In this paper, a new long term survival model called Nadarajah-Haghighi model for survival data with long term survivors was proposed. The model is used in fitting data where the population of interest is a mixture of individuals that are susceptible to the event of interest and individuals that are not susceptible to the event of interest. The statistical properties of the proposed model including quantile function, moments, mean and variance were provided. Maximum likelihood estimation procedure was used to estimate the parameters of the model assuming right censoring. Furthermore, Bayesian method of estimation was also employed in estimating the parameters of the model assuming right censoring. Simulations study was performed in order to ascertain the performances of the MLE estimators. Random samples of different sample sizes were generated from the model with some arbitrary values for the parameters for 5%, 1:3% and 1:5% cure fraction values. Bias, standard error and mean square error were used as discrimination criteria. Additionally, we compared the performance of the proposed model with some competing models. The results of the applications indicates that the proposed model is more efficient than the models compared with. Finally, we fitted some models considering type of treatment as a covariate. It was observed that the covariate have effect on the shape parameter of the proposed model.
Hypertension is a worldwide public health challenge. The study investigated the time it takes to attain an optimal control of hypertension and the major factors that influence the control in Specialist Hospital, Sokoto. A retrospective cohort study was conducted involving 300 patient records. The population consisted all hypertensive patients on follow-ups at Specialist Hospital Sokoto from1st February, 2015 to 1st February, 2021.Statistical Package for the Social Sciences version 20 and R software were used for descriptive, Kaplan-Meier estimator, Cox Proportional Regression (CPH) Model and Weibull Regression Model analyses. Hypertensive patients attain an optimal control after a median survival time of 40.43 (at 95% CI: 33.67- 47.19) months (3.37 years) and mean survival time of 44.18 (CI: 37.24-51.12) months (3.68 years). The CPH analysis revealed that the factors that influenced an optimal control of hypertension were body mass index (BMI) (P <0.001), number of anti-hypertensive drugs (P <0.001), place of residence (P = 0.030). similarly, the Weibull model revealed that the factors that affected an optimal control of hypertension were BMI (P <0.01), number of anti-hypertensive drugs (P <0.001), place of residence (P = 0.042) and educational status (P = 0.036). In conclusion, BMI, number of anti-hypertensive drugs, Place of residence, Educational status. should be watched out during management of hypertensive patients. This also call for an extension of this study through a prospective design to be able to measure the effect of other factors in the achievement of optimal control of hypertension
In this article, an alternative method of defining the probability density function of Generalized Weibull-exponential distributions is proposed. Based on the method, the distribution can also be called Weibull exponentiated exponential distribution. This distribution includes the exponential, Weibull and exponentiated exponential distributions as special cases. Comprehensive mathematical treatment of the distribution is provided. The quantile function, mode, characteristic function, moment generating function among other mathematical properties of the distribution were derived. The parameters of the distribution were estimated by applying the Maximum Likelihood Procedure.The elements of the Fisher Information Matrix is also provided. Finally, a data set is fitted to the model and its sub-models. It is observed that the new distribution is more flexible and can be used quiet effectively in analysing real life data in place of exponential, Weibull and exponentiated exponential distributions.
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