Approximate bayesian estimates of weibull parameters with Lindley’s method

One of the most important lifetime distributions that is used for modelling and analysing data in clinical, life sciences and engineering is the Weibull distribution. The main objective of this paper was to determine the best estimator for the two-parameter Weibull distribution. The methods under consideration are the frequentist maximum likelihood estimator, least square regression estimator and the Bayesian estimator by using two loss functions, which are squared error and linear exponential. Lindley approximation is used to obtain the Bayes estimates. Comparisons are made through simulation study to determine the performance of these methods. Based on the results obtained from this simulation study the Bayesian approach used in estimating the Weibull parameters under linear exponential loss function is found to be superior as compared to the conventional maximum likelihood and least squared methods

Methods for estimating the 2-parameter Weibull distribution with type-1 censored data

This study is concerned with the two-parameter Weibull distribution which has and is still being used as a model in life testing and reliability engineering. We seek to find out whether Rank Regression Method can be a good alternative to that of the world publicised traditional method known as Maximum Likelihood for estimating two parameters of the Weibull distribution. The methods under consideration are: Maximum Likelihood Estimation, Least Square Estimation on Y and that of Least Square Estimation on X. These estimators are derived for Random Type-I censored samples. These methods were compared using Mean Square Error and Mean Percentage Error through simulation study with small, medium and large sample sizes in estimating the Weibull parameters under Type-I censored data. The observations that are made based on this study are that Maximum Likelihood Estimator stands out when estimating the scale parameter followed by Least Square Estimator on X but for the shape parameter Least Square Estimator on X performed better than Maximum Likelihood Estimator thereby making it a good alternative method to MLE

Bayesian statistical inference of loglogistic model with interval-censored lifetime data

The properties of Palm Oil (PO) and Coconut Oil (CO) offer the potential for transformers Interval-censored data arise when a failure time say, T cannot be observed directly but can only be determined to lie in an interval obtained from a series of inspection times. The frequentist approach for analysing interval-censored data has been developed for some time now. It is very common due to unavailability of software in the field of biological, medical and reliability studies to simplify the interval censoring structure of the data into that of a more standard right censoring situation by imputing the midpoints of the censoring intervals. In this research paper, we apply the Bayesian approach by employing Lindley's 1980, and Tierney and Kadane 1986 numerical approximation procedures when the survival data under consideration are interval-censored. The Bayesian approach to interval-censored data has barely been discussed in literature. The essence of this study is to explore and promote the Bayesian methods when the survival data been analysed are is interval-censored. We have considered only a parametric approach by assuming that the survival data follow a loglogistic distribution model. We illustrate the proposed methods with two real data sets. A simulation study is also carried out to compare the performances of the methods

Universal coverage and utilization of free long-lasting insecticidal nets for malaria prevention in Ghana: a cross-sectional study

BackgroundMalaria continues to be one of the leading causes of mortality and morbidity, especially among children and pregnant women. The use of Long-Lasting Insecticide Nets (LLINs) has been recognized and prioritized as a major intervention for malaria prevention in Ghana. This study aims to establish the factors influencing the universal coverage and utilization of LLINs in Ghana.MethodsThe data used for this study was from a cross-sectional survey carried out to assess LLINs ownership and use in 9 out of the 10 old regions of Ghana from October 2018 to February 2019 where free LLIN distribution interventions were implemented. The EPI “30 × 7” cluster sampling method (three-stage sampling design) was modified to “15 × 14” and used for the study. A total of 9,977 households were interviewed from 42 districts. Descriptive statistics using percentages as well as tests of associations such as Pearson Chi-square and the magnitude of the associations using simple and multivariable logistic regression were implemented.ResultsOf the 9,977 households in the study, 88.0% of them owned at least one LLIN, universal coverage was 75.6%, while utilization was 65.6% among households with at least one LLIN. In the rural and urban areas, 90.8% and 83.2% of households, respectively, owned at least one LLIN. The was a 44% increase in universal coverage of LLINs in rural areas compared to urban areas (AOR: 1.44, 95% CI: 1.02–2.02). There were 29 higher odds of households being universally covered if they received LLIN from the PMD (AOR: 29.43, 95% CI: 24.21–35.79). Households with under-five children were 40% more likely to utilize LLIN (AOR: 1.40, 95% CI: 1.26–1.56). Respondents with universal coverage of LLIN had 25% increased odds of using nets (AOR: 1.25 95% CI: 1.06–1.48). Rural dwelling influences LLIN utilization, thus there was about 4-fold increase in household utilization of LLINs in rural areas compared to urban areas (AOR: 3.78, 95% CI: 2.73–5.24). Household size of more than 2 has high odds of LLINs utilization and awareness of the benefit of LLINs (AOR: 1.42, 95% CI: 1.18–1.71).ConclusionAbout nine in 10 households in Ghana have access at least to one LLIN, three-quarters had universal coverage, and over two-thirds of households with access used LLIN. The predictors of universal coverage included region of residence, rural dwellers, and PMD campaign, while households with child under-five, in rural areas, and with universal coverage were positively associated with utilization

Bayesian Estimation of Two-Parameter Weibull Distribution Using Extension of Jeffreys' Prior Information with Three Loss Functions

The Weibull distribution has been observed as one of the most useful distribution, for modelling and analysing lifetime data in engineering, biology, and others. Studies have been done vigorously in the literature to determine the best method in estimating its parameters. Recently, much attention has been given to the Bayesian estimation approach for parameters estimation which is in contention with other estimation methods. In this paper, we examine the performance of maximum likelihood estimator and Bayesian estimator using extension of Jeffreys prior information with three loss functions, namely, the linear exponential loss, general entropy loss, and the square error loss function for estimating the two-parameter Weibull failure time distribution. These methods are compared using mean square error through simulation study with varying sample sizes. The results show that Bayesian estimator using extension of Jeffreys' prior under linear exponential loss function in most cases gives the smallest mean square error and absolute bias for both the scale parameter α and the shape parameter β for the given values of extension of Jeffreys' prior

Bayesian parameter and reliability estimate of Weibull failure time distribution

Bayes and frequentist estimators are obtained for the two-parameter Weibull failure time distribution with uncensored observations as well as the survival/reliability and hazard function. The Weibull distribution is used extensively in life testing and reliability/ survival analysis. The Bayes approach is obtained using Lindleys approximation technique with standard non-informative (vague) prior and a proposed generalisation of the noninformative prior. A simulation study is carried out to compare the performances of the methods. It is observed from the study that the unknown parameters, the reliability and hazard functions are best estimated by Bayes using linear exponential loss with the proposed prior followed by general entropy loss function

Biobehavioral survey using time location sampling among female sex workers living in Ghana in 2020

BackgroundThe HIV epidemic in Ghana is characterized as a mix of a low-level generalized epidemic with significant contributions from transmission among female sex workers (FSW) and their clients. This study seeks to identify and describe key characteristics and sexual behaviors of FSW and estimate the prevalence of HIV, syphilis, gonorrhea, chlamydia, and hepatitis B virus (HBV) among FSW in Ghana.MethodA total of 7,000 FSW were recruited for the study using Time Location Sampling (TLS) approach with 5,990 (85.6%) participants completing both biological and the behavioral aspects of the study. A structured questionnaire was administered to respondents to assess several factors, such as background characteristics, sexual risk behaviors, condom usage, HIV/AIDS knowledge, opinions, and attitudes. Trained staff conducted face-to-face interviews using mobile data collection software (REDCap) after provision of specimens for HIV and STI testing. Descriptive statistics such as medians, ranges, charts, and percentages are performed and presented. Also included, are bivariate analyses to establish relationships between FSW type and other relevant characteristics of the study.ResultsAmong the 7,000 (100%) FSW sampled from all regions, 6,773 took part in the behavioral and 6,217 the biological. There were 783 (11.2%) respondents who took part only in the behavioral and 227 (3.2%) only in the biological. Most were young, with a median age of 26 years, majority had never been married or were widowed/divorced and a quarter had no education or had only primary education. Majority (74.8%) of FSW first sold sex at age 25 years or less with a median age of 20 years. Most (84.8%) of the FSW indicated that they entered sex work for money, either for self or family and had an average of eleven (11) sexual partners per week. More than half (55.2%) of the FSW were new entrants who had been in sex work for less than 5 years before the study. Consistent condom use with paying clients was generally unsatisfactory (71%), and was however, very low (24%) with their intimate partners or boyfriends. Only about half (54.6%) of FSW have been exposed to HIV prevention services in the last three months preceding the survey, and this varies across regions. Overall, comprehensive knowledge about HIV and AIDS was low. Only 35% of FSW had comprehensive knowledge. HIV prevalence was 4.6% and was higher among seaters (brothel-based) and older FSW who had been sex work for a longer period. The HIV prevalence from the previous bio-behavioral survey (BBS) in 2015 and 2011 were estimated to be 6.9 and 11.1%, respectively.ConclusionCompared to the results from the previous studies, the findings give an indication that Ghana is making significant progress in reducing the burden of HIV among FSW in the country. However, risky behaviors such as low consistent condom use, low coverage of HIV services across the regions, and low comprehensive knowledge could reverse the gains made so far. Immediate actions should be taken to expand coverage of HIV services to all locations. Efforts must be made to reach out to the new entrants while also addressing strongly held myths and misconceptions about HIV

Biobehavioral survey using time location sampling among female sex workers living in Ghana in 2020

Background The HIV epidemic in Ghana is characterized as a mix of a low-level generalized epidemic with significant contributions from transmission among female sex workers (FSW) and their clients. This study seeks to identify and describe key characteristics and sexual behaviors of FSW and estimate the prevalence of HIV, syphilis, gonorrhea, chlamydia, and hepatitis B virus (HBV) among FSW in Ghana. Method A total of 7,000 FSW were recruited for the study using Time Location Sampling (TLS) approach with 5,990 (85.6%) participants completing both biological and the behavioral aspects of the study. A structured questionnaire was administered to respondents to assess several factors, such as background characteristics, sexual risk behaviors, condom usage, HIV/AIDS knowledge, opinions, and attitudes. Trained staff conducted face-to-face interviews using mobile data collection software (REDCap) after provision of specimens for HIV and STI testing. Descriptive statistics such as medians, ranges, charts, and percentages are performed and presented. Also included, are bivariate analyses to establish relationships between FSW type and other relevant characteristics of the study. Results Among the 7,000 (100%) FSW sampled from all regions, 6,773 took part in the behavioral and 6,217 the biological. There were 783 (11.2%) respondents who took part only in the behavioral and 227 (3.2%) only in the biological. Most were young, with a median age of 26 years, majority had never been married or were widowed/divorced and a quarter had no education or had only primary education. Majority (74.8%) of FSW first sold sex at age 25 years or less with a median age of 20 years. Most (84.8%) of the FSW indicated that they entered sex work for money, either for self or family and had an average of eleven (11) sexual partners per week. More than half (55.2%) of the FSW were new entrants who had been in sex work for less than 5 years before the study. Consistent condom use with paying clients was generally unsatisfactory (71%), and was however, very low (24%) with their intimate partners or boyfriends. Only about half (54.6%) of FSW have been exposed to HIV prevention services in the last three months preceding the survey, and this varies across regions. Overall, comprehensive knowledge about HIV and AIDS was low. Only 35% of FSW had comprehensive knowledge. HIV prevalence was 4.6% and was higher among seaters (brothel-based) and older FSW who had been sex work for a longer period. The HIV prevalence from the previous bio-behavioral survey (BBS) in 2015 and 2011 were estimated to be 6.9 and 11.1%, respectively. Conclusion Compared to the results from the previous studies, the findings give an indication that Ghana is making significant progress in reducing the burden of HIV among FSW in the country. However, risky behaviors such as low consistent condom use, low coverage of HIV services across the regions, and low comprehensive knowledge could reverse the gains made so far. Immediate actions should be taken to expand coverage of HIV services to all locations. Efforts must be made to reach out to the new entrants while also addressing strongly held myths and misconceptions about HIV

Bayesian approach to meta-analysis with joint modelling of longitudinal and time-to-event outcomes in dementia and subtypes

Meta-analysis is a statistical approach that combines results from published literature in order to obtain an overall grand mean effect estimate. The main problem that affects meta-analysis is publication bias; the first part of this thesis thus seeks to address this problem. This work goes further to address heterogeneity which affects the mean effect being evaluated due to the combination of different studies. Meta-analyses of cognitive decline, Alzheimers disease, vascular dementia and all causes of dementia are undertaken to evaluate the effect of physical activity on these diseases. Dementia is an organic disorder, related to the physical deterioration of the human brain tissue that is detected after a number of medical examinations. The relationship between exercise and the risk of developing cognitive decline is further evaluated using data from the Osteoporotic Fracture Study in the United States. Meta-analytic data is obtained and used as a prior information to the secondary data. The final part of this thesis looks at a study in dementia where measurements are collected on death of participants in addition to other covariates over a period of time. These types of repeated measurements collected from each individual over time violate a number of statistical models assumptions, especially when the interest is to determine the risk factors that affect the study outcome. The aim of this approach is to examine and use these measurements to predict dementia patients probability of survival in the future. Copas selection model which was developed to assess and account for publication bias is implemented in this research. One major disadvantage of this model is that, it relies on a number of sensitivity analysis which results in many effect size estimates with even a single meta-analytic data. In order to overcome the problems of the Copas selection model, a new Bayesian prior known as triangular prior has been developed and used to fit the parameters of the Copas model via a probability distribution. The developed prior is assessed through sensitivity analysis with comparison to other priors. It is also applied to antidepressant meta-analytic dataset. The newly developed prior is further applied to a meta-analyses of dementia and its subtypes. In order to control for the heterogeneity (between-study variation), a proposed Bayesian non-parametric modelling is implemented via a Dirichlet Process. A power prior is also proposed and applied to the meta-analytic (historical) data that is used as a prior to determine whether exercise has any effect on cognitive decline. The power prior is transformed into probabilistic values out of which posterior estimates are obtained. To analyse the repeated measurements and the time to event data in order to assess their effect on dementia, we propose to use a joint modelling approach. The proposed modelling framework involves the standard and extended relative risk models as well as linear mixed effects sub-models on the repeated measures of the longitudinal covariate. The results from the simulations indicate that the triangular prior should be used. The estimated number of studies was similar to that of the frequentist trim and fill method. Our analysis reveal a protective effect of 21% for high physical activity on all cause dementia with an odds ratio of 0.79, 95% Credible Interval (CI) (0.69,0.88), a higher and better protective effect of 38% for Alzheimer’s disease with an odds ratio of 0.62, 95% CI (0.49,0.75), a 33% for cognitive decline with odds ratio of 0.67, 95% CI (0.55, 0.78) and a non-protective effect for vascular dementia of 0.92, 95% CI (0.62, 1.30). Statistically significant results were obtained when the informative prior formulated from the meta-analytic data was used at face value for higher against lowest with odds of 0.69 95% CI (0.58, 0.80) and moderate against lowest 0.63 95% CI (0.50, 0.79) physical activity. The joint modelling approach found a strong relationship between the 3MS scores and the risk of mortality, where every unit decrease in 3MS scores results in a 1.135 (13%) increased risk of death via cognitive impairment with a 95% CI of (1.056, 1.215). The triangular prior is a better alternative prior to use. The prior gives an overall or grand mean effect that is far better than conducting several sensitivity analysis. The implementation of the Dirichlet process in the meta-analyses overcomes the problem of heterogeneity. In evaluating the effect of exercise on cognitive decline with the power prior, it becomes clear that elderly women who engage in moderate exercise will have a reduced risk of developing cognitive decline. In the joint modelling of the longitudinal measurements, the results show that a decrease in 3MS scores has a significant increase risk of mortality due to cognitive impairment when implemented via the joint model but insignificant under the standard relative risk model

Bayesian inference of Weibull distribution for right and interval censored data

The main purpose of this work is to draw comparisons between the classical maximum likelihood and the Bayesian estimators on the parameters, the survival function and hazard rate of the Weibull distribution when the data under consideration are right and interval censored. We have considered the survival data to follow Weibull distribution due to its adaptability in fitting time-to-failure of a very widespread multiplicity to multifaceted mechanisms in the field of life-testing and survival analysis. In Bayesian estimations, prior distributions as well as loss functions need to be specified. The prior distributions can be obtained via previous study in relation to the current study or by soliciting information from experts. We have considered in this study, different types of priors, such as, Jeffreys prior, extension of Jeffreys’ prior information, gamma priors and have also proposed a generalised non-informative prior. The loss functions considered in this study are asymmetric and symmetric loss functions. Lindley’s approximation procedure is used in the Bayesian estimation approach to reduce the ratio of integrals in the posterior distributions which cannot be obtained in close forms. When we consider both the scale and shape parameters under the right and interval censored data, we observed that the estimate of the shape parameter under the maximum likelihood method cannot be obtained in close form; therefore, a numerical approach known as Newton-Raphson has been employed to estimate the shape parameter. The mean squared errors and mean absolute biases of the estimates under Bayes and its maximum likelihood counterpart are examined through simulation study under several conditions to evaluate the performance of both methods. Overall, it has been observed that, the proposed Bayesian estimation under the generalised non-informative prior performed better than the other estimators for the scale and shape parameters, the survival function and hazard rate. The Bayesian estimator via the generalised non-informative prior occurred largely with the linear exponential loss function followed by general entropy loss function