Exact Moments of Generalized Pareto Distribution based on Generalized Order Statistics and Characterizations

In this paper, we present simple explicit expressions for single and product moments of generalized order statistics from generalized Pareto distribution. These relations are deduced for the moments of order statistics and record values and tabulated the mean and variance of this distribution. Further, conditional expectation, recurrence relations for single as well as for product moments of generalized order statistics and truncated moment are used to characterize this distribution

Some Results on Exponentiated Weibull Distribution via Dual Generalized Order Statistics

In this paper, we use the concept of dual generalized order statistics dgos which was given by Pawlas and Syznal (2001). By using this, we obtain the various theorems and some relations through ratio and inverse moment by using exponentiated-Weibull distribution. Cases for order statistics and lower record values are also considered. Further, we characterize the exponentiated-Weibull distribution through three different methods by using the results obtained in this paper

Moments of Generalized Upper Record Values from Weibull- Power Function Distribution and Characterization

Tahir et al. (2014) proposed a new four parameter lifetime distribution called Weibull-power function distribution. In this article, some simple recurrence relations for the single and product moments as well as for inverse and quotient moments have been derived for the generalized upper record values ( k−th upper record values). Moreover, these relations are deduced for moments of upper record values. Furthermore, conditional expectation, recurrence relations for the single and product moments and truncated moment have been used to characterize this distribution

Characterizations of Topp–Leone Lomax Distribution based on the Generalized Lower Record Values

In this paper, we derive the exact expressions as well as recurrence relations for single and product moment of generalized lower record values from Topp–Leone Lomax distribution. Further, we characterize the given distribution through conditional expectation, recurrence relations and truncated moment

Model-based survival estimates of female breast cancer data

Background: Statistical methods are very important to precisely measure breast cancer patient survival times for healthcare management. Previous studies considered basic statistics to measure survival times without incorporating statistical modeling strategies. The objective of this study was to develop a data-based statistical probability model from the female breast cancer patients’ survival times by using the Bayesian approach to predict future inferences of survival times. Materials and Methods: A random sample of 500 female patients was selected from the Surveillance Epidemiology and End Results cancer registry database. For goodness of fit, the standard model building criteria were used. The Bayesian approach is used to obtain the predictive survival times from the data-based Exponentiated Exponential Model. Markov Chain Monte Carlo method was used to obtain the summary results for predictive inference. Results: The highest number of female breast cancer patients was found in California and the lowest in New Mexico. The majority of them were married. The mean (SD) age at diagnosis (in years) was 60.92 (14.92). The mean (SD) survival time (in months) for female patients was 90.33 (83.10). The Exponentiated Exponential Model found better fits for the female survival times compared to the Exponentiated Weibull Model. The Bayesian method is used to obtain predictive inference for future survival times. Conclusions: The findings with the proposed modeling strategy will assist healthcare researchers and providers to precisely predict future survival estimates as the recent growing challenges of analyzing healthcare data have created new demand for model-based survival estimates. The application of Bayesian will produce precise estimates of future survival times

Methods needed to measure predictive accuracy: A study of diabetic patients

Diabetes is one of the leading causes of morbidity and mortality and it can result in several complications such as kidney failure, heart failure, stroke, and blindness making it a major medical and public health concern in the United States. Statistical methods are important to detect risk factors and identify the best sampling plan to determine predictive bounds for diabetic patients\u27 data. The main objective of this paper is to identify the best fit bootstrapping sampling method and to draw the predictive bound considering diabetes patient data. A random sample was used from the National Health and Nutritional Examination Survey (NHANES) for this study. We found that there were significant relationships between age, marital status, and race/ethnicity with diabetes status (p \u3c 0.001) and no relationship was observed between gender and diabetes status. We ran the logistic regression to identify the risk factors from the data. We identified that the significant risk factors are age (p \u3c 0.001), total protein (p \u3c 0.001), fast food (p \u3c 0.0339), and direct HDL (p \u3c 0.001). This study provides evidence that the parametric bootstrapping method is the best fit method compared with other methods to estimate the predictive error bounds. These findings will be of great significance for identifying the best sampling methods, which can increase the statistical accuracy of laboratory clinical research of diabetes. This will also allow for the determination of precise risk factors that will best represent the data by detecting mild and extreme outliers from disease observations. Therefore, these results will be useful for researchers and clinicians to select the best sampling methods to study diabetes and other diseases in order to maximize the accuracy of their results. This article is part of a Special Issue entitled: Oxidative Stress and Mitochondrial Quality in Diabetes/Obesity and Critical Illness Spectrum of Diseases - edited by P. Hemachandra Reddy

Survival analysis for white non-Hispanic female breast cancer patients

Background: Race and ethnicity are significant factors in predicting survival time of breast cancer patients. In this study, we applied advanced statistical methods to predict the survival of White non-Hispanic female breast cancer patients, who were diagnosed between the years 1973 and 2009 in the United States (U.S.). Materials and Methods: Demographic data from the Surveillance Epidemiology and End Results (SEER) database were used for the purpose of this study. Nine states were randomly selected from 12 U.S. cancer registries. A stratified random sampling method was used to select 2,000 female breast cancer patients from these nine states. We compared four types of advanced statistical probability models to identify the best-fit model for the White nonHispanic female breast cancer survival data. Three model building criterion were used to measure and compare goodness of fit of the models. These include Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), and Deviance Information Criteria (DIC). In addition, we used a novel Bayesian method and the Markov Chain Monte Carlo technique to determine the posterior density function of the parameters. After evaluating the model parameters, we selected the model having the lowest DIC value. Using this Bayesian method, we derived the predictive survival density for future survival time and its related inferences. Results: The analytical sample of White non-Hispanic women included 2,000 breast cancer cases from the SEER database (1973-2009). The majority of cases were married (55.2%), the mean age of diagnosis was 63.61 years (SD = 14.24) and the mean survival time was 84 months (SD = 35.01). After comparing the four statistical models, results suggested that the exponentiated Weibull model (DIC= 19818.220) was a better fit for White non-Hispanic females’ breast cancer survival data. This model predicted the survival times (in months) for White non-Hispanic women after implementation of precise estimates of the model parameters. Conclusions: By using modern model building criteria, we determined that the data best fit the exponentiated Weibull model. We incorporated precise estimates of the parameter into the predictive model and evaluated the survival inference for the White non-Hispanic female population. This method of analysis will assist researchers in making scientific and clinical conclusions when assessing survival time of breast cancer patients

Statistical applications for the prediction of white hispanic breast cancer survival

Background: The ability to predict the survival time of breast cancer patients is important because of the potential high morbidity and mortality associated with the disease. To develop a predictive inference for determining the survival of breast cancer patients, we applied a novel Bayesian method. In this paper, we propose the development of a databased statistical probability model and application of the Bayesian method to predict future survival times for White Hispanic female breast cancer patients, diagnosed in the US during 1973-2009. Materials and Methods: A stratified random sample of White Hispanic female patient survival data was selected from the Surveillance Epidemiology and End Results (SEER) database to derive statistical probability models. Four were considered to identify the best-fit model. We used three standard model-building criteria, which included Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), and Deviance Information Criteria (DIC) to measure the goodness of fit. Furthermore, the Bayesian method was used to derive future survival inferences for survival times. Results: The highest number of White Hispanic female breast cancer patients in this sample was from New Mexico and the lowest from Hawaii. The mean (SD) age at diagnosis (years) was 58.2 (14.2). The mean (SD) of survival time (months) for White Hispanic females was 72.7 (32.2). We found that the exponentiated Weibull model best fit the survival times compared to other widely known statistical probability models. The predictive inference for future survival times is presented using the Bayesian method. Conclusions: The findings are significant for treatment planning and health-care cost allocation. They should also contribute to further research on breast cancer survival issues

Health disparities between Black Hispanic and Black non-Hispanic cervical cancer cases in the USA

Background: Globally, cervical cancer is a major public health concern. Cervical cancer is the second most common cancer among women, resulting in approximately 500,000 cases per year. The purpose of this study is to compare disease characteristics between Black Hispanic (BH) and Black non-Hispanic (BNH) women in the US. Materials and Methods: We used stratified random sampling to select cervical cancer patient records from the SEER database (1973-2009). We used Chi-square and independent samples t-test to examine differences in proportions and means. Results: The sample included 2,000 cervical cancer cases of Black non-Hispanic and 91 Black Hispanic women. There were statistically significant differences between black Hispanic and black non- Hispanics in mean age at diagnosis (p\u3c0.001), mean survival time (p\u3c0.001), marital status (p\u3c0.001), primary site of cancer (p\u3c0.001); lymph node involvement (p\u3c0.001); grading and differentiation (p\u3c0.0001); and tumor behavior (p\u3c0.001). Black women were more likely to develop cervical cancer and to have the highest mortality rates from the disease. Conclusions: Findings from this study show clear racial and ethnic disparities in cervical cancer incidence and prognosis that should be addressed

Disparities in cervical cancer characteristics and survival between white Hispanics and white non-Hispanic women

Background:Cervical cancer is the second most common cancer among women resulting in nearly 500,000cases annually. Screening leads to better treatment and survival time. However, human papillomavirus (HPV)exposure, screening, and treatment vary among races and ethnicities in the United States. The purpose of thisstudy is to examine disparities in characteristics of cervical cancer and survival of cases between White Hispanic(WH) and White non-Hispanic (WNH) women in the United States.Methods:We used a stratified random sampling method to select cervical cancer patient records from ninestates; a simple random sampling method to extract the demographic and disease characteristics data withinstates from the Surveillance Epidemiology and End Results (SEER) database. We used statistical probabilitydistribution methods for discrete and continuous data. The chi-square test and independent samplest-testwere used to evaluate statistically significant differences. Furthermore, the Cox Proportional Regression andthe Kaplan–Meier survival estimators were used to compare WH and WNH population survival times in theUnited States.Results:The samples of WNH and WH women included 4,000 cervical cancer cases from 1973–2009. Therewere statistically significant differences between ethnicities: marital status (p\u3c0.001); primary site of cancer(p\u3c0.001); lymph node involvement (p\u3c0.001); grading and differentiation (p\u3c0.0001); and tumor behavior(p\u3c0.001). The mean age of diagnosis for both groups showed no statistical differences. However, the meansurvival time for WNH was 221.7 (standard deviation [SD]=118.1) months and for WH was 190.3 (SD=120.3),which differed significantly (p\u3c0.001).Conclusions:Clear disparities exist in risk factors, cervical cancer characteristics, and survival time betweenWH and WNH women