The Retention Rates of Students In Public Secondary Schools Using The Cox Proportional Hazard Model: A Case of Kisumu County, Kenya

The study sought to propose a statistical model for the public Secondary School students' retention rates for Kisumu County. We used survival regression analysis in which students were grouped according to the their  performance in KCSE, mean school fee payment, school category, sex, mean age and teacher - student ratio using a desirable survival function. The model was of interest because the study sought to address a life testing experience mostly restricted to survival models and most of the existing models on student retention addressed Universities and tertiary colleges' trend and were particularly developed outside the country. This was in spite of the fact that Kenya suffers from high dropout rates at the Secondary level. The annual Secondary School students data traced from a cohort in form one in the year 2010  to form four in the year 2013 were obtained from the Kisumu County Ministry of Education headquarters and analyzed using survival regression. The variables which were insignificant were dropped to get the desirable function. Survival rates of students in the Secondary Schools were traced at the end of each and every level. It was found out that dropping out of students was influenced by; the category of the school, average fee payment, performance in KCSE and sex, with more girls dropping out than boys and the dropping out mostly rampant at form two. The model will be of relevance to the concerned Secondary education stakeholders in improving the quality of education for it will inform the planning of necessary educational interventions to ensure enhanced retention rate and transition. Keywords: Retention, Cox Regression, Drop-out rate, Probability Density function, Kaplan Meier

Modeling the Survival of Stomach Cancer Patients in Meru County using The Stratified Cox Model

Cancer is a disease that can affect anyone regardless of age, social-economic status, or sex. Research has shown there are over 28,000 new cancer cases in a year in Kenya, with a mortality of 22,000, implying a 78.5% chance that the victims do not survive. If not detected early, treated on time, and the right treatment chosen, cancer treatment is less likely to succeed, reducing the chances of survival. One of the most common types of cancer is stomach cancer. It is also the most prevalent cancer in Meru County. The purpose of the study was to find the relationship between the various treatment methods and the survivorship of stomach cancer patients. By doing so, patients and health workers can select the best treatment for cancer patients at different stages. The study modeled the survival of stomach cancer patients using the Stratified Cox model in the case of Meru County, Kenya. The study's general objective was to model the survival of stomach cancer patients in Meru County using the Stratified Cox model. The data was first fitted in a Stratified Cox model to do this. Then hazard functions were determined. From the hazard functions, hazard rates were calculated using R version 4.3.1. Chemotherapy was used as a reference category. The study used secondary data obtained from Meru General Hospital between 2017 and 2021. Different treatment methods: radiotherapy, chemotherapy, hormone therapy, and surgery are compared for each stage while considering several demographic characteristics such as age and sex. The research investigated the hazard rates that, in turn, helped find the survival of patients with stomach cancer based on the treatment method used. Hazard ratios were obtained from the collected data to determine and recommend the best treatment method at a particular stage of stomach cancer. After analysis, results showed that surgery is the best treatment for stage 1 and 2 cancer, while radiotherapy and chemotherapy are the best for stage 3 and 4, respectively. Notably, patients below 50 have higher survival rates than those above 50. It was also noted that women have higher survival rates than men. The three objectives were met, where the first objective involved fitting the data into the model. Hazard functions were formed, and the hazard rates were calculated using the coefficients from the hazard functions.   Based on the objectives, it was recommended that modeling data after combining several treatments should be done. Also, the survivorship of patients after combining treatments should be found and compared with the survivorship after using one treatment at a time. Lastly, since herbal treatment is becoming a common treatment, enough data should be corrected and the treatment compared with other treatment methods. Keywords: Stomach Cancer, Stratified Cox model, Hazard ratio/rates, chemotherapy, radiotherapy, hormone therapy, surger

Non-Parametric Estimator for a Finite Population Total Under Stratified Sampling Incorporating a Hybrid of Data Transformation and Reflection Techniques

Survey sampling methods are used in the estimation of population parameters of interest. This field has received increased demand due to the reliable statistics they produce. Information is extracted from the samples and used to make inferences about the population. In this paper, a nonparametric estimator for a finite population total that addresses the problem of boundary bias is proposed. The properties of this estimator were studied in order to determine its accuracy. The estimator was applied to a simulated data and the analysis was done using R statistical package version i386 4.0.3 and the results of the bias confirmed. The performance of the proposed estimator was tested and compared to the design-based Horvitz-Thompson estimator, the model-based approach proposed by Dorfman and the ratio estimator. This was done by studying both the unconditional and conditional properties of the estimators under the linear, quadratic and exponential mean functions. The proposed estimator outperformed other estimators in quadratic and exponential mean functions and therefore can be recommended for estimation and addressing the boundary problem. Keywords: data transformation, data reflection, boundary bia