Survival analysis of cancer patients using a new extended Weibull distribution

Generalization of Odd Ramos-Louzada generated family of distributions: Properties, characterizations, and applications to diabetes and cancer survival datasets

Probability distributions offer the best description of survival data and as a result, various lifetime models have been proposed. However, some of these survival datasets are not followed or sufficiently fitted by the existing proposed probability distributions. This paper presents a novel Kumaraswamy Odd Ramos-Louzada-G (KumORL-G) family of distributions together with its statistical features, including the quantile function, moments, probability-weighted moments, order statistics, and entropy measures. Some relevant characterizations were obtained using the hazard rate function and the ratio of two truncated moments. In light of the proposed KumORL-G family, a five-parameter sub-model, the Kumaraswamy Odd Ramos-Louzada Burr XII (KumORLBXII) distribution was introduced and its parameters were determined with the maximum likelihood estimation (MLE) technique. Monte Carlo simulation was performed and the numerical results were used to evaluate the MLE technique. The proposed probability distribution's significance and applicability were empirically demonstrated using various complete and censored datasets on the survival times of cancer and diabetes patients. The analytical results showed that the KumORLBXII distribution performed well in practice in comparison to its sub-models and several other competing distributions. The new KumORL-G for diabetes and cancer survival data is found extremely efficient and offers an enhanced and novel technique for modeling survival datasets.

The development of an extended Weibull model with applications to medicine, industry and actuarial sciences

This paper delves into the theoretical and practical exploration of the complementary Bell Weibull (CBellW) model, which serves as an analogous counterpart to the complementary Poisson Weibull model. The study encompasses a comprehensive examination of various statistical properties of the CBellW model. Real data applications are carried out in three different fields, namely the medical, industrial and actuarial fields, to show the practical versatility of the CBellW model. For the medical data segment, the study utilizes four data sets, including information on daily confirmed COVID-19 cases and cancer data. Additionally, a Group Acceptance Sampling Plan (GASP) is designed by using the median as quality parameter. Furthermore, some actuarial risk measures for the CBellW model are obtained along with a numerical illustration of the Value at Risk and the Expected Shortfall. The research is substantiated by a comprehensive numerical analysis, model comparisons, and graphical illustrations that complement the theoretical foundation.

A new family of distributions using a trigonometric function: Properties and applications in the healthcare sector

Probability distributions play a pivotal and significant role in modeling real-life data in every field. For this activity, a series of probability distributions have been introduced and exercised in applied sectors. This paper also contributes a new method for modeling continuous data sets. The proposed family is called the exponent power sine-G family of distributions. Based on the exponent power sine-G method, a new model, namely, the exponent power sine-Weibull model is studied. Several mathematical properties such as quantile function, identifiability property, and r t h moment are derived. For the exponent power sine-G method, the maximum likelihood estimators are obtained. Simulation studies are also presented. Finally, the optimality of the exponent power sine-Weibull model is shown by taking two applications from the healthcare sector. Based on seven evaluating criteria, it is demonstrated that the proposed model is the best competing distribution for analyzing healthcare phenomena.

Prioritizing Disease Diagnosis in Neonatal Cohorts through Multivariate Survival Analysis: A Nonparametric Bayesian Approach

Understanding the intricate relationships between diseases is critical for both prevention and recovery. However, there is a lack of suitable methodologies for exploring the precedence relationships within multiple censored time-to-event data, resulting in decreased analytical accuracy. This study introduces the Censored Event Precedence Analysis (CEPA), which is a nonparametric Bayesian approach suitable for understanding the precedence relationships in censored multivariate events. CEPA aims to analyze the precedence relationships between events to predict subsequent occurrences effectively. We applied CEPA to neonatal data from the National Health Insurance Service, identifying the precedence relationships among the seven most commonly diagnosed diseases categorized by the International Classification of Diseases. This analysis revealed a typical diagnostic sequence, starting with respiratory diseases, followed by skin, infectious, digestive, ear, eye, and injury-related diseases. Furthermore, simulation studies were conducted to demonstrate CEPA suitability for censored multivariate datasets compared to traditional models. The performance accuracy reached 76% for uniform distribution and 65% for exponential distribution, showing superior performance in all four tested environments. Therefore, the statistical approach based on CEPA enhances our understanding of disease interrelationships beyond competitive methodologies. By identifying disease precedence with CEPA, we can preempt subsequent disease occurrences and propose a healthcare system based on these relationships.

A new flexible Weibull extension model: Different estimation methods and modeling an extreme value data

The word extreme events refer to unnatural or undesirable events. Due to the general destructive effects on society and scientific problems in various applied fields, the study of extreme events is an important subject for researchers. Many real-life phenomena exhibit clusters of extreme observations that cannot be adequately predicted and modeled by the traditional distributions. Therefore, we need new flexible probability distributions that are useful in modeling extreme-value data in various fields such as the financial sector, telecommunications, hydrology, engineering, and meteorology. In this piece of research work, a new flexible probability distribution is introduced, which is attained by joining together the flexible Weibull distribution with the weighted T-X strategy. The new model is named a new flexible Weibull extension distribution. The distributional properties of the new model are derived. Furthermore, some frequently implemented estimation approaches are considered to obtain the estimators of the new flexible Weibull extension model. Finally, we demonstrate the utility of the new flexible Weibull extension distribution by analyzing an extreme value data set.

Uni-variate and bi-variate Inverted Exponential Teissier distribution in Bayesian and non-Bayesian framework to model stochastic dynamic variation of climate data

This article provides a new Inverted Exponential Teissier (IET) distribution to model an extreme value data set and explain temporal dependence in environmental statistics employing bi-variate probability distribution. We deduce its various statistical properties, including descriptive statistics, characterization, and different measurements of reliability. The model parameters are estimated using Bayesian and non-Bayesian frameworks. For exploring the dependency structures between two geographical Random Variables (RV), we extend the IET to bi-variate IET (BIET) distribution. We introduce a novel time series forecasting algorithm based upon copula assuming stationarity of the data set. We validate the proposed method using extensive simulation studies with different possible combinations of parameter values. This method is applied to the seasonal rainfall data of Kerala from 1901 to 2017. We estimate the monsoon rainfall using median regression derived from BIET, where summer rainfall data is used as an important covariate. We found the Mean Absolute Percentage Error (MAPE) is 19.242 % on the test data set.

Applicability of modified weibull extension distribution in modeling censored medical datasets: a bayesian perspective

There are some contributions analyzing the censored medical datasets using modifications of the conventional lifetime distribution; however most of the said contributions did not considered the modification of the Weibull distribution (WD). The WD is an important lifetime model. Due to its prime importance in modeling life data, many researchers have proposed different modifications of WD. One of the most recent modifications of WD is Modified Weibull Extension distribution (MWED). However, the ability of MWED to model the censored medical data has not yet been explored in the literature. We have explored the suitability of the model in modeling censored medical datasets. The analysis has been carried out using Bayesian methods under different loss functions and informative priors. The approximate Bayes estimates have been computed using Lindley's approximation. Based on detailed simulation study and real life analysis, it has been concluded that Bayesian methods performed better as compared to maximum likelihood estimates. In case of small samples, the performance of Bayes estimates under ELF and informative prior was the best. However, in case of large samples, the choice of prior and loss function did not affect the efficiency of the results to a large extend. The MWED performed efficiently in modeling real censored datasets relating to survival times of the leukemia and bile duct cancer patients. The MWED was explored to be a very promising candidate model for modeling censored medical datasets.

A new statistical approach for modeling the bladder cancer and leukemia patients data sets: Case studies in the medical sector

Statistical methods are frequently used in numerous healthcare and other related sectors. One of the possible applications of the statistical methods is to provide the best description of the data sets in the healthcare sector. Keeping in view the applicability of statistical methods in the medical sector, numerous models have been introduced. In this paper, we also introduce a novel statistical method called, a new modified-G family of distributions. Several mathematical properties of the new modified-G family are derived. Based on the new modified-G method, a new updated version of the Weibull model called, a new modified-Weibull distribution is introduced. Furthermore, the estimators of the parameters of the new modified-G distributions are also obtained. Finally, the applicability of the new modified-Weibull distribution is illustrated by analyzing two medical sets. Using certain analytical tools, it is observed that the new modified-Weibull distribution is the best choice to deal with the medical data sets.