificial Neural Network in Survival Analysis
This chapter introduces the theoretical background of artificial neural network and then a detailed discussion of ANN architecture, ANN learning process, and the back propagation algorithm also it focused on the feed forward neural network and how to construct the FFNN by using Ms Excel.
Chapter Five: The Application of the Statistical Techniques
This chapter applies the different statistical techniques (K-M estimate, Cox PH regression model, Stratified Cox regression model, AFT models, piecewise constant exponential Model, and FFNN by using Ms Excel) discussed in the previous chapters .
Chapter Six: Results Conclusions and Future Work