scholarly journals Optimal Sample Size for the Birnbaum–Saunders Distribution under Decision Theory with Symmetric and Asymmetric Loss Functions

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 926
Author(s):  
Eliardo Costa ◽  
Manoel Santos-Neto ◽  
Víctor Leiva
Keyword(s):  
Sample Size ◽  
Real Data ◽  
Loss Functions ◽  
Theoretic Approach ◽  
Optimal Sample Size ◽  
Asymmetric Loss ◽  
Optimal Sample ◽  
Decision Theoretic Approach ◽  
Potential Applications ◽  
Asymmetrical Model

The fatigue-life or Birnbaum–Saunders distribution is an asymmetrical model that has been widely applied in several areas of science and mainly in reliability. Although diverse methodologies related to this distribution have been proposed, the problem of determining the optimal sample size when estimating its mean has not yet been studied. In this paper, we derive a methodology to determine the optimal sample size under a decision-theoretic approach. In this approach, we consider symmetric and asymmetric loss functions for point and interval inference. Computational tools in the R language were implemented to use this methodology in practice. An illustrative example with real data is also provided to show potential applications.

Effectiveness and policies analysis of pool testing method for COVID-19

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yang Liu ◽  
Yi Chen ◽  
Kefan Xie ◽  
Jia Liu
Keyword(s):  
Sample Size ◽  
Infection Rate ◽  
Large Population ◽  
Optimal Sample Size ◽  
Content Type ◽  
Testing Method ◽  
Multiple Sampling ◽  
Optimal Sample ◽  
Test Result ◽  
Sampling Approach

PurposeThis research aims to figure out whether the pool testing method of SARS-CoV-2 for COVID-19 is effective and the optimal sample size is in one bunch. Additionally, since the infection rate was unknown at the beginning, this research aims to propose a multiple sampling approach that enables the pool testing method to be utilized successfully.Design/methodology/approachThe authors verify that the pool testing method of SARS-CoV-2 for COVID-19 is effective under the situation of the shortage of nucleic acid detection kits based on probabilistic modeling. In this method, the testing is performed on several samples of the cases together as a bunch. If the test result of the bunch is negative, then it is shown that none of the cases in the bunch has been infected with the novel coronavirus. On the contrary, if the test result of the bunch is positive, then the samples are tested one by one to confirm which cases are infected.FindingsIf the infection rate is extremely low, while the same number of detection kits is used, the expected number of cases that can be tested by the pool testing method is far more than that by the one-by-one testing method. The pool testing method is effective only when the infection rate is less than 0.3078. The higher the infection rate, the smaller the optimal sample size in one bunch. If N samples are tested by the pool testing method, while the sample size in one bunch is G, the number of detection kits required is in the interval (N/G, N).Originality/valueThis research proves that the pool testing method is not only suitable for the situation of the shortage of detection kits but also the situation of the overall or sampling detection for a large population. More importantly, it calculates the optimal sample size in one bunch corresponding to different infection rates. Additionally, a multiple sampling approach is proposed. In this approach, the whole testing process is divided into several rounds in which the sample sizes in one bunch are different. The actual infection rate is estimated gradually precisely by sampling inspection in each round.

Estimation of optimum sample size allocation: An illustration with body mass index for evaluating the effect of a dietetic supplement

2019 ◽  
Vol 12 (08) ◽  
pp. 1950086
Author(s):  
Carlos N. Bouza-Herrera ◽  
Sira M. Allende-Alonso ◽  
Gajendra K. Vishwakarma ◽  
Neha Singh
Keyword(s):  
Body Mass Index ◽  
Numerical Methods ◽  
Sample Size ◽  
Body Mass ◽  
Optimal Allocation ◽  
Computing Time ◽  
Optimal Sample Size ◽  
Optimum Sample Size ◽  
Optimal Sample ◽  
Sample Size Allocation

In many medical researches, it is needed to determine the optimal sample size allocation in a heterogeneous population. This paper proposes the algorithm for optimal sample size allocation. We consider the optimal allocation problem as an optimization problem and the solution is obtained by using Bisection, Secant, Regula–Falsi and other numerical methods. The performance of the algorithm for different numerical methods are analyzed and evaluated in terms of computing time, number of iterations and gain in accuracy using stratification. The efficacy of algorithm is evaluated for the response in terms of body mass index (BMI) to the dietetic supplement with diabetes mellitus, HIV/AIDS and cancer post-operatory recovery patients.

scholarly journals Regulator Loss Functions and Hierarchical Modeling for Safety Decision Making

2017 ◽  
Vol 37 (5) ◽  
pp. 512-522
Author(s):  
Laura A. Hatfield ◽  
Christine M. Baugh ◽  
Vanessa Azzone ◽  
Sharon-Lise T. Normand
Keyword(s):  
Decision Making ◽  
Medical Device ◽  
Hierarchical Modeling ◽  
Loss Functions ◽  
Safety Signal ◽  
Theoretic Approach ◽  
Z Score ◽  
Bayes Risk ◽  
Decision Theoretic Approach ◽  
Safety Signals

Background. Regulators must act to protect the public when evidence indicates safety problems with medical devices. This requires complex tradeoffs among risks and benefits, which conventional safety surveillance methods do not incorporate. Objective. To combine explicit regulator loss functions with statistical evidence on medical device safety signals to improve decision making. Methods. In the Hospital Cost and Utilization Project National Inpatient Sample, we select pediatric inpatient admissions and identify adverse medical device events (AMDEs). We fit hierarchical Bayesian models to the annual hospital-level AMDE rates, accounting for patient and hospital characteristics. These models produce expected AMDE rates (a safety target), against which we compare the observed rates in a test year to compute a safety signal. We specify a set of loss functions that quantify the costs and benefits of each action as a function of the safety signal. We integrate the loss functions over the posterior distribution of the safety signal to obtain the posterior (Bayes) risk; the preferred action has the smallest Bayes risk. Using simulation and an analysis of AMDE data, we compare our minimum-risk decisions to a conventional Z score approach for classifying safety signals. Results. The 2 rules produced different actions for nearly half of hospitals (45%). In the simulation, decisions that minimize Bayes risk outperform Z score–based decisions, even when the loss functions or hierarchical models are misspecified. Limitations. Our method is sensitive to the choice of loss functions; eliciting quantitative inputs to the loss functions from regulators is challenging. Conclusions. A decision-theoretic approach to acting on safety signals is potentially promising but requires careful specification of loss functions in consultation with subject matter experts.

scholarly journals Multiple sensitive estimation and optimal sample size allocation in the item sum technique

2017 ◽  
Vol 60 (1) ◽  
pp. 155-173 ◽  
Author(s):  
Pier Francesco Perri ◽  
María del Mar Rueda García ◽  
Beatriz Cobo Rodríguez
Keyword(s):  
Sample Size ◽  
Optimal Sample Size ◽  
Optimal Sample ◽  
Sample Size Allocation
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