Prediction Limits for the Last Failure Time of a (Log) Normal Sample from Early Failures

AbstractHeart failure is a failure of the heart to pump blood with normal efficiency and a globally growing public health issue with a high death rate all over the world, including Ethiopia. The goal of this study was to identify factors affecting the survival time of heart failure patients. To achieve the aim, 409 heart failure patients were included in the study based on data taken from medical records of patients enrolled from January 2016 to January 2019 at Jimma University Medical Center, Jimma, Ethiopia. The Kaplan Meier plots and log-rank test were used for comparison of survival functions; the Cox-PH model and the Bayesian parametric survival models were used to analyze the survival time of heart failure patients using R-software. Integrated nested Laplace approximation methods have been applied. Out of the total heart failure patients in the study, 40.1% died, and 59.9% were censored. The estimated median survival time of patients was 31 months. Using model selection criteria, the Bayesian log-normal accelerated failure time model was found to be appropriate. The results of this model show that age, chronic kidney disease, diabetes mellitus, etiology of heart failure, hypertension, anemia, smoking cigarettes, and stages of heart failure all have a significant impact on the survival time of heart failure patients. The Bayesian log-normal accelerated failure time model described the survival time of heart failure patient's data-set well. The findings of this study suggested that the age group (49 to 65 years, and greater than or equal to 65 years); etiology of heart failure (rheumatic valvular heart disease, hypertensive heart disease, and other diseases); the presence of hypertension; the presence of anemia; the presence of chronic kidney disease; smokers; diabetes mellitus (type I, and type II); and stages of heart failure (II, III, and IV) shortened their survival time of heart failure patients.

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Novel Approaches to Prediction of a Future Number of Failures Based on Previous In-Service Inspections

Soft Computing Techniques and Applications in Mechanical Engineering - Advances in Mechatronics and Mechanical Engineering ◽

10.4018/978-1-5225-3035-0.ch011 ◽

2018 ◽

pp. 225-248

Author(s):

Nicholas A. Nechval ◽

Konstantin N. Nechval

Keyword(s):

Performance Index ◽

Failure Time ◽

Parametric Uncertainty ◽

Statistical Problem ◽

Unknown Parameters ◽

Invariant Embedding ◽

Prediction Limits ◽

Novel Approaches ◽

Special Case ◽

Two Parameter

In this chapter, we present novel approaches to predictions of the number of failures that will be observed in a future inspection of a sample of units, based only on the results of the previous in-service inspections of the same sample. The failure-time of such units is modeled with a distribution from a two-parameter Weibull distribution. The different cases of parametric uncertainty are considered. The pivotal quantity averaging approach proposed here for constructing point prediction and simple prediction limits emphasizes pivotal quantities relevant for eliminating unknown parameters from the problems and represents a special case of the method of invariant embedding of sample statistics into a performance index applicable whenever the statistical problem is invariant under a group of transformations, which acts transitively on the parameter space. For illustration, a numerical example is given.

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STUDY OF EFFICIENCY TIME OF RECOMBINANT DNA INSULIN VIA ACCELERATED LIFE TESTING AND INTERVAL CENSORING

REVISTA BRASILEIRA DE BIOMETRIA ◽

10.28951/rbb.v36i1.165 ◽

2018 ◽

Vol 36 (1) ◽

pp. 207

Author(s):

Patrícia De Sousa ILAMBWETSI ◽

Graziela Dutra Rocha GOUVEIA ◽

Frederico Rodrigues Borges CRUZ ◽

Fernando Luiz Pereira de OLIVEIRA

Keyword(s):

Lower Limit ◽

Failure Time ◽

Recombinant Dna ◽

Weibull Model ◽

Interval Censoring ◽

Accelerated Life Tests ◽

Accelerated Life ◽

Stress Variable ◽

Life Tests ◽

Log Normal

This paper aims to study the efficiency of recombinant DNA insulin via models for accelerated life tests. The potency loss of these insulin products was evaluated periodically, subject to the conditions of temperature of 8°C, 25°C and 37°C. Insulin samples with potency at less than 100% were considered unfit for consumption, which characterizes the event of interest. Samples suitable for consumption were considered to be censored. The response variable was observed periodically for 736 days. For data analysis, statistical models of stress-response regression were used. The deterministic part of these models is the Arrhenius model because the stress variable is the temperature, while the probabilistic part was comprised of the Exponential, Weibull, and Log-normal models. The techniques of accelerated life tests proved adequate to address the time of potency loss of the insulin for the various temperature levels. The times of occurrence of the events were treated in three different ways, which were compared in this study. First, interval censoring was considered, or only the upper and lower limits of the interval in which the failure occurred were known. Then, the midpoint of this interval was considered as a failure time. Finally, only the lower limit of the interval in which the failure occurred was considered. According to the results, it is concluded that the use of the interval lower limit is more appropriate for estimating the reliability curves, as the estimates are closer to those using interval censoring then using the midpoint of the interval. For the specific case of the recombinant DNA insulin data, it was observed that the Arrhenius-Weibull model and the Arrhenius-lognormal are suitable for adjusting the data. It follows also that the temperature affects the power of the insulin: The higher the temperature are, the lesser the efficiency.

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Incident Duration Modeling Using Flexible Parametric Hazard-Based Models

Computational Intelligence and Neuroscience ◽

10.1155/2014/723427 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 8

Author(s):

Ruimin Li ◽

Pan Shang

Keyword(s):

Failure Time ◽

Economic Losses ◽

Incident Management ◽

Accelerated Failure Time ◽

Traffic Incidents ◽

Traffic Incident ◽

Duration Time ◽

Incident Duration ◽

Traffic Incident Management ◽

Log Normal

Assessing and prioritizing the duration time and effects of traffic incidents on major roads present significant challenges for road network managers. This study examines the effect of numerous factors associated with various types of incidents on their duration and proposes an incident duration prediction model. Several parametric accelerated failure time hazard-based models were examined, including Weibull, log-logistic, log-normal, and generalized gamma, as well as all models with gamma heterogeneity and flexible parametric hazard-based models with freedom ranging from one to ten, by analyzing a traffic incident dataset obtained from the Incident Reporting and Dispatching System in Beijing in 2008. Results show that different factors significantly affect different incident time phases, whose best distributions were diverse. Given the best hazard-based models of each incident time phase, the prediction result can be reasonable for most incidents. The results of this study can aid traffic incident management agencies not only in implementing strategies that would reduce incident duration, and thus reduce congestion, secondary incidents, and the associated human and economic losses, but also in effectively predicting incident duration time.

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Length of Stay in ICU of Covid-19 Patients in England, March - May 2020

International Journal for Population Data Science ◽

10.23889/ijpds.v5i4.1411 ◽

2021 ◽

Vol 5 (4) ◽

Author(s):

Nick Shryane ◽

Maria Pampaka ◽

Andrea Lisette Aparicio Castro ◽

Shazaad Ahmad ◽

Mark Elliot ◽

...

Keyword(s):

Risk Factors ◽

Failure Time ◽

Admission Policy ◽

Survival Models ◽

Accelerated Failure Time ◽

Disease Treatment ◽

Icu Admission ◽

Accelerated Failure ◽

Log Normal ◽

Potential Pressure

IntroductionLength of Stay (LoS) in Intensive Care Units (ICUs) is an important measure for planning beds capacity during the Covid-19 pandemic. However, as the pandemic progresses and we learn more about the disease, treatment and subsequent LoS in ICU may change. ObjectivesTo investigate the LoS in ICUs in England associated with Covid-19, correcting for censoring, and to evaluate the effect of known predictors of Covid-19 outcomes on ICU LoS. Data sourcesWe used retrospective data on Covid-19 patients, admitted to ICU between 6 March and 24 May, from the “Covid-19 Hospitalisation in England Surveillance System” (CHESS) database, collected daily from England’s National Health Service, and collated by Public Health England. MethodsWe used Accelerated Failure Time survival models with Weibull and log-normal distributional assumptions to investigate the effect of predictors, which are known to be associated with poor Covid-19 outcomes, on the LoS in ICU. ResultsPatients admitted before 25 March had significantly longer LoS in ICU (mean = 18.4 days, median = 12), controlling for age, sex, whether the patient received Extracorporeal Membrane Oxygenation, and a co-morbid risk factors score, compared with the period after 7 April (mean = 15.4, median = 10). The periods of admission reflected the changes in the ICU admission policy in England. Patients aged 50-65 had the longest LoS, while higher co-morbid risk factors score led to shorter LoS. Sex and ethnicity were not associated with ICU LoS. ConclusionsThe skew of the predicted LoS suggests that a mean LoS, as compared with median, might be better suited as a measure used to assess and plan ICU beds capacity. This is important for the ongoing second and any future waves of Covid-19 cases and potential pressure on the ICU resources. Also, changes in the ICU admission policy are likely to be confounded with improvements in clinical knowledge of Covid-19.

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Duration of Postdiarrheal Enteric Pathogen Carriage in Young Children in Low-resource Settings

Clinical Infectious Diseases ◽

10.1093/cid/ciaa1528 ◽

2020 ◽

Author(s):

Timothy L McMurry ◽

Elizabeth T Rogawski McQuade ◽

Jie Liu ◽

Gagandeep Kang ◽

Margaret N Kosek ◽

...

Keyword(s):

Median Duration ◽

Failure Time ◽

Quantitative Polymerase Chain Reaction ◽

Pathogen Transmission ◽

Probability Of Detection ◽

Accelerated Failure Time ◽

Wide Range ◽

Before And After ◽

Prevalence Difference ◽

Log Normal

Abstract Background Prolonged enteropathogen shedding after diarrhea complicates the identification of etiology in subsequent episodes and is an important driver of pathogen transmission. A standardized approach has not been applied to estimate the duration of shedding for a wide range of pathogens. Methods We used a multisite birth cohort of children 0–24 months of age from whom diarrheal and monthly nondiarrheal stools were previously tested by quantitative polymerase chain reaction for 29 enteropathogens. We modeled the probability of detection of the etiologic pathogen before and after diarrhea using a log-normal accelerated failure time survival model and estimated the median duration of pathogen carriage as well as differences in subclinical pathogen carriage 60 days after diarrhea onset in comparison to a prediarrhea baseline. Results We analyzed 3247 etiologic episodes of diarrhea for the 9 pathogens with the highest attributable burdens of diarrhea. The median duration of postdiarrheal carriage varied widely by pathogen, from about 1 week for rotavirus (median, 8.1 days [95% confidence interval {CI}, 6.2–9.6]) to >1 month for Cryptosporidium (39.5 days [95% CI, 30.6–49.0]). The largest increases in subclinical pathogen carriage before and after diarrhea were seen for Cryptosporidium (prevalence difference between 30 days prior and 60 days after diarrhea onset, 0.30 [95% CI, .23–.39]) and Shigella (prevalence difference, 0.21 [95% CI, .16–.27]). Conclusions Postdiarrheal shedding was widely variable between pathogens, with strikingly prolonged shedding seen for Cryptosporidium and Shigella. Targeted antimicrobial therapy and vaccination for these pathogens may have a relatively large impact on transmission.

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Bayesian Hierarchical Scale Mixtures of Log-Normal Models for Inference in Reliability with Stochastic Constraint

10.20944/preprints201705.0043.v1 ◽

2017 ◽

Author(s):

Hea-Jung Kim

Keyword(s):

Bayesian Inference ◽

Method Development ◽

Failure Time ◽

A Priori ◽

Data Sets ◽

Bayesian Hierarchical ◽

Scale Mixtures ◽

Model Reliability ◽

Heavy Tailed ◽

Log Normal

This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT) models with stochastic (or uncertain) constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT) models (such as log-normal, log-Cauchy, and log-logistic FT models) as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC) sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt) prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works.

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