On Bayesian Estimation and Predictions for Two-Component Mixture of the Gompertz Distribution

Mixtures models have received sizeable attention from analysts in the recent years. Some work on Bayesian estimation of the parameters of mixture models have appeared. However, the were restricted to the Bayes point estimation The methodology for the Bayesian interval estimation of the parameters for said models is still to be explored. This paper proposes the posterior interval estimation (along with point estimation) for the parameters of a two-component mixture of the Gompertz distribution. The posterior predictive intervals are also derived and evaluated. Different informative and non-informative priors are assumed under a couple of loss functions for the posterior analysis. A simulation study was carried out in order to make comparisons among different point and interval estimators. The applicability of the results is illustrated via a real life example

Doubly Censored Data from Two-Component Mixture of Inverse Weibull Distributions: Theory and Applications

Finite mixture distributions consist of a weighted sum of standard distributions and are a useful tool for reliability analysis of a heterogeneous population. They provide the necessary flexibility to model failure distributions of components with multiple failure models. The analysis of the mixture models under Bayesian framework has received sizable attention in the recent years. However, the Bayesian estimation of the mixture models under doubly censored samples has not yet been introduced in the literature. The main objective of this paper is to discuss the Bayes estimation of the inverse Weibull mixture distributions under doubly censoring. Different priors and loss functions were assumed for the posterior estimation. The performance of the different estimators has been compared in terms of posterior risks

Study of the Left Censored Data from the Gumbel Type II Distribution under a Bayesian Approach

Based on left type II censored samples from a Gumbel type II distribution, the Bayes estimators and corresponding risks of the unknown parameter were obtained under different asymmetric loss functions, assuming different informative and non-informative priors. Elicitation of hyper-parameters through prior predictive approach has also been discussed. The expressions for the credible intervals and posterior predictive distributions have been derived. Comparisons of these estimators are made through simulation study using numerical and graphical methods

Bayesian Estimation of the Parameters of Two-Component Mixture of Rayleigh Distribution under Doubly Censoring

Recently, the Bayesian analysis of the two-component mixture of lifetime models under singly type I censored samples was discussed. The Bayes estimation of the parameters of mixture of two Rayleigh distributions (MTRD) is developed under doubly censoring. Different informative priors, under squared error loss function and k-loss function, have been assumed for the posterior estimation. The performance of different estimators has been compared in terms of posterior risks by analyzing the simulated and real life data sets

Global, regional, and national burden of stroke and its risk factors, 1990–2019: a systematic analysis for the Global Burden of Disease Study 2019

Background Regularly updated data on stroke and its pathological types, including data on their incidence, prevalence, mortality, disability, risk factors, and epidemiological trends, are important for evidence-based stroke care planning and resource allocation. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) aims to provide a standardised and comprehensive measurement of these metrics at global, regional, and national levels. Methods We applied GBD 2019 analytical tools to calculate stroke incidence, prevalence, mortality, disability-adjusted life-years (DALYs), and the population attributable fraction (PAF) of DALYs (with corresponding 95% uncertainty intervals [UIs]) associated with 19 risk factors, for 204 countries and territories from 1990 to 2019. These estimates were provided for ischaemic stroke, intracerebral haemorrhage, subarachnoid haemorrhage, and all strokes combined, and stratified by sex, age group, and World Bank country income level. Findings In 2019, there were 12·2 million (95% UI 11·0–13·6) incident cases of stroke, 101 million (93·2–111) prevalent cases of stroke, 143 million (133–153) DALYs due to stroke, and 6·55 million (6·00–7·02) deaths from stroke. Globally, stroke remained the second-leading cause of death (11·6% [10·8–12·2] of total deaths) and the third-leading cause of death and disability combined (5·7% [5·1–6·2] of total DALYs) in 2019. From 1990 to 2019, the absolute number of incident strokes increased by 70·0% (67·0–73·0), prevalent strokes increased by 85·0% (83·0–88·0), deaths from stroke increased by 43·0% (31·0–55·0), and DALYs due to stroke increased by 32·0% (22·0–42·0). During the same period, age-standardised rates of stroke incidence decreased by 17·0% (15·0–18·0), mortality decreased by 36·0% (31·0–42·0), prevalence decreased by 6·0% (5·0–7·0), and DALYs decreased by 36·0% (31·0–42·0). However, among people younger than 70 years, prevalence rates increased by 22·0% (21·0–24·0) and incidence rates increased by 15·0% (12·0–18·0). In 2019, the age-standardised stroke-related mortality rate was 3·6 (3·5–3·8) times higher in the World Bank low-income group than in the World Bank high-income group, and the age-standardised stroke-related DALY rate was 3·7 (3·5–3·9) times higher in the low-income group than the high-income group. Ischaemic stroke constituted 62·4% of all incident strokes in 2019 (7·63 million [6·57–8·96]), while intracerebral haemorrhage constituted 27·9% (3·41 million [2·97–3·91]) and subarachnoid haemorrhage constituted 9·7% (1·18 million [1·01–1·39]). In 2019, the five leading risk factors for stroke were high systolic blood pressure (contributing to 79·6 million [67·7–90·8] DALYs or 55·5% [48·2–62·0] of total stroke DALYs), high body-mass index (34·9 million [22·3–48·6] DALYs or 24·3% [15·7–33·2]), high fasting plasma glucose (28·9 million [19·8–41·5] DALYs or 20·2% [13·8–29·1]), ambient particulate matter pollution (28·7 million [23·4–33·4] DALYs or 20·1% [16·6–23·0]), and smoking (25·3 million [22·6–28·2] DALYs or 17·6% [16·4–19·0]). Interpretation The annual number of strokes and deaths due to stroke increased substantially from 1990 to 2019, despite substantial reductions in age-standardised rates, particularly among people older than 70 years. The highest age-standardised stroke-related mortality and DALY rates were in the World Bank low-income group. The fastest-growing risk factor for stroke between 1990 and 2019 was high body-mass index. Without urgent implementation of effective primary prevention strategies, the stroke burden will probably continue to grow across the world, particularly in low-income countries.publishedVersio

The global burden of adolescent and young adult cancer in 2019 : a systematic analysis for the Global Burden of Disease Study 2019

Background In estimating the global burden of cancer, adolescents and young adults with cancer are often overlooked, despite being a distinct subgroup with unique epidemiology, clinical care needs, and societal impact. Comprehensive estimates of the global cancer burden in adolescents and young adults (aged 15-39 years) are lacking. To address this gap, we analysed results from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019, with a focus on the outcome of disability-adjusted life-years (DALYs), to inform global cancer control measures in adolescents and young adults. Methods Using the GBD 2019 methodology, international mortality data were collected from vital registration systems, verbal autopsies, and population-based cancer registry inputs modelled with mortality-to-incidence ratios (MIRs). Incidence was computed with mortality estimates and corresponding MIRs. Prevalence estimates were calculated using modelled survival and multiplied by disability weights to obtain years lived with disability (YLDs). Years of life lost (YLLs) were calculated as age-specific cancer deaths multiplied by the standard life expectancy at the age of death. The main outcome was DALYs (the sum of YLLs and YLDs). Estimates were presented globally and by Socio-demographic Index (SDI) quintiles (countries ranked and divided into five equal SDI groups), and all estimates were presented with corresponding 95% uncertainty intervals (UIs). For this analysis, we used the age range of 15-39 years to define adolescents and young adults. Findings There were 1.19 million (95% UI 1.11-1.28) incident cancer cases and 396 000 (370 000-425 000) deaths due to cancer among people aged 15-39 years worldwide in 2019. The highest age-standardised incidence rates occurred in high SDI (59.6 [54.5-65.7] per 100 000 person-years) and high-middle SDI countries (53.2 [48.8-57.9] per 100 000 person-years), while the highest age-standardised mortality rates were in low-middle SDI (14.2 [12.9-15.6] per 100 000 person-years) and middle SDI (13.6 [12.6-14.8] per 100 000 person-years) countries. In 2019, adolescent and young adult cancers contributed 23.5 million (21.9-25.2) DALYs to the global burden of disease, of which 2.7% (1.9-3.6) came from YLDs and 97.3% (96.4-98.1) from YLLs. Cancer was the fourth leading cause of death and tenth leading cause of DALYs in adolescents and young adults globally. Interpretation Adolescent and young adult cancers contributed substantially to the overall adolescent and young adult disease burden globally in 2019. These results provide new insights into the distribution and magnitude of the adolescent and young adult cancer burden around the world. With notable differences observed across SDI settings, these estimates can inform global and country-level cancer control efforts. Copyright (C) 2021 The Author(s). Published by Elsevier Ltd.Peer reviewe

Cancer Incidence, Mortality, Years of Life Lost, Years Lived With Disability, and Disability-Adjusted Life Years for 29 Cancer Groups From 2010 to 2019: A Systematic Analysis for the Global Burden of Disease Study 2019.

The Global Burden of Diseases, Injuries, and Risk Factors Study 2019 (GBD 2019) provided systematic estimates of incidence, morbidity, and mortality to inform local and international efforts toward reducing cancer burden. To estimate cancer burden and trends globally for 204 countries and territories and by Sociodemographic Index (SDI) quintiles from 2010 to 2019. The GBD 2019 estimation methods were used to describe cancer incidence, mortality, years lived with disability, years of life lost, and disability-adjusted life years (DALYs) in 2019 and over the past decade. Estimates are also provided by quintiles of the SDI, a composite measure of educational attainment, income per capita, and total fertility rate for those younger than 25 years. Estimates include 95% uncertainty intervals (UIs). In 2019, there were an estimated 23.6 million (95% UI, 22.2-24.9 million) new cancer cases (17.2 million when excluding nonmelanoma skin cancer) and 10.0 million (95% UI, 9.36-10.6 million) cancer deaths globally, with an estimated 250 million (235-264 million) DALYs due to cancer. Since 2010, these represented a 26.3% (95% UI, 20.3%-32.3%) increase in new cases, a 20.9% (95% UI, 14.2%-27.6%) increase in deaths, and a 16.0% (95% UI, 9.3%-22.8%) increase in DALYs. Among 22 groups of diseases and injuries in the GBD 2019 study, cancer was second only to cardiovascular diseases for the number of deaths, years of life lost, and DALYs globally in 2019. Cancer burden differed across SDI quintiles. The proportion of years lived with disability that contributed to DALYs increased with SDI, ranging from 1.4% (1.1%-1.8%) in the low SDI quintile to 5.7% (4.2%-7.1%) in the high SDI quintile. While the high SDI quintile had the highest number of new cases in 2019, the middle SDI quintile had the highest number of cancer deaths and DALYs. From 2010 to 2019, the largest percentage increase in the numbers of cases and deaths occurred in the low and low-middle SDI quintiles. The results of this systematic analysis suggest that the global burden of cancer is substantial and growing, with burden differing by SDI. These results provide comprehensive and comparable estimates that can potentially inform efforts toward equitable cancer control around the world.Funding/Support: The Institute for Health Metrics and Evaluation received funding from the Bill & Melinda Gates Foundation and the American Lebanese Syrian Associated Charities. Dr Aljunid acknowledges the Department of Health Policy and Management of Kuwait University and the International Centre for Casemix and Clinical Coding, National University of Malaysia for the approval and support to participate in this research project. Dr Bhaskar acknowledges institutional support from the NSW Ministry of Health and NSW Health Pathology. Dr Bärnighausen was supported by the Alexander von Humboldt Foundation through the Alexander von Humboldt Professor award, which is funded by the German Federal Ministry of Education and Research. Dr Braithwaite acknowledges funding from the National Institutes of Health/ National Cancer Institute. Dr Conde acknowledges financial support from the European Research Council ERC Starting Grant agreement No 848325. Dr Costa acknowledges her grant (SFRH/BHD/110001/2015), received by Portuguese national funds through Fundação para a Ciência e Tecnologia, IP under the Norma Transitória grant DL57/2016/CP1334/CT0006. Dr Ghith acknowledges support from a grant from Novo Nordisk Foundation (NNF16OC0021856). Dr Glasbey is supported by a National Institute of Health Research Doctoral Research Fellowship. Dr Vivek Kumar Gupta acknowledges funding support from National Health and Medical Research Council Australia. Dr Haque thanks Jazan University, Saudi Arabia for providing access to the Saudi Digital Library for this research study. Drs Herteliu, Pana, and Ausloos are partially supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNDS-UEFISCDI, project number PN-III-P4-ID-PCCF-2016-0084. Dr Hugo received support from the Higher Education Improvement Coordination of the Brazilian Ministry of Education for a sabbatical period at the Institute for Health Metrics and Evaluation, between September 2019 and August 2020. Dr Sheikh Mohammed Shariful Islam acknowledges funding by a National Heart Foundation of Australia Fellowship and National Health and Medical Research Council Emerging Leadership Fellowship. Dr Jakovljevic acknowledges support through grant OI 175014 of the Ministry of Education Science and Technological Development of the Republic of Serbia. Dr Katikireddi acknowledges funding from a NHS Research Scotland Senior Clinical Fellowship (SCAF/15/02), the Medical Research Council (MC_UU_00022/2), and the Scottish Government Chief Scientist Office (SPHSU17). Dr Md Nuruzzaman Khan acknowledges the support of Jatiya Kabi Kazi Nazrul Islam University, Bangladesh. Dr Yun Jin Kim was supported by the Research Management Centre, Xiamen University Malaysia (XMUMRF/2020-C6/ITCM/0004). Dr Koulmane Laxminarayana acknowledges institutional support from Manipal Academy of Higher Education. Dr Landires is a member of the Sistema Nacional de Investigación, which is supported by Panama’s Secretaría Nacional de Ciencia, Tecnología e Innovación. Dr Loureiro was supported by national funds through Fundação para a Ciência e Tecnologia under the Scientific Employment Stimulus–Institutional Call (CEECINST/00049/2018). Dr Molokhia is supported by the National Institute for Health Research Biomedical Research Center at Guy’s and St Thomas’ National Health Service Foundation Trust and King’s College London. Dr Moosavi appreciates NIGEB's support. Dr Pati acknowledges support from the SIAN Institute, Association for Biodiversity Conservation & Research. Dr Rakovac acknowledges a grant from the government of the Russian Federation in the context of World Health Organization Noncommunicable Diseases Office. Dr Samy was supported by a fellowship from the Egyptian Fulbright Mission Program. Dr Sheikh acknowledges support from Health Data Research UK. Drs Adithi Shetty and Unnikrishnan acknowledge support given by Kasturba Medical College, Mangalore, Manipal Academy of Higher Education. Dr Pavanchand H. Shetty acknowledges Manipal Academy of Higher Education for their research support. Dr Diego Augusto Santos Silva was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil Finance Code 001 and is supported in part by CNPq (302028/2018-8). Dr Zhu acknowledges the Cancer Prevention and Research Institute of Texas grant RP210042

Global, regional, and national burden of stroke and its risk factors, 1990-2019: a systematic analysis for the Global Burden of Disease Study 2019

Background Regularly updated data on stroke and its pathological types, including data on their incidence, prevalence, mortality, disability, risk factors, and epidemiological trends, are important for evidence-based stroke care planning and resource allocation. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) aims to provide a standardised and comprehensive measurement of these metrics at global, regional, and national levels. Methods We applied GBD 2019 analytical tools to calculate stroke incidence, prevalence, mortality, disability-adjusted life-years (DALYs), and the population attributable fraction (PAF) of DALYs (with corresponding 95% uncertainty intervals UIs]) associated with 19 risk factors, for 204 countries and territories from 1990 to 2019. These estimates were provided for ischaemic stroke, intracerebral haemorrhage, subarachnoid haemorrhage, and all strokes combined, and stratified by sex, age group, and World Bank country income level. Findings In 2019, there were 12.2 million (95% UI 11.0-13.6) incident cases of stroke, 101 million (93.2-111) prevalent cases of stroke, 143 million (133-153) DALYs due to stroke, and 6.55 million (6.00-7.02) deaths from stroke. Globally, stroke remained the second-leading cause of death (11.6% 10.8-12.2] of total deaths) and the third-leading cause of death and disability combined (5.7% 5.1-6.2] of total DALYs) in 2019. From 1990 to 2019, the absolute number of incident strokes increased by 70.0% (67.0-73.0), prevalent strokes increased by 85.0% (83.0-88.0), deaths from stroke increased by 43.0% (31.0-55.0), and DALYs due to stroke increased by 32.0% (22.0-42.0). During the same period, age-standardised rates of stroke incidence decreased by 17.0% (15.0-18.0), mortality decreased by 36.0% (31.0-42.0), prevalence decreased by 6.0% (5.0-7.0), and DALYs decreased by 36.0% (31.0-42.0). However, among people younger than 70 years, prevalence rates increased by 22.0% (21.0-24.0) and incidence rates increased by 15.0% (12.0-18.0). In 2019, the age-standardised stroke-related mortality rate was 3.6 (3.5-3.8) times higher in the World Bank low-income group than in the World Bank high-income group, and the age-standardised stroke-related DALY rate was 3.7 (3.5-3.9) times higher in the low-income group than the high-income group. Ischaemic stroke constituted 62.4% of all incident strokes in 2019 (7.63 million 6.57-8.96]), while intracerebral haemorrhage constituted 27.9% (3.41 million 2.97-3.91]) and subarachnoid haemorrhage constituted 9.7% (1.18 million 1.01-1.39]). In 2019, the five leading risk factors for stroke were high systolic blood pressure (contributing to 79.6 million 67.7-90.8] DALYs or 55.5% 48.2-62.0] of total stroke DALYs), high body-mass index (34.9 million 22.3-48.6] DALYs or 24.3% 15.7-33.2]), high fasting plasma glucose (28.9 million 19.8-41.5] DALYs or 20.2% 13.8-29.1]), ambient particulate matter pollution (28.7 million 23.4-33.4] DALYs or 20.1% 16.6-23.0]), and smoking (25.3 million 22.6-28.2] DALYs or 17.6% 16.4-19.0]). Interpretation The annual number of strokes and deaths due to stroke increased substantially from 1990 to 2019, despite substantial reductions in age-standardised rates, particularly among people older than 70 years. The highest age-standardised stroke-related mortality and DALY rates were in the World Bank low-income group. The fastest-growing risk factor for stroke between 1990 and 2019 was high body-mass index. Without urgent implementation of effective primary prevention strategies, the stroke burden will probably continue to grow across the world, particularly in low-income countries

Parameter Estimations Based On Kumaraswamy Progressive Type II Censored Data with Random Removals

The estimation of two parameters of the Kumaraswamy distribution is considered under Type II progressive censoring with random removals, where the number of units removed at each failure time has a binomial distribution. The MLE was used to obtain the estimators of the unknown parameters, and the asymptotic variance - covariance matrix was also obtained. The formula to compute the expected test time was derived. A numerical study was carried out for different combinations of model parameters. Different censoring schemes were used for the estimation, and performance of these schemes was compared

Bayesian Inference of a Finite Mixture of Inverse Weibull Distributions with an Application to Doubly Censoring Data

The families of mixture distributions have a wider range of applications in different fields such as fisheries, agriculture, botany, economics, medicine, psychology, electrophoresis, finance, communication theory, geology and zoology. They provide the necessary flexibility to model failure distributions of components with multiple failure modes. Mostly, the Bayesian procedure for the estimation of parameters of mixture model is described under the scheme of Type-I censoring. In particular, the Bayesian analysis for the mixture models under doubly censored samples has not been considered in the literature yet. The main objective of this paper is to develop the Bayes estimation of the inverse Weibull mixture distributions under doubly censoring. The posterior estimation has been conducted under the assumption of gamma and inverse levy using precautionary loss function and weighted squared error loss function. The comparisons among the different estimators have been made based on analysis of simulated and real life data sets