scholarly journals On Stress-Strength Reliability with a Time-Dependent Strength

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Serkan Eryilmaz
Keyword(s):  
Stochastic Process ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Time Dependent ◽  
Special Case ◽  
Weibull Process ◽  
Over Time

The study of stress-strength reliability in a time-dependent context needs to model at least one of the stress or strength quantities as dynamic. We study the stress-strength reliability for the case in which the strength of the system is decreasing in time and the stress remains fixed over time; that is, the strength of the system is modeled as a stochastic process and the stress is considered to be a usual random variable. We present stochastic ordering results among the lifetimes of the systems which have the same strength but are subjected to different stresses. Multicomponent form of the aforementioned stress-strength interference is also considered. We illustrate the results for the special case when the strength is modeled by a Weibull process.

Existence and positivity of the limit in processes with a branching structure

1999 ◽  
Vol 36 (1) ◽  
pp. 132-138
Author(s):  
M. P. Quine ◽  
W. Szczotka
Keyword(s):  
Stochastic Process ◽  
Branching Process ◽  
Random Variables ◽  
Random Variable ◽  
Natural Generalization ◽  
Partial Sums ◽  
Urn Model ◽  
Special Case ◽  
Independent And Identically Distributed

We define a stochastic process {Xn} based on partial sums of a sequence of integer-valued random variables (K0,K1,…). The process can be represented as an urn model, which is a natural generalization of a gambling model used in the first published exposition of the criticality theorem of the classical branching process. A special case of the process is also of interest in the context of a self-annihilating branching process. Our main result is that when (K1,K2,…) are independent and identically distributed, with mean a ∊ (1,∞), there exist constants {cn} with cn+1/cn → a as n → ∞ such that Xn/cn converges almost surely to a finite random variable which is positive on the event {Xn ↛ 0}. The result is extended to the case of exchangeable summands.

Existence and positivity of the limit in processes with a branching structure

1999 ◽  
Vol 36 (01) ◽  
pp. 132-138
Author(s):  
M. P. Quine ◽  
W. Szczotka
Keyword(s):  
Stochastic Process ◽  
Branching Process ◽  
Random Variables ◽  
Random Variable ◽  
Natural Generalization ◽  
Partial Sums ◽  
Urn Model ◽  
Special Case ◽  
Independent And Identically Distributed

We define a stochastic process {X n } based on partial sums of a sequence of integer-valued random variables (K 0,K 1,…). The process can be represented as an urn model, which is a natural generalization of a gambling model used in the first published exposition of the criticality theorem of the classical branching process. A special case of the process is also of interest in the context of a self-annihilating branching process. Our main result is that when (K 1,K 2,…) are independent and identically distributed, with mean a ∊ (1,∞), there exist constants {c n } with c n+1/c n → a as n → ∞ such that X n /c n converges almost surely to a finite random variable which is positive on the event {X n ↛ 0}. The result is extended to the case of exchangeable summands.

scholarly journals Detection of Acetaminophen and Its Glucuronide in Fingerprint by SALDI Mass Spectrometry Using Zeolite and Study of Time-Dependent Changes in Detected Ion Amount

Analytica ◽  
2021 ◽  
Vol 2 (3) ◽  
pp. 66-75
Author(s):  
Toshiki Horikoshi ◽  
Chihiro Kitaoka ◽  
Yosuke Fujii ◽  
Takashi Asano ◽  
Jiawei Xu ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Glucuronic Acid ◽  
Laser Desorption ◽  
The Body ◽  
Time Dependent ◽  
Laser Desorption Ionization ◽  
Fingerprint Analysis ◽  
Desorption Ionization ◽  
Acid Conjugate ◽  
Over Time

The ingredients of an antipyretic (acetaminophen, AAP) and their metabolites excreted into fingerprint were detected by surface-assisted laser desorption ionization (SALDI) mass spectrometry using zeolite. In the fingerprint taken 4 h after AAP ingestion, not only AAP but also the glucuronic acid conjugate of AAP (GAAP), caffeine (Caf), ethenzamide (Eth), salicylamide (Sala; a metabolite of Eth), and urea were detected. Fingerprints were collected over time to determine how the amounts of AAP and its metabolite changed with time, and the time dependence of the peak intensities of protonated AAP and GAAP was measured. It was found that the increase of [GAAP+H]+ peak started later than that of [AAP+H]+ peak, reflecting the metabolism of AAP. Both AAP and GAAP reached maximum concentrations approximately 3 h after ingestion, and were excreted from the body with a half-life of approximately 3.3 h. In addition, fingerprint preservation was confirmed by optical microscopy, and fingerprint shape was retained even after laser irradiation of the fingerprint. Our method may be used in fingerprint analysis.

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

scholarly journals Coagulation Processes with Gibbsian Time Evolution

2012 ◽  
Vol 49 (03) ◽  
pp. 612-626
Author(s):  
Boris L. Granovsky ◽  
Alexander V. Kryvoshaev
Keyword(s):  
Stochastic Process ◽  
Recurrence Relation ◽  
Time Evolution ◽  
Nonnegative Function ◽  
Gibbs Distribution ◽  
Time Dependent ◽  
Explicit Solutions ◽  
Gibbs Distributions ◽  
Giant Cluster ◽  
Positive Integers

We prove that a stochastic process of pure coagulation has at any timet≥ 0 a time-dependent Gibbs distribution if and only if the rates ψ(i,j) of single coagulations are of the form ψ(i;j) =if(j) +jf(i), wherefis an arbitrary nonnegative function on the set of positive integers. We also obtain a recurrence relation for weights of these Gibbs distributions that allow us to derive the general form of the solution and the explicit solutions in three particular cases of the functionf. For the three corresponding models, we study the probability of coagulation into one giant cluster by timet> 0.

scholarly journals Risk Factors for Prostate Cancer Detection After a Negative Biopsy: A Novel Multivariable Longitudinal Approach

2010 ◽  
Vol 28 (10) ◽  
pp. 1714-1720 ◽  
Author(s):  
Peter H. Gann ◽  
Angela Fought ◽  
Ryan Deaton ◽  
William J. Catalona ◽  
Edward Vonesh
Keyword(s):  
Prostate Cancer ◽  
Risk Factors ◽  
Specific Antigen ◽  
Time Dependent ◽  
Negative Biopsy ◽  
Gland Volume ◽  
Piecewise Exponential ◽  
Over Time ◽  
Negative Biopsies

Purpose To introduce a novel approach for the time-dependent quantification of risk factors for prostate cancer (PCa) detection after an initial negative biopsy. Patients and Methods Data for 1,871 men with initial negative biopsies and at least one follow-up biopsy were available. Piecewise exponential regression models were developed to quantify hazard ratios (HRs) and define cumulative incidence curves for PCa detection for subgroups with specific patterns of risk factors over time. Factors evaluated included age, race, serum prostate-specific antigen (PSA) concentration, PSA slope, digital rectal examination, dysplastic glands or prostatitis on biopsy, ultrasound gland volume, urinary symptoms, and number of negative biopsies. Results Four hundred sixty-five men had PCa detected, after a mean follow-up time of 2.8 years. All of the factors were independent predictors of PCa detection except for PSA slope, as a result of its correlation with time-dependent PSA level, and race. PSA (HR = 3.90 for > 10 v 2.5 to 3.9 ng/mL), high-grade prostatic intraepithelial neoplasia/atypical glands (HR = 2.97), gland volume (HR = 0.39 for > 50 v < 25 mL), and number of repeat biopsies (HR = 0.36 for two v zero repeat biopsies) were the strongest predictors. Men with high-risk versus low-risk event histories had a 20-fold difference in PCa detection over 5 years. Conclusion Piecewise exponential models provide an approach to longitudinal analysis of PCa risk that allows clinicians to see the interplay of risk factors as they unfold over time for individual patients. With these models, it is possible to identify distinct subpopulations with dramatically different needs for monitoring and repeat biopsy.

scholarly journals A Tutorial on Evaluating the Time-Varying Discrimination Accuracy of Survival Models Used in Dynamic Decision Making

2018 ◽  
Vol 38 (8) ◽  
pp. 904-916 ◽  
Author(s):  
Aasthaa Bansal ◽  
Patrick J. Heagerty
Keyword(s):  
Decision Making ◽  
Statistical Methods ◽  
Sensitivity And Specificity ◽  
Prognostic Model ◽  
Dynamic Decision Making ◽  
Time Dependent ◽  
Survival Models ◽  
Biliary Cirrhosis ◽  
Time Varying ◽  
Over Time

Many medical decisions involve the use of dynamic information collected on individual patients toward predicting likely transitions in their future health status. If accurate predictions are developed, then a prognostic model can identify patients at greatest risk for future adverse events and may be used clinically to define populations appropriate for targeted intervention. In practice, a prognostic model is often used to guide decisions at multiple time points over the course of disease, and classification performance (i.e., sensitivity and specificity) for distinguishing high-risk v. low-risk individuals may vary over time as an individual’s disease status and prognostic information change. In this tutorial, we detail contemporary statistical methods that can characterize the time-varying accuracy of prognostic survival models when used for dynamic decision making. Although statistical methods for evaluating prognostic models with simple binary outcomes are well established, methods appropriate for survival outcomes are less well known and require time-dependent extensions of sensitivity and specificity to fully characterize longitudinal biomarkers or models. The methods we review are particularly important in that they allow for appropriate handling of censored outcomes commonly encountered with event time data. We highlight the importance of determining whether clinical interest is in predicting cumulative (or prevalent) cases over a fixed future time interval v. predicting incident cases over a range of follow-up times and whether patient information is static or updated over time. We discuss implementation of time-dependent receiver operating characteristic approaches using relevant R statistical software packages. The statistical summaries are illustrated using a liver prognostic model to guide transplantation in primary biliary cirrhosis.

scholarly journals A joint modeling approach for longitudinal microbiome data improves ability to detect microbiome associations with disease

2020 ◽  
Vol 16 (12) ◽  
pp. e1008473
Author(s):  
Pamela N. Luna ◽  
Jonathan M. Mansbach ◽  
Chad A. Shaw
Keyword(s):  
Joint Modeling ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Time Dependent ◽  
Time To Event ◽  
Modeling Framework ◽  
Microbial Composition ◽  
Disease Outcomes ◽  
Microbiome Data ◽  
Over Time

Changes in the composition of the microbiome over time are associated with myriad human illnesses. Unfortunately, the lack of analytic techniques has hindered researchers’ ability to quantify the association between longitudinal microbial composition and time-to-event outcomes. Prior methodological work developed the joint model for longitudinal and time-to-event data to incorporate time-dependent biomarker covariates into the hazard regression approach to disease outcomes. The original implementation of this joint modeling approach employed a linear mixed effects model to represent the time-dependent covariates. However, when the distribution of the time-dependent covariate is non-Gaussian, as is the case with microbial abundances, researchers require different statistical methodology. We present a joint modeling framework that uses a negative binomial mixed effects model to determine longitudinal taxon abundances. We incorporate these modeled microbial abundances into a hazard function with a parameterization that not only accounts for the proportional nature of microbiome data, but also generates biologically interpretable results. Herein we demonstrate the performance improvements of our approach over existing alternatives via simulation as well as a previously published longitudinal dataset studying the microbiome during pregnancy. The results demonstrate that our joint modeling framework for longitudinal microbiome count data provides a powerful methodology to uncover associations between changes in microbial abundances over time and the onset of disease. This method offers the potential to equip researchers with a deeper understanding of the associations between longitudinal microbial composition changes and disease outcomes. This new approach could potentially lead to new diagnostic biomarkers or inform clinical interventions to help prevent or treat disease.

scholarly journals Mortality Risk and The Progression of The Electronic Frailty Index and Hospital Frailty Risk Score Over Time

2020 ◽  
Vol 5 (5) ◽  
Author(s):  
Joe Hollinghurst ◽  
Alan Watkins
Keyword(s):  
Risk Score ◽  
Frailty Index ◽  
Time Frame ◽  
Time Dependent ◽  
Cox Models ◽  
Hazard Ratios ◽  
Increased Risk ◽  
The Matrix ◽  
Time Dependent Covariates ◽  
Over Time

IntroductionThe electronic Frailty Index (eFI) and the Hospital Frailty Risk Score (HFRS) have been developed in primary and secondary care respectively. Objectives and ApproachOur objective was to investigate how frailty progresses over time, and to include the progression of frailty in a survival analysis.To do this, we performed a retrospective cohort study using linked data from the Secure Anonymised Information Linkage Databank, comprising 445,771 people aged 65-95 living in Wales (United Kingdom) on 1st January 2010. We calculated frailty, using both the eFI and HFRS, for individuals at quarterly intervals for 8 years with a total of 11,702,242 observations. ResultsWe created a transition matrix for frailty states determined by the eFI (states: fit, mild, moderate, severe) and HFRS (states: no score, low, intermediate, high), with death as an absorbing state. The matrix revealed that frailty progressed over time, but that on a quarterly basis it was most likely that an individual remained in the same state. We calculated Hazard Ratios (HRs) using time dependent Cox models for mortality, with adjustments for age, gender and deprivation. Independent eFI and HFRS models showed increased risk of mortality as frailty severity increased. A combined eFI and HFRS revealed the highest risk was primarily determined by the HFRS and revealed further subgroups of individuals at increased risk of an adverse outcome. For example, the HRs (95% Confidence Interval) for individuals with an eFI as fit, mild, moderate and severe with a high HFRS were 18.11 [17.25,19.02], 20.58 [19.93,21.24], 21.45 [20.85,22.07] and 23.04 [22.34,23.76] respectively with eFI fit and no HFRS score as the reference category. ConclusionFrailty was found to vary over time, with progression likely in the 8-year time-frame analysed. We refined HR estimates of the eFI and HFRS for mortality by including time dependent covariates.

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