Estimating the survival time of Covid-19 patients based on the effect of the most important factors affecting it

A Thesis Submitted to the Council of College of Economic and Administration holy Kerbala University as a Partial Fulfillment of the Requirements for the Degree of Doctor of (Ph.D.) of Philosophy in Statistics

By

Rawaa Noori Hussain hasan

Supervised By

Prof Dr. awad Kadim Shaalan AL-Khalidy

ABSTRACT

The thesis depends on estimating the relative risk models of the method of teachers, non-teachers and semi-teachers to determine the impact of risk factors on the survival times of patients with Covid 19, which is among the most serious diseases that threaten human life and an important cause of death all over the world, the problem of the thesis is the lack of an accurate diagnosis of the factors Affecting the survival times of patients, and the research aims to diagnose the important factors that affect the survival times of patients and to estimate the parameters of risk models that enable improving ways to confront and prevent the disease, as well as to predict the future when new infections occur. The thesis is divided into four chapters, the first being the introduction and research methodology, and the second chapter contains the theoretical aspect of risk models and the derivation of the information matrix for the model and how to estimate parameters according to the gamma models (Cox, Kaplan Meier), and the third chapter contains the practical aspect where the researcher made multiple visits to the city Imam Al-Hussein Medical Center in the holy governorate of Karbala for the purpose of collecting the necessary data to achieve the objectives of the research for the infected cases during the third, fourth and fifth months of 2020 for the values ​​of (11) risk factors for the injured For the injured, who numbered (126) patients, and among the group of risk factors, we relied on the most important factors represented in age, blood pressure and diabetes, which were determined using the factorial method and the source of the information, and based on the sub-program (spc) which is linked with the excel program), where it was found that the survival times data The general gamma distribution is distributed with three parameters, then the values ​​of the risk models and the information matrix were found, then the parameters were estimated according to the gamma models (Cox, Kaplan Meier) The fourth chapter is a discussion of the results that were reached in analyzing the data, where the results of the Newton-Raffson method for the derivatives of the risk functions in the gamma distribution showed a little deviation from the estimated values ​​of the parameters of the general gamma distribution α, λ, T, while the results of the estimation converged for the semi-parametric cox model, almost in a way that It is identical, while the non-parametric Kaplan-meier model led to values ​​that are close to the estimates of the parameters of the gamma general distribution. The Cox model is better than the Gamma model and the Kaplan-maier model by using the mean squared error criterion as a criterion for differentiation.

Estimating the survival time of Covid-19 patients based on the effect of the most important factors affecting it

A Thesis Submitted to the Council of College of Economic and Administration holy Kerbala University as a Partial Fulfillment of the Requirements for the Degree of Doctor of (Ph.D.) of Philosophy in Statistics

By

Rawaa Noori Hussain hasan

Supervised By

Prof Dr. awad Kadim Shaalan AL-Khalidy

ABSTRACT

The thesis depends on estimating the relative risk models of the method of teachers, non-teachers and semi-teachers to determine the impact of risk factors on the survival times of patients with Covid 19, which is among the most serious diseases that threaten human life and an important cause of death all over the world, the problem of the thesis is the lack of an accurate diagnosis of the factors Affecting the survival times of patients, and the research aims to diagnose the important factors that affect the survival times of patients and to estimate the parameters of risk models that enable improving ways to confront and prevent the disease, as well as to predict the future when new infections occur. The thesis is divided into four chapters, the first being the introduction and research methodology, and the second chapter contains the theoretical aspect of risk models and the derivation of the information matrix for the model and how to estimate parameters according to the gamma models (Cox, Kaplan Meier), and the third chapter contains the practical aspect where the researcher made multiple visits to the city Imam Al-Hussein Medical Center in the holy governorate of Karbala for the purpose of collecting the necessary data to achieve the objectives of the research for the infected cases during the third, fourth and fifth months of 2020 for the values ​​of (11) risk factors for the injured For the injured, who numbered (126) patients, and among the group of risk factors, we relied on the most important factors represented in age, blood pressure and diabetes, which were determined using the factorial method and the source of the information, and based on the sub-program (spc) which is linked with the excel program), where it was found that the survival times data The general gamma distribution is distributed with three parameters, then the values ​​of the risk models and the information matrix were found, then the parameters were estimated according to the gamma models (Cox, Kaplan Meier) The fourth chapter is a discussion of the results that were reached in analyzing the data, where the results of the Newton-Raffson method for the derivatives of the risk functions in the gamma distribution showed a little deviation from the estimated values ​​of the parameters of the general gamma distribution α, λ, T, while the results of the estimation converged for the semi-parametric cox model, almost in a way that It is identical, while the non-parametric Kaplan-meier model led to values ​​that are close to the estimates of the parameters of the gamma general distribution. The Cox model is better than the Gamma model and the Kaplan-maier model by using the mean squared error criterion as a criterion for differentiation.