Bayesian survival estimator for Weibull distribution with censored data.

As the most useful distribution for modeling and analyzing life time data in the medical, paramedical and applied sciences among others, Weibull distribution stands out. Nowadays great attention has been given to Bayesian approach and is in contention with other estimation methods. This study explores and compares the performance of Maximum Likelihood and Bayesian using Jeffrey prior and the extension of Jeffrey prior information for estimating the survival function of Weibull distribution with right censored data. On the performance of these estimators with respect to the mean square error and mean percentage error, comparisons are made through simulation study. For all the varying sample size, several specific values of the scale parameter of the Weibull distribution and for the values given for the extension of Jeffrey prior, the estimate of survival function of maximum likelihood is the best compared to the others when the value of extension of Jeffrey prior is 0.4. But then, extension of Jeffrey prior result is the best compared to others when the value of extension of Jeffrey is 1.4. © 2011 Asian Network for Scientific Information

Comparison of the Bayesian and maximum likelilhood estimation for Weibull distribution

Problem statement: The Weibull distribution has been widely used especially in the modeling of lifetime event data. It provides a statistical model which has a wide variety of applications in many areas, and the main advantage is its ability in the context of lifetime event, to provide reasonably accurate failure analysis and failure for ecasts especially with extremely small samples. The conventional maximum likelihood method is the usual way to estimate the parameters of a distribution. Bayesian approach has received much attention and in contention with other estimation methods. In this study we explore and compare the performance of the maximum likelihood estimate with the Bayesian estimate for the Weibull distribution. Approach: The maximum likelihood estimation, Bayesian using Jeffrey prior and the extension of Jeffrey prior information for estimating the parameters of Weibull distribution of life time are presented. We explore the performance of these estimators numerically under varyin g conditions. Through the simulation study comparison are made on the performance of these estimators with respect to the Mean Square Error (MSE) and Mean Percentage Error(MPE). Results: For all the varying sample size, several specific values of the scale parameter of the Weibull distribution and for the values specify for the extension of Jeffrey prior, the estimators of the maximum likelihood method result in smaller MSE and MPE compared to Bayesian in majority of the cases. Nevertheless in all cases for both methods the MSE and MPE decrease as sample size increases. Conclusion: Based on the results of this simulation study the Bayesian approach used in the estimating of Weibull parameters is found to be not superior compared to the conventional maximum likelihood method with respect to MSE and MPE values

Effectiveness of Sterilization by Microwave Irradiation on Polyvinyl Siloxane Contaminated with Candida Albicans: An Invitro Study

Aims: This in-vitro study aimed to evaluate the effect of microwave irradiation on polyvinyl siloxane impression material contaminated with candida Albicans. Materials and methods: 30 samples were fabricated from the acrylic mold with disk shape 5*2 (diameter*thickness). Samples incubated with Brain Heart Infusion Broth (BHI) media containing Candida albicans. Then were divided into 30 samples into 6 groups: C (positive control); 5 non-irradiated specimens, 3MWD ( samples irradiated for 3minute in dry condition), 6MWD (samples irradiated for 6minute in dry condition), 3MWW (samples irradiated for 3minute in wet condition), 6MWW (samples irradiated for 6minute in wet condition), CHX (samples immersed in 0.5% chlorhexidine) After incubation of all samples for 24 hours at 37°C, the samples were got vortex and then serial dilution carried out of suspensions then cultured on Sabouraude Dextrose Agar after incubation for 24 hours at 37°C bacteria were counted. A further 7 days of incubation for microwaved samples was done to verify the effectiveness of both dry and wet microwave sterilization for two periods of time. Results: There was a significant reduction in cfu /ml of candida albicans at 24 hours of incubation. No growth of C. albicans was recorded after 7 days of incubation. Conclusions: Microwave irradiation at 640W for both wet and dry conditions for 3 and 6 min was proved to be effective in the disinfection of polyvinyl siloxane specimens contaminated with. Candida. albicans

Effectiveness of Microwave Sterilization on Surface Roughness of Polyvinyl Siloxane Impression Material

Aims: The study aimed to investigate the effect of sterilization by microwave irradiation at 640W on the surface roughness of polyvinyl siloxane. Materials and methods: 30 samples of addition silicone impression material with a thickness of 20mm and 3mm as diameter. The acrylic mold was used for the samples' fabrication. The samples were divided into six groups each group had five specimens (C) control (3MWD) Samples irradiated for 3minute in dry conditions, (6MWD) samples irradiated for 6minute in dry conditions, (3MWW) samples irradiated for 3minute in wet condition, (6MWW) samples irradiated for 6minute in wet condition and (CHX) samples immersed in chlorhexidine with 0.5% concentration for one hour. A profilometer (Talysurf 10, R.P.I. LTD, Metrology Division) is used for measuring surface roughness by taking the means of three points with the aid of a stylus. Results: There were statistical differences between the control group and the tested groups. Mann-Whitney showed that only 3MWD had no statistical differences from the control group. Conclusions: Disinfection of polyvinyl siloxane using the microwave at 640W for 3 minutes is safe or recommended regarding its least effect on the surface roughness

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

Extension of Jeffreys's prior estimate for Weibull censored data using Lindley's approximation

The Weibull distribution has attracted the attention of statisticians working on theory and methods as well as in various fields of applied statistics. In this paper the Jeffreys's and extension Jeffreys's priors with the squared loss function are considered in the estimation. The Bayesian estimates of the scale and shape parameters of the Weibull distribution obtained using Lindley's approximation are then compared to its maximum likelihood counterparts. The comparison criteria is the mean square error (MSE) and the performance of these two estimates are assessed using simulation considering various sample size, several specific values of Weibull parameters and several values of extension Jeffreys's prior. The Maximum Likelihood estimates of θ and p are more efficient than their Bayesian using Jeffreys's prior and extension of Jeffreys's prior, but the extension of Jeffreys's is better than maximum likelihood for some conditions

Parametric maximum likelihood estimation of cure fraction using interval-censored data

A significant proportion of patients in cancer clinical trials can be cured. That is, the symptoms of the disease disappear completely and the disease never recurs. In this article, the focus is on estimation of the proportion of patients who are cured. The parametric maximum likelihood estimation method was used for estimation of the cure fraction based on application of the bounded cumulative hazard (BCH) model to interval-censored data. We ran the analysis using the EM algorithm considering two cases: i) when no covariates were involved in the estimation, and ii) when some covariates were involved. This paper shows derivation of the estimation equations for the cure rate parameter followed by a simulation study

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

System effectiveness of a targeted free mass distribution of long lasting insecticidal nets in Zanzibar, Tanzania

Insecticide-treated nets (ITN) and long-lasting insecticidal treated nets (LLIN) are important means of malaria prevention. Although there is consensus regarding their importance, there is uncertainty as to which delivery strategies are optimal for dispensing these life saving interventions. A targeted mass distribution of free LLINs to children under five and pregnant women was implemented in Zanzibar between August 2005 and January 2006. The outcomes of this distribution among children under five were evaluated, four to nine months after implementation. Two cross-sectional surveys were conducted in May 2006 in two districts of Zanzibar: Micheweni (MI) on Pemba Island and North A (NA) on Unguja Island. Household interviews were conducted with 509 caretakers of under-five children, who were surveyed for socio-economic status, the net distribution process, perceptions and use of bed nets. Each step in the distribution process was assessed in all children one to five years of age for unconditional and conditional proportion of success. System effectiveness (the accumulated proportion of success) and equity effectiveness were calculated, and predictors for LLIN use were identified. The overall proportion of children under five sleeping under any type of treated net was 83.7% (318/380) in MI and 91.8% (357/389) in NA. The LLIN usage was 56.8% (216/380) in MI and 86.9% (338/389) in NA. Overall system effectiveness was 49% in MI and 87% in NA, and equity was found in the distribution scale-up in NA. In both districts, the predicting factor of a child sleeping under an LLIN was caretakers thinking that LLINs are better than conventional nets (OR = 2.8, p = 0.005 in MI and 2.5, p = 0.041 in NA), in addition to receiving an LLIN (OR = 4.9, p < 0.001 in MI and in OR = 30.1, p = 0.001 in NA). Targeted free mass distribution of LLINs can result in high and equitable bed net coverage among children under five. However, in order to sustain high effective coverage, there is need for complimentary distribution strategies between mass distribution campaigns. Considering the community's preferences prior to a mass distribution and addressing the communities concerns through information, education and communication, may improve the LLIN usage

Mortality from gastrointestinal congenital anomalies at 264 hospitals in 74 low-income, middle-income, and high-income countries: a multicentre, international, prospective cohort study

Background: Congenital anomalies are the fifth leading cause of mortality in children younger than 5 years globally. Many gastrointestinal congenital anomalies are fatal without timely access to neonatal surgical care, but few studies have been done on these conditions in low-income and middle-income countries (LMICs). We compared outcomes of the seven most common gastrointestinal congenital anomalies in low-income, middle-income, and high-income countries globally, and identified factors associated with mortality. // Methods: We did a multicentre, international prospective cohort study of patients younger than 16 years, presenting to hospital for the first time with oesophageal atresia, congenital diaphragmatic hernia, intestinal atresia, gastroschisis, exomphalos, anorectal malformation, and Hirschsprung's disease. Recruitment was of consecutive patients for a minimum of 1 month between October, 2018, and April, 2019. We collected data on patient demographics, clinical status, interventions, and outcomes using the REDCap platform. Patients were followed up for 30 days after primary intervention, or 30 days after admission if they did not receive an intervention. The primary outcome was all-cause, in-hospital mortality for all conditions combined and each condition individually, stratified by country income status. We did a complete case analysis. // Findings: We included 3849 patients with 3975 study conditions (560 with oesophageal atresia, 448 with congenital diaphragmatic hernia, 681 with intestinal atresia, 453 with gastroschisis, 325 with exomphalos, 991 with anorectal malformation, and 517 with Hirschsprung's disease) from 264 hospitals (89 in high-income countries, 166 in middle-income countries, and nine in low-income countries) in 74 countries. Of the 3849 patients, 2231 (58·0%) were male. Median gestational age at birth was 38 weeks (IQR 36–39) and median bodyweight at presentation was 2·8 kg (2·3–3·3). Mortality among all patients was 37 (39·8%) of 93 in low-income countries, 583 (20·4%) of 2860 in middle-income countries, and 50 (5·6%) of 896 in high-income countries (p<0·0001 between all country income groups). Gastroschisis had the greatest difference in mortality between country income strata (nine [90·0%] of ten in low-income countries, 97 [31·9%] of 304 in middle-income countries, and two [1·4%] of 139 in high-income countries; p≤0·0001 between all country income groups). Factors significantly associated with higher mortality for all patients combined included country income status (low-income vs high-income countries, risk ratio 2·78 [95% CI 1·88–4·11], p<0·0001; middle-income vs high-income countries, 2·11 [1·59–2·79], p<0·0001), sepsis at presentation (1·20 [1·04–1·40], p=0·016), higher American Society of Anesthesiologists (ASA) score at primary intervention (ASA 4–5 vs ASA 1–2, 1·82 [1·40–2·35], p<0·0001; ASA 3 vs ASA 1–2, 1·58, [1·30–1·92], p<0·0001]), surgical safety checklist not used (1·39 [1·02–1·90], p=0·035), and ventilation or parenteral nutrition unavailable when needed (ventilation 1·96, [1·41–2·71], p=0·0001; parenteral nutrition 1·35, [1·05–1·74], p=0·018). Administration of parenteral nutrition (0·61, [0·47–0·79], p=0·0002) and use of a peripherally inserted central catheter (0·65 [0·50–0·86], p=0·0024) or percutaneous central line (0·69 [0·48–1·00], p=0·049) were associated with lower mortality. // Interpretation: Unacceptable differences in mortality exist for gastrointestinal congenital anomalies between low-income, middle-income, and high-income countries. Improving access to quality neonatal surgical care in LMICs will be vital to achieve Sustainable Development Goal 3.2 of ending preventable deaths in neonates and children younger than 5 years by 2030