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Islam, A. F. M. Saiful. "Loss functions, utility functions and Bayesian sample size determination." Thesis, Queen Mary, University of London, 2011. http://qmro.qmul.ac.uk/xmlui/handle/123456789/1259.
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This thesis consists of two parts. The purpose of the first part of the research is to obtain Bayesian sample size determination (SSD) using loss or utility function with a linear cost function. A number of researchers have studied the Bayesian SSD problem. One group has considered utility (loss) functions and cost functions in the SSD problem and others not. Among the former most of the SSD problems are based on a symmetrical squared error (SE) loss function. On the other hand, in a situation when underestimation is more serious than overestimation or vice-versa, then an asymmetric loss function should be used. For such a loss function how many observations do we need to take to estimate the parameter under study? We consider different types of asymmetric loss functions and a linear cost function for sample size determination. For the purposes of comparison, firstly we discuss the SSD for a symmetric squared error loss function. Then we consider the SSD under different types of asymmetric loss functions found in the literature. We also introduce a new bounded asymmetric loss function and obtain SSD under this loss function. In addition, to estimate a parameter following a particular model, we present some theoretical results for the optimum SSD problem under a particular choice of loss function. We also develop computer programs to obtain the optimum SSD where the analytic results are not possible. In the two parameter exponential family it is difficult to estimate the parameters when both are unknown. The aim of the second part is to obtain an optimum decision for the two parameter exponential family under the two parameter conjugate utility function. In this case we discuss Lindley’s (1976) optimum decision for one 6 parameter exponential family under the conjugate utility function for the one parameter exponential family and then extend the results to the two parameter exponential family. We propose a two parameter conjugate utility function and then lay out the approximation procedure to make decisions on the two parameters. We also offer a few examples, normal distribution, trinomial distribution and inverse Gaussian distribution and provide the optimum decisions on both parameters of these distributions under the two parameter conjugate utility function.
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Gibbons, Christopher. "Determination of power and sample size for Levene's test." Connect to online resource, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1447667.
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Chang, Yu-Wei. "Sample Size Determination for a Three-arm Biosimilar Trial." Diss., Temple University Libraries, 2014. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/298932.
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Statistics<br>Ph.D.<br>The equivalence assessment usually consists of three tests and is often conducted through a three-arm clinical trial. The first two tests are to demonstrate the superiority of the test treatment and the reference treatment to placebo, and they are followed by the equivalence test between the test treatment and the reference treatment. The equivalence is commonly defined in terms of mean difference, mean ratio or ratio of mean differences, i.e. the ratio of the mean difference of the test and placebo to the mean difference of the reference and placebo. In this dissertation, the equivalence assessment for both continuous data and discrete data are discussed. For the continuous case, the test of the ratio of mean differences is applied. The advantage of this test is that it combines a superiority test of the test treatment over the placebo and an equivalence test through one hypothesis. For the discrete case, the two-step equivalence assessment approach is studied for both Poisson and negative binomial data. While a Poisson distribution implies that population mean and variance are the same, the advantage of applying a negative binomial model is that it accounts for overdispersion, which is a common phenomenon of count medical endpoints. The test statistics, power function, and required sample size examples for a three-arm equivalence trial are given for both continuous and discrete cases. In addition, discussions on power comparisons are complemented with numerical results.<br>Temple University--Theses
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Cheng, Dunlei Stamey James D. "Topics in Bayesian sample size determination and Bayesian model selection." Waco, Tex. : Baylor University, 2007. http://hdl.handle.net/2104/5039.
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Meganathan, Karthikeyan. "Sample Size Determination in Simple Logistic Regression: Formula versus Simulation." University of Cincinnati / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1627663458916666.
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Banton, Dwaine Stephen. "A BAYESIAN DECISION THEORETIC APPROACH TO FIXED SAMPLE SIZE DETERMINATION AND BLINDED SAMPLE SIZE RE-ESTIMATION FOR HYPOTHESIS TESTING." Diss., Temple University Libraries, 2016. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/369007.
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Statistics<br>Ph.D.<br>This thesis considers two related problems that has application in the field of experimental design for clinical trials: • fixed sample size determination for parallel arm, double-blind survival data analysis to test the hypothesis of no difference in survival functions, and • blinded sample size re-estimation for the same. For the first problem of fixed sample size determination, a method is developed generally for testing of hypothesis, then applied particularly to survival analysis; for the second problem of blinded sample size re-estimation, a method is developed specifically for survival analysis. In both problems, the exponential survival model is assumed. The approach we propose for sample size determination is Bayesian decision theoretical, using explicitly a loss function and a prior distribution. The loss function used is the intrinsic discrepancy loss function introduced by Bernardo and Rueda (2002), and further expounded upon in Bernardo (2011). We use a conjugate prior, and investigate the sensitivity of the calculated sample sizes to specification of the hyper-parameters. For the second problem of blinded sample size re-estimation, we use prior predictive distributions to facilitate calculation of the interim test statistic in a blinded manner while controlling the Type I error. The determination of the test statistic in a blinded manner continues to be nettling problem for researchers. The first problem is typical of traditional experimental designs, while the second problem extends into the realm of adaptive designs. To the best of our knowledge, the approaches we suggest for both problems have never been done hitherto, and extend the current research on both topics. The advantages of our approach, as far as we see it, are unity and coherence of statistical procedures, systematic and methodical incorporation of prior knowledge, and ease of calculation and interpretation.<br>Temple University--Theses
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Pedersen, Kristen E. "Sample Size Determination in Auditing Accounts Receivable Using a Zero-Inflated Poisson Model." Digital WPI, 2010. https://digitalcommons.wpi.edu/etd-theses/421.
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In the practice of auditing, a sample of accounts is chosen to verify if the accounts are materially misstated, as opposed to auditing all accounts; it would be too expensive to audit all acounts. This paper seeks to find a method for choosing a sample size of accounts that will give a more accurate estimate than the current methods for sample size determination that are currently being used. A review of methods to determine sample size will be investigated under both the frequentist and Bayesian settings, and then our method using the Zero-Inflated Poisson (ZIP) model will be introduced which explicitly considers zero versus non-zero errors. This model is favorable due to the excess zeros that are present in auditing data which the standard Poisson model does not account for, and this could easily be extended to data similar to accounting populations.
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Chen, Yanran. "Influence of Correlation and Missing Data on Sample Size Determination in Mixed Models." Bowling Green State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1370448410.
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Huh, Seungho. "SAMPLE SIZE DETERMINATION AND STATIONARITY TESTING IN THE PRESENCE OF TREND BREAKS." NCSU, 2001. http://www.lib.ncsu.edu/theses/available/etd-20010222-121906.
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<p>Traditionally it is believed that most macroeconomic time series represent stationary fluctuations around a deterministic trend. However, simple applications of the Dickey-Fuller test have, in many cases, been unable to show that major macroeconomic variables are stationary univariate time series structure. One possible reason for non-rejection of unit roots is that the simple mean or linear trend function used by the tests are not sufficient to describe the deterministic part of the series. To address this possibility, unit root tests in the presence of trend breaks have been studied by several researchers.In our work, we deal with some issues associated with unit root testing in time series with a trend break.The performance of various unit root test statistics is compared with respect to the break induced size distortion problem. We examine the effectiveness of tests based on symmetric estimators as compared to those based on the least squares estimator.In particular, we show that tests based on the weighted symmetric estimator not only eliminate thespurious rejection problem but also have reasonably good power properties when modified to allow for a break.We suggest alternative test statistics for testing the unit root null hypothesis in the presence of a trend break. Our new test procedure, which we call the ``bisection'' method, is based on the idea of subgrouping. This is simpler than other methods since the necessity of searching for the break is avoided.Using stream flow data from the US Geological Survey, we perform a temporal analysis of some hydrologicvariables. We first show that the time series for the target variables are stationary, then focus on finding the sample size necessary to detect a mean change if one occurs. Three different approaches are used to solve this problem: OLS, GLS and a frequency domain method. A cluster analysis of stations is also performed using these sample sizes as data.We investigate whether available geographic variables can be used to predict cluster membership. <P>
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Safaie, Nasser. "A fully Bayesian approach to sample size determination for verifying process improvement." Diss., Wichita State University, 2010. http://hdl.handle.net/10057/3656.
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There has been significant growth in the development and application of Bayesian
methods in industry. The Bayes’ theorem describes the process of learning from experience and
shows how knowledge about the state of nature is continually modified as new data become
available. This research is an effort to introduce the Bayesian approach as an effective tool for
evaluating process adjustments aimed at causing a change in a process parameter. This is usually
encountered in scenarios where the process is found to be stable but operating away from the
desired level. In these scenarios, a number of changes are proposed and tested as part of the
improvement efforts. Typically, it is desired to evaluate the effect of these changes as soon as
possible and take appropriate actions. Despite considerable research efforts to utilize the
Bayesian approach, there are few guidelines for loss computation and sample size determination.
This research proposed a fully Bayesian approach for determining the maximum economic
number of measurements required to evaluate and verify such efforts. Mathematical models were
derived and used to establish implementation boundaries from economic and technical
viewpoints. In addition, numerical examples were used to illustrate the steps involved and
highlight the economic advantages of the proposed procedures.<br>Thesis (Ph.D.)--Wichita State University, College of Engineering, Dept. of Industrial and Manufacturing Engineering
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Price, Tonia. "A faster simulation approach to sample size determination for random effect models." Thesis, University of Bristol, 2017. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730872.
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Ma, Junheng. "Contributions to Numerical Formal Concept Analysis, Bayesian Predictive Inference and Sample Size Determination." Case Western Reserve University School of Graduate Studies / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=case1285341426.
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Oymak, Okan. "Sample size determination for estimation of sensor detection probabilities based on a test variable." Thesis, Monterey, Calif. : Naval Postgraduate School, 2007. http://bosun.nps.edu/uhtbin/hyperion-image.exe/07Jun%5FOymak.pdf.
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Thesis (M.S. in Operations Research)--Naval Postgraduate School, June 2007.<br>Thesis Advisor(s): Lyn R. Whitaker. "June 2007." Includes bibliographical references (p. 95-96). Also available in print.
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Kikuchi, Takashi. "A Bayesian cost-benefit approach to sample size determination and evaluation in clinical trials." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:f5cb4e27-8d4c-4a80-b792-469e50efeea2.
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Current practice for sample size computations in clinical trials is largely based on frequentist or classical methods. These methods have the drawback of requiring a point estimate of the variance of treatment effect and are based on arbitrary settings of type I and II errors. They also do not directly address the question of achieving the best balance between the costs of the trial and the possible benefits by using a new medical treatment, and fail to consider the important fact that the number of users depends on evidence for improvement compared with the current treatment. A novel Bayesian approach, Behavioral Bayes (or BeBay for short) (Gittins and Pezeshk, 2000a,b, 2002a,b; Pezeshk, 2003), assumes that the number of patients switching to the new treatment depends on the strength of the evidence which is provided by clinical trials, and takes a value between zero and the number of potential patients in the country. The better a new treatment, the more patients switch to it and the more the resulting benefit. The model defines the optimal sample size to be the sample size that maximises the expected net benefit resulting from a clinical trial. Gittins and Pezeshk use a simple form of benefit function for paired comparisons between two medical treatments and assume that the variance of the efficacy is known. The research in this thesis generalises these original conditions by introducing a logistic benefit function to take account of differences in efficacy and safety between two drugs. The model is also extended to the more general cases of unpaired comparisons and unknown variance. The expected net benefit defined by Gittins and Pezeshk is based on the efficacy of the new drug only. It does not consider the incidence of adverse reactions and their effect on patients’ preferences. Here we include the costs of treating adverse reactions and calculate the total benefit in terms of how much the new drug can reduce societal expenditure. We describe how our model may be used for the design of phase III clinical trials, cluster randomised clinical trials and bridging studies. This is done in some detail and using illustrative examples based on published studies. For phase III trials we allow the possibility of unequal treatment group sizes, which often occur in practice. Bridging studies are those carried out to extend the range of applicability of an established drug, for example to new ethnic groups. Throughout the objective of our procedures is to optimise the costbenefit in terms of national health-care. BeBay is the leading methodology for determining sample sizes on this basis. It explicitly takes account of the roles of three decision makers, namely patients and doctors, pharmaceutical companies and the health authority.
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Rahme, Elham H. "Sample size determination for prevalence estimation in the absence of a gold standard diagnostic test." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape16/PQDD_0010/NQ30366.pdf.
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Rahme, Elham H. "Sample size determination for prevalence estimation in the absence of a gold standard diagnostic test." Thesis, McGill University, 1996. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=34434.
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A common problem in medical research is the estimation of the prevalence of a disease in a given population. This is usually accomplished by applying a diagnostic test to a sample of subjects from the target population. In this thesis, we investigate the sample size requirements for the accurate estimation of disease prevalence for such experiments. When a gold standard diagnostic test is available, estimating the prevalence of a disease can be viewed as a problem in estimating a binomial proportion. In this case, we discuss some anomalies in the classical sample size criteria for binomial parameter estimation. These are especially important with small sample sizes. When a gold standard test is not available, one must take into account misclassification errors in order to avoid misleading results. When the sensitivity and the specificity of the diagnostic test are both known, a new adjustment to the maximum likelihood estimator of the prevalence is suggested, and confidence intervals and sample size estimates that arise from this estimator are given. A Bayesian approach is taken when the sensitivity and specificity of the diagnostic test are not exactly known. Here, a method to determine the sample size needed to satisfy a Bayesian sample size criterion that averages over the preposterior marginal distribution of the data is provided. Exact methods are given in some cases, and a sampling importance resampling algorithm is used for more complex situations. A main conclusion is that the degree to which the properties of a diagnostic test are known can have a very large effect on the sample size requirements.
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Wang, Jie Stamey James D. "Sample size determination for Emax model, equivalence / non-inferiority test and drug combination in fixed dose trials." Waco, Tex. : Baylor University, 2008. http://hdl.handle.net/2104/5182.
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Brown, Eric C. "Estimates of statistical power and accuracy for latent trajectory class enumeration in the growth mixture model." [Tampa, Fla.] : University of South Florida, 2003. http://purl.fcla.edu/fcla/etd/SFE0000622.
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Costa, Eliardo Guimarães da. "Aspectos estatísticos da amostragem de água de lastro." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-06052013-172123/.
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A água de lastro de navios é um dos principais agentes dispersivos de organismos nocivos à saúde humana e ao meio ambiente e normas internacionais exigem que a concentração desses organismos no tanque seja menor que um valor previamente especificado. Por limitações de tempo e custo, esse controle requer o uso de amostragem. Sob a hipótese de que a concentração desses organismos no tanque é homogênea, vários autores têm utilizado a distribuição Poisson para a tomada de decisão com base num teste de hipóteses. Como essa proposta é pouco realista, estendemos os resultados para casos em que a concentração de organismos no tanque é heterogênea utilizando estratificação, processos de Poisson não-homogêneos ou assumindo que ela obedece a uma distribuição Gama, que induz uma distribuição Binomial Negativa para o número de organismos amostrados. Além disso, propomos uma nova abordagem para o problema por meio de técnicas de estimação baseadas na distribuição Binomial Negativa. Para fins de aplicação, implementamos rotinas computacionais no software R<br>Ballast water is a leading dispersing agent of harmful organisms to human health and to the environment and international standards require that the concentration of these organisms in the tank must be less than a prespecified value. Because of time and cost limitations, this inspection requires the use of sampling. Under the assumption of an homogeneous organism concentration in the tank, several authors have used the Poisson distribution for decision making based on hypothesis testing. Since this proposal is unrealistic, we extend the results for cases in which the organism concentration in the tank is heterogeneous, using stratification, nonhomogeneous Poisson processes or assuming that it follows a Gamma distribution, which induces a Negative Binomial distribution for the number of sampled organisms. Furthermore, we propose a novel approach to the problem through estimation techniques based on the Negative Binomial distribution. For practical applications, we implemented computational routines using the R software
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Darishchev, Alexander. "Analyse de connectivité et techniques de partitionnement de données appliquées à la caractérisation et la modélisation d'écoulement au sein des réservoirs très hétérogènes." Thesis, Rennes 1, 2015. http://www.theses.fr/2015REN1S162.
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Les techniques informatiques ont gagné un rôle primordial dans le développement et l'exploitation des ressources d'hydrocarbures naturelles ainsi que dans d'autres opérations liées à des réservoirs souterrains. L'un des problèmes cruciaux de la modélisation de réservoir et les prévisions de production réside dans la présélection des modèles de réservoir appropriés à la quantification d'incertitude et au le calage robuste des résultats de simulation d'écoulement aux réelles mesures et observations acquises du gisement. La présente thèse s'adresse à ces problématiques et à certains autres sujets connexes.Nous avons élaboré une stratégie pour faciliter et accélérer l'ajustement de tels modèles numériques aux données de production de champ disponibles. En premier lieu, la recherche s'était concentrée sur la conceptualisation et l'implémentation des modèles de proxy reposant sur l'analyse de la connectivité, comme une propriété physique intégrante et significative du réservoir, et des techniques avancées du partitionnement de données et de l'analyse de clusters. La méthodologie développée comprend aussi plusieurs approches originales de type probabiliste orientées vers les problèmes d'échantillonnage d'incertitude et de détermination du nombre de réalisations et de l'espérance de la valeur d'information d'échantillon. Afin de cibler et donner la priorité aux modèles pertinents, nous avons agrégé les réalisations géostatistiques en formant des classes distinctes avec une mesure de distance généralisée. Ensuite, afin d'améliorer la classification, nous avons élargi la technique graphique de silhouettes, désormais appelée la "séquence entière des silhouettes multiples" dans le partitionnement de données et l'analyse de clusters. Cette approche a permis de recueillir une information claire et compréhensive à propos des dissimilarités intra- et intre-cluster, particulièrement utile dans le cas des structures faibles, voire artificielles. Finalement, la séparation spatiale et la différence de forme ont été visualisées graphiquement et quantifiées grâce à la mesure de distance probabiliste.Il apparaît que les relations obtenues justifient et valident l'applicabilité des approches proposées pour améliorer la caractérisation et la modélisation d'écoulement. Des corrélations fiables ont été obtenues entre les chemins de connectivité les plus courts "injecteur-producteur" et les temps de percée d'eau pour des configurations différentes de placement de puits, niveaux d'hétérogénéité et rapports de mobilité de fluides variés. Les modèles de connectivité proposés ont produit des résultats suffisamment précis et une performance compétitive au méta-niveau. Leur usage comme des précurseurs et prédicateurs ad hoc est bénéfique en étape du traitement préalable de la méthodologie. Avant le calage d'historique, un nombre approprié et gérable des modèles pertinents peut être identifié grâce à la comparaison des données de production disponibles avec les résultats de<br>Computer-based workflows have gained a paramount role in development and exploitation of natural hydrocarbon resources and other subsurface operations. One of the crucial problems of reservoir modelling and production forecasting is in pre-selecting appropriate models for quantifying uncertainty and robustly matching results of flow simulation to real field measurements and observations. This thesis addresses these and other related issues. We have explored a strategy to facilitate and speed up the adjustment of such numerical models to available field production data. Originally, the focus of this research was on conceptualising, developing and implementing fast proxy models related to the analysis of connectivity, as a physically meaningful property of the reservoir, with advanced cluster analysis techniques. The developed methodology includes also several original probability-oriented approaches towards the problems of sampling uncertainty and determining the sample size and the expected value of sample information. For targeting and prioritising relevant reservoir models, we aggregated geostatistical realisations into distinct classes with a generalised distance measure. Then, to improve the classification, we extended the silhouette-based graphical technique, called hereafter the "entire sequence of multiple silhouettes" in cluster analysis. This approach provided clear and comprehensive information about the intra- and inter-cluster dissimilarities, especially helpful in the case of weak, or even artificial, structures. Finally, the spatial separation and form-difference of clusters were graphically visualised and quantified with a scale-invariant probabilistic distance measure. The obtained relationships appeared to justify and validate the applicability of the proposed approaches to enhance the characterisation and modelling of flow. Reliable correlations were found between the shortest "injector-producer" pathways and water breakthrough times for different configurations of well placement, various heterogeneity levels and mobility ratios of fluids. The proposed graph-based connectivity proxies provided sufficiently accurate results and competitive performance at the meta-level. The use of them like precursors and ad hoc predictors is beneficial at the pre-processing stage of the workflow. Prior to history matching, a suitable and manageable number of appropriate reservoir models can be identified from the comparison of the available production data with the selected centrotype-models regarded as the class representatives, only for which the full fluid flow simulation is pre-requisite. The findings of this research work can easily be generalised and considered in a wider scope. Possible extensions, further improvements and implementation of them may also be expected in other fields of science and technology
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Assareh, Hassan. "Bayesian hierarchical models in statistical quality control methods to improve healthcare in hospitals." Thesis, Queensland University of Technology, 2012. https://eprints.qut.edu.au/53342/1/Hassan_Assareh_Thesis.pdf.
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Quality oriented management systems and methods have become the dominant business and governance paradigm. From this perspective, satisfying customers’ expectations by supplying reliable, good quality products and services is the key factor for an organization and even government. During recent decades, Statistical Quality Control (SQC) methods have been developed as the technical core of quality management and continuous improvement philosophy and now are being applied widely to improve the quality of products and services in industrial and business sectors. Recently SQC tools, in particular quality control charts, have been used in healthcare surveillance. In some cases, these tools have been modified and developed to better suit the health sector characteristics and needs. It seems that some of the work in the healthcare area has evolved independently of the development of industrial statistical process control methods.
Therefore analysing and comparing paradigms and the characteristics of quality control charts and techniques across the different sectors presents some opportunities for transferring knowledge and future development in each sectors. Meanwhile considering capabilities of Bayesian approach particularly Bayesian hierarchical models and computational techniques in which all uncertainty are expressed as a structure of probability, facilitates decision making and cost-effectiveness analyses.
Therefore, this research investigates the use of quality improvement cycle in a health vii setting using clinical data from a hospital. The need of clinical data for monitoring purposes is investigated in two aspects. A framework and appropriate tools from the industrial context are proposed and applied to evaluate and improve data quality in available datasets and data flow; then a data capturing algorithm using Bayesian decision making methods is developed to determine economical sample size for statistical analyses within the quality improvement cycle.
Following ensuring clinical data quality, some characteristics of control charts in the health context including the necessity of monitoring attribute data and correlated quality characteristics are considered. To this end, multivariate control charts from an industrial context are adapted to monitor radiation delivered to patients undergoing diagnostic coronary angiogram and various risk-adjusted control charts are constructed and investigated in monitoring binary outcomes of clinical interventions as well as postintervention survival time.
Meanwhile, adoption of a Bayesian approach is proposed as a new framework in estimation of change point following control chart’s signal. This estimate aims to facilitate root causes efforts in quality improvement cycle since it cuts the search for the potential causes of detected changes to a tighter time-frame prior to the signal. This approach enables us to obtain highly informative estimates for change point parameters since probability distribution based results are obtained.
Using Bayesian hierarchical models and Markov chain Monte Carlo computational methods, Bayesian estimators of the time and the magnitude of various change scenarios including step change, linear trend and multiple change in a Poisson process are developed and investigated.
The benefits of change point investigation is revisited and promoted in monitoring hospital outcomes where the developed Bayesian estimator reports the true time of the shifts, compared to priori known causes, detected by control charts in monitoring rate of excess usage of blood products and major adverse events during and after cardiac surgery in a local hospital.
The development of the Bayesian change point estimators are then followed in a healthcare surveillances for processes in which pre-intervention characteristics of patients are viii affecting the outcomes. In this setting, at first, the Bayesian estimator is extended to capture the patient mix, covariates, through risk models underlying risk-adjusted control charts. Variations of the estimator are developed to estimate the true time of step changes and linear trends in odds ratio of intensive care unit outcomes in a local hospital. Secondly, the Bayesian estimator is extended to identify the time of a shift in mean survival time after a clinical intervention which is being monitored by riskadjusted survival time control charts. In this context, the survival time after a clinical intervention is also affected by patient mix and the survival function is constructed using survival prediction model.
The simulation study undertaken in each research component and obtained results highly recommend the developed Bayesian estimators as a strong alternative in change point estimation within quality improvement cycle in healthcare surveillances as well as industrial and business contexts. The superiority of the proposed Bayesian framework and estimators are enhanced when probability quantification, flexibility and generalizability of the developed model are also considered.
The empirical results and simulations indicate that the Bayesian estimators are a strong alternative in change point estimation within quality improvement cycle in healthcare surveillances. The superiority of the proposed Bayesian framework and estimators are enhanced when probability quantification, flexibility and generalizability of the developed model are also considered. The advantages of the Bayesian approach seen in general context of quality control may also be extended in the industrial and business domains where quality monitoring was initially developed.
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Huang, Dong-Si, and 黃東溪. "Sample Size Determination in a Microarray Experiment." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/37217728505587250306.
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Ye, Shang-bo, and 葉尚柏. "Sample Size Determination for Two-stage Equivalence Test." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/87773637833284788175.
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碩士<br>國立成功大學<br>統計學系碩博士班<br>97<br>In clinical research, several experimential treaments were considered and compared to a standard teratment in the pilot study. If an experimental treatment is the best in the pilot study, then it will be confirmed whether it is better than the standard control or it is equivalent to the standard control. The general sample size determination of noninferiority test or equivalent test had been studied. This paper proposed a two-stage design which selects the best of several experimental treatments and tests whether it is equivalent to a standard control or better than a standard control. The design allows early termination with acceptance of the null hypothesis for noninferiority test or equivalent test. By minimizing expected total sample size for fixed significance level and power, optimal sample size and cut-off parameters were obtained.
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Da-ChingLiao and 廖大慶. "Sample Size Determination for Setting up the Statistical Tolerance Limits." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/96153113922119361607.
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碩士<br>國立成功大學<br>統計學系<br>103<br>The statistical tolerance limits plays an important role in determining product’s engineering specifications due to the fact that the engineering specifications will cause crucial effects on the calculation of process capability indices. Over the decades, several researchers have proposed the algorithms for computing statistical tolerance limits under normal distribution and non-normal distribution. For the situation that the quality characteristic follows normal distribution, we compare all the possible algorithms under normal distribution and then develop a table of statistical tolerance limits corresponding to the current manufacturing situation in industry. For the situation that the quality characteristic does not follow the normal distribution, we firstly use Kolmogorov-Smirnov test to determine the appropriate fitted distribution; if there is no suitable fitted distribution, we apply the nonparametric statistical method to resolve it. In addition, concerning the current manufacturing situation in industry, we add the Six Sigma consideration during the setup of statistical tolerance limits and further perform the trade-off analysis between sample size and yield rate.
Finally, we summarize the research results and propose a standard operating procedure for determining the statistical tolerance limits. Three numerical examples are also given to demonstrate the usefulness of our proposed approach. Hopefully, the results of this research can be served as a valuable guideline and references for manufacturing industries to set up statistical tolerance limits.
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Pei-Lin, Li, and 李珮苓. "The Determination of Sample Size in an Oligonucleotide Array Experiment." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/31962418964768679726.
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碩士<br>國立臺灣大學<br>農藝學研究所<br>91<br>Microarray have made it possible to measure the abundance of mRNA transcripts
for thousands of genes simultaneously. There are two kinds of microarray commonly used in various biological experiments, one is the two-dye cDNA array, and the other is the Affymetrix oligonucleotide array. In this study, first we introduce some methods of oligonucleotide arrays probe level data normalization and conversion probe level data to gene expression, available in the literature.
We then apply a calibration model presented in Rocke and Durbin (2001) to describe the gene expression data. In this study, we simply focus on the comparative experiment between two biological states of cells, typically mutant and wildtype ; diseased and healthy ; treated and untreated, etc. For convenience, we call it the test-control experiment. Three data sets available from public websites are analyzed to provide us some preliminary knowledge about the values of the parameters in the underlying calibration model for the test-control experiments. We then estimate the number of arrays that is required in order to gain reliable results on the identification of differentially expressed genes via a statistical simulation study. Some practical solutions will be recommended to assist the biologists conducting the test-control experiments using the oligonucleotide arrays. Finally, we develop an algorithm to determine the sample size and the significance level for the statistical tests.
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Chou, Hsin-Ju, and 周鑫汝. "The Sample Size Determination for Accuracy of Diagnostic Test Studies." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/54841455700840634560.
Full textAbstract:
碩士<br>國立臺北大學<br>統計學系<br>103<br>With the progressive development in science and technology,some medical researches are aimed to invest diagnostic tests to detect and treat the disease earlier.Under the limited resources, the development of the diagnostic reagent must have a certain degree of accuracy.To have a persuasive result, how to design the experiment to test the diagnostic test is very important.In particular, the sample size determination is a key step for the design.
The accuracy of the diagnostic test is often measured through the receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC).They can be estimated parametrically and nonparametrically.This thesis reviews the sample size determination for testing the AUC for one-sample problem.The result is easily generated to two independent sample problems.For the paired problem of comparing two diagnostic tests, the results proposed by Hwang, Wang ,Tung (2015) is used to determine the sample size.Finally, since most of the results do not have a closed form, this thesis provides the numeric sample size results under various scenarios.Finally, since most of the results do not have a closed form, this thesis provides the numeric sample size results under various scenarios.
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謝孟芳. "Sample size determination when exploring large itemset in data mining." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/80616395923148082315.
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碩士<br>國立臺灣科技大學<br>資訊管理系<br>90<br>Data mining, which discovers useful knowledge from large collection of data,is a fast developing field of computer science and technology.Current technology makes it fairly easy to collect a large amount of data,but conducting analysis on these fast growing data becomes a formidable task.Complete census tends to be slow and expensive.A natural and simple alternative way is to mine on a sample instead of the whole database,which mitigates computational effort at the cost of sampling error.Discovery of associtaion rules is a typical problem in data mining.Finding large itemsets is essential to forming the association rules.When using random sampling to find the large itemsets,we study the relationship between the computation effort (sample size) and the sampling performance indicated by the probability of effectively finding the correct large itemsets.
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Azzolina, Danila. "Bayesian HPD-based sample size determination using semi-parametric prior elicitation." Doctoral thesis, 2019. http://hdl.handle.net/2158/1152426.
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In several clinical trial settings, it is challenging to recruit the overall sample provided at the design stage. Several factors (i.e., high costs, regulatory barriers, narrow eligibility criteria and cultural attitudes towards research) can impact on the recruitment process. The poor accrual problem is evident in the clinical research involving adults but also in the pediatric research, but also in pediatric research, where 37% of clinical trials terminate early due to inadequate accrual.
From a methodological-statistical standpoint, reduced sample size and the rarity of some diseases under consideration reduce a study’s statistical power, compromising the ability to accurately answer the primary research question due to a reduction in the likelihood to detect a treatment effect. This statistical point of view favors the use of a Bayesian approach to the analysis of clinical trial data. In recent years, Bayesian methods have increasingly been used in the design, monitoring, and analysis of clinical trials due to their flexibility. In clinical trials candidate for early termination for poor accrual reasons, a Bayesian approach can incorporate the available knowledge provided by literature (objective prior) or by elicitation of Experts’ opinions (subjective prior) on the treatment effect under investigation in order to reduce uncertainty in treatment effect estimation.
The first article (Chapter 1) shows the potentiality of the Bayesian method for use in pediatric research, demonstrating the possibility to include, in the final inference, prior information and trial data, especially when the small sample size is available to estimate the treatment effect. Moreover, this study aims to underline the importance of a sensitivity analysis conducted on prior definitions in order to investigate the stability of inferential conclusions concerning the different prior choices. In a research setting where objective data to derive prior distribution are not available, an informative inference complemented with an expert elicitation procedure can be used to translate into prior probability distribution (elicitation) the available expert knowledge about treatment effect. The elicitation process in the Bayesian inference can quantify the presence of uncertainty in
treatment effect belief. Additionally, this information can be used to plan a study design, e.g., the sample size calculations] and interim analysis. Elicitation may be conducted in a parametric setting, assuming that experts’ opinion may be represented by a good note family of probability distributions identified by hyper-parameters, or in a not parametric and semiparametric hybrid setting. It is widely assessed that the primary limit of a parametric approach is to constrain expert belief into a pre-specified family distribution.
The second article (Chapter 2) aims to investigate the state-of-art of the Bayesian prior elicitation methods in clinical trial research performing an in-depth analysis of the discrepancy between the approaches available in the statistical literature and the elicitation procedures currently applied within the clinical trial research. A Bayesian approach to clinical trial data may be defined before the start of the study, by the protocol, defining a sample size taking into account of expert opinion providing the possibility to
use also nonparametric approaches. A more flexible sample size method may be suitable, for example, to design a study conducted on small sample sizes as a Phase II clinical trial, which is generally one sample, single stage in which accrued patients, are treated, and are then observed for a possible response.
Generally, Bayesian methods, available in the literature to obtain a sample size estimation for binary data, are based on parametric Beta-binomial solutions, considering an inference performed in term of posterior Highest Posterior Density interval (HPD). The aim of the third article (Chapter 3) is to extend the main criteria adopted for the Bayesian Sample size estimation, Average Coverage Criterion (ACC), Average Length Criterion (ALC) and Worse Outcome Criterion (WOC), proposing a sample size estimation method which includes also prior defined in a semiparametric approach to the prior elicitation of the expert’s opinion. In the research article also a practical application of the method to a Phase II clinical trial study design has been reported. The semiparametric solution adopted is a very flexible considering a prior distribution obtained as a balanced optimization of a weighed sum two components; one is a linear combination of B-Spline adapted among expert’s quantiles, another one is an uninformative prior distribution.
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Susarla, Hari Krishna. "Optimal sample size determination in seed health testing : a simulation study." Thesis, 2005. http://spectrum.library.concordia.ca/8582/1/MR10215.pdf.
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Selection of an appropriate sample size is an important prerequisite to any statistical investigation. In this thesis the problem of identifying the sample size for testing the seed health by noting the presence or the absence of pathogen(s) is considered. The cross-classified data of variety by seed by pathogen is collected for the purpose, which consists of N observations for each variety of seed. Here N is regarded as population size and the outcome is a Bernoulli random variable. A simulation method for identifying the sample size is developed and is compared with five existing methods. The simulation method is based on chi-square ({2) measure of goodness of fit of empirical distribution with that of a theoretical distribution. Here k repeated samples for each of the sample sizes n=10(10)50(25)100(100)500, using a simple random sampling without replacement (SRSWOR), are considered. For each of the k samples of size n, the chi-square ({2) measure of goodness of fit is computed.
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Kao, Song-Chu, and 高松楚. "Sample Size Determination for Tolerance Interval – With Application to Pharmaceutical Testing." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/9ys575.
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碩士<br>國立交通大學<br>統計學研究所<br>101<br>Tolerance is a widely used statistical tools, and has been a useful tool for pharmaceutical testing. The determination of sample size of a pharmaceutical testing has been one of important issues for pharmaceutical companies, because it does not only represent cost considerations, but also is a quality assurance.Therefore, in this study, we develop an algorithm for determining the sample size of a tolerance interval based on historical data under some criteria provided in literatures focusing on the study of determination of sample size for tolerance interval. The required sample sizes for different cases are provided in this study. A simulation study is conducted to verify the result derived from the algorithm. The method proposed in this study can help pharmaceutical companies in choosing the sample size for drugs testing.
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Liao, Hsin-Chih, and 廖杏芝. "Sample Size Determination for Grouped Weibull Experiment: A Cost Function Aooroach." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/92236004365015218284.
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碩士<br>淡江大學<br>統計學系<br>88<br>Abstract :
When calculating the required sample size for a desired power at a given significant level, we often assume that we know the exact time of all responses whenever they occur during our study period. It is very common, however, in practice that we only monitor subjects periodically and, therefore, we know only whether responses occur or not during an interval. Under equi-class grouped data assumption, this paper includes a quantitative discussion of the effect resulting from experiment grouping or experiment time on the required sample size when we have two Wibull treatment groups. Furthermore, with the goal of exploring the optimum in the number of subjects, the number of examinations for test responses, and the total length of a study time period, this paper also provides a general guideline about how to determine these to minimize the total cost of a study for a desired power at a given significant level. A specified linear cost function that incorporates the costs of obtaining subjects, periodic examinations for test responses of subjects, and the total length of a study period, is assumed primarily for illustrative purpose. We also provide optimal sample sizes, length of experiments and group numbers under various experimental setup.
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Tsai, Wei-Ju, and 蔡薇茹. "Sample Size Determination for Effectiveness of Mass Screening for Breast Cancer." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/69527203738475298223.
Full textAbstract:
碩士<br>國立臺灣大學<br>流行病學與預防醫學研究所<br>100<br>Background Evaluation of mass screening for cancer based on primary endpoint often encounters long-term follow-up and enormous costs, especially when rare diseases are investigated. These problems are also particularly serious for young women screening with mammography and also the determination of optimal inter-screening interval by using randomized controlled trials. The expedient strategy is to use surrogate endpoint which can reduce variance which in turn reduce sample size. The application of surrogate endpoint to evaluation of cancer screening for the comparison of required sample sizes between surrogate endpoint and primary endpoint have been barely addressed.
Objective The objectives of this thesis were
(1) to expand the statistical operational definition for surrogate endpoints defined by Prentice. We also aim to assess whether tumor size, lymph node involvement, histological grade, and combined use of these tumor attributes can be used as surrogate endpoints for replacing breast cancer mortality reduction as a result of mammography screening.
(2) to demonstrate how the variance can be reduced by comparing a simple binary outcome and informative surrogate endpoints, and to compare the required sample sizes with primary endpoint and surrogate endpoint.
(3) to apply computer simulation in the light of multi-state Markov model for breast cancer natural history using tumor size or lymph node involvement to compare the required sample sizes with primary endpoint and surrogate endpoint with different inter-screening intervals.
Data source We used the Swedish Two-county breast screening trial data to illustrate the application of our statistical method to calculate sample size based on primary and surrogate endpoint, respectively.
Results
1. Based on the statistical operational definition for surrogate endpoints from Prentice, we found that tumour size can explain partial effect of screening group by 49.4% by using Cox proportional hazards regression model. The magnitude of partial effect were 45.2% and 62% for use of lymph node involvement and for combined use of lymph node involvement and tumour size for surrogate endpoints.
2. By using tumour size (DCIS、<20 mm and ≧20 mm) as surrogate endpoint, the required sample size was 38,914, which was smaller than the corresponding figure using lymph node involvement (n=75,764).
3. The required sample size was further reduced to 33,657 with combined use of tumor size and lymph node involvement as surrogate endpoint, which was 40.9% of 82,261 women required for primary endpoint.
4. We estimated that 261,292 women were required to demonstrate the screening effect between annual and biennial program for women aged 40-49 years with surrogate endpoint, tumour size. The required sizes were 120,916 and 1,192,296 for the comparison between annual and three-yearly screening programs and between biennial and three-yearly programs, respectively. If primary endpoint was used, the required sample sizes were four times of their corresponding figures mentioned above.
Conclusions The proposed statistical method for calculating sample size by surrogate endpoint and primary endpoint is very useful for planning mass screening for cancer particularly for randomized controlled trials.
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Phatakwala, Shantanu. "Estimation of form-error and determination of sample size in precision metrology." 2005. http://proquest.umi.com/pqdweb?did=1014319851&sid=16&Fmt=2&clientId=39334&RQT=309&VName=PQD.
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Thesis (M.S.)--State University of New York at Buffalo, 2005.<br>Title from PDF title page (viewed on Apr. 13, 2006) Available through UMI ProQuest Digital Dissertations. Thesis adviser: Gosavi, Abhijit.
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GUBBIOTTI, STEFANIA. "Bayesian Methods for Sample Size Determination and their use in Clinical Trials." Doctoral thesis, 2009. http://hdl.handle.net/11573/918542.
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Wu, Chia Han, and 吳嘉翰. "Sample Size Determination for the Two One-Sided Tests Procedure in Bioavailability/Bioequivalence." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/29221493711150597391.
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"Sample size determination for Poisson regression when the exposure variable contains misclassification errors." Tulane University, 1994.
Find full textAbstract:
Sample size calculation methods for Poisson regression to detect linear trend in logarithm of incidence rates (multiplicative models) and incidence rates (additive models) over ordered exposure groups are developed. These methods are parallel to those of Bull (1993) for logistic regression Moreover, when reliable ancillary misclassification information is available, a slight modification of these calculation methods can be used to determine the required sample size based on the correction of the estimate of the trend parameter in the analysis stage. In which the correction methods is modified from Reade-Christopher and Kupper (1991) We find that, as would be expected, the gradient of incidence rates over these groups and misclassification rate strongly affect the sample size requirements. In a one year study, when exposure variable contains no misclassification, the sample size required varies from 5,054 to 64,534, according to different gradients. Moreover, when a misclassification rate of 30% is assumed, these numbers are multiplied by approximately 1.3 for all gradients The distribution of subjects across exposure groups also affect the sample size requirements. In environmental and occupational studies, subjects may be grouped according to the continuous exposure and the groups chosen are often terciles, quartiles or quintiles, i.e., even distribution over the exposure groups. We find that less sample size is required for this type of distribution Finally, although the use of correction methods reduces the bias of the estimates, there was always greater variance in the estimate than when no correction is used. It would appreciate that when the gradient of incidence rate is small and the misclassification is not severe, then, based on the percentage of the true parameter included in the 95% confidence interval, use of the correction method may not be necessary<br>acase@tulane.edu
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Huang, Chih-Yang, and 黃智揚. "A study on a Simplified Approach to the Sample Size Determination in Bioequivalence Testing." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/35925396903299382961.
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碩士<br>國立臺灣大學<br>農藝學研究所<br>101<br>The equivalence hypothesis plays an important role on assessing the differences between the generic drugs and original patented drugs. The two-one-sided test ( TOST) procedure is usually applied to test the equivalence hypothesis based on average of two treatments. When the difference in population between the two treatments is not 0 but still within the equivalence limits, the power function is not symmetric. There is no exact formula to calculate the sample sizes. Hence the approximate formulas are proposed to determine the sample size for the equivalence hypothesis. Consequently the sample sizes may provide either insufficient power or unnecessarily high power. Geometric approach to the sample size determination for the equivalence hypothesis has been proposed. However , it requires a complicated iterative procedure. In this thesis, we suggest an iterative method in conjunction of the ideal of multiple co-primary endpoints sample size method for determination of the sample size for equivalence hypothesis. A numerical study was conducted to compare the performance of our proposed method with the current methods. Numerical examples are used to illustrate the applications to bioequivalence on the logarithmic scale and to clinical equivalence on the original scale.
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Lin, Yun-Hsuan, and 林耘亘. "A Study on an Exact Method for the Sample Size Determination in Equivalence Test." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/fa2hnq.
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碩士<br>國立臺灣大學<br>農藝學研究所<br>105<br>The equivalence test is a hypothesis to confirm whether the new test product conforms to the standard reference product. It has many applications such as evaluation of GMO crop and its conventional crop, or generic drugs and their innovative drugs. The equivalence hypothesis can be decomposed into the non-inferiority (NI) and non-superiority (NS) hypothesis. The two one-sided tests (TOST) procedure is usually proposed to test the difference between two treatments. When the difference in population means between two treatments is not 0 but within the equivalence limits, the proportion of the type II error rate allocated to each of the two tails of the central t-distribution cannot be analytically determined. Hence, no close form of the exact sample size for the equivalence hypothesis is available.
Current methods provide the sample sizes by assuming the sample standard deviation as a constant. In fact, the lower and upper limits for the power calculation contains s, which is a random variable. By integrating the probability density function of s, the power can be computed. We suggest a method with consideration of type II error rates for both one-sided hypotheses to determine the sample size for the equivalence hypothesis, by treating the sample standard deviation as a random variable.
In addition, the covariance matrix of multiple responses was transformed by orthogonal diagonalization. We obtained a new distribution in which multiple responses are independent of each other. Consequently, we apply the proposed method to the determination of the sample size for multiple responses. Numerical examples illustrate the applications of the proposed method.
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Chiang, Chieh, and 姜杰. "A Study on Sample Size Determination for Evaluating Within-Device Precision, Heritability, and Bioequivalence Based on Modified Large-Sample Method." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/69389568825164889986.
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博士<br>國立臺灣大學<br>農藝學研究所<br>103<br>Statistical criteria for evaluation of precision or variation often involve functions of the second moments of the normal distribution. Under the two-stage nested random-effects model, heritability is defined as the ratio of genetic variance to the total variance. Under replicated crossover designs, the criteria for individual bioequivalence (IBE) proposed by the guidance of the US Food and Drug Administration (FDA) contain the squared mean difference, variance of treatment-by-subject interaction, and the difference in within-subject variances between the generic and innovative products. On the other hand, the criterion for evaluation of the within precision for in-vitro diagnostic devices (IVD) is the sum of the variance components due to day, run, and replicates. The criterion for the in-vitro population bioequivalence (PBE) proposed by the draft guidance of the US FDA consists of the squared mean difference, the sum of the differences in variance components due to batch, sample, and life-stage. These criteria can be reformulated as linear combinations of variance components under the logarithmic transformation. The one-sided confidence limits for the linearized criteria derived by the modified large sample (MLS) method have been proposed as the test statistics for the inference in different applications. However, due to complexity of the power function, the literature for the sample size determination for the inference based on the second moments is scarce. We proved that the distribution of the one-sided confidence bound of the linearized criterion is asymptotically normal. Hence the asymptotic power can be derived for sample size determination with different applications to within-device precision, heritability, IBE and in-vitro PBE. Simulation studies were conducted to investigate the impact of magnitudes of means differences and variance components on sample sizes. In addition, empirical powers obtained from simulation studies are compared with the asymptotic powers to examine whether the sample sizes determined by our proposed methods can provide sufficient power. The proposed methods are illustrated with real data for practical applications. Discussion, final remarks and future research are also presented.
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Yu, Ting-Wan, and 余亭琬. "Data Analysis and Determination of Sample Size for the Dye-Swap Two-Color Spotted Microarray Experiments." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/99503312928143480675.
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碩士<br>國立臺灣大學<br>農藝學研究所<br>92<br>Microarray technology is a powerful tool to detect the expression level of many thousands of genes. However there are many sources of systematic variation which may bias the estimation of the gene expression. Hence how to remove the systematic variation and estimate the gene expression correctly are important topics in the micr- oarray experiment.
In this study, we focus on the dye-swap two-color DNA spotted microarray experiments. We try to analyze the data collected from this kind of microarray experiments by some log-ratio models, which can be classified as one-stage log-ratio models and two-stage log-ratio models. In one-stage log- ratio models, we assume the variances of the gene expression for different genes are homogenous. However most genes in microarray experiments are not significantly expressed, hence the estimate of this unique variance may be actually smaller than the true values for the rest significant genes. Consider the two-stage log-ratio models, the first part of the two-stage log-ratio models can be regarded as a global normalization model and the second part is a gene-specific model. Moreover the gene-specific model can be regarded as gene-by-gene models or mixture probability density function models under different assumptions. The variances of the gene expression are assumed to be different in the gene-bye-gene models, leading to that every gene has it own model. Mixture probability density function models regard genes in microarray experiments as significantly expressed genes and non-significantly expressed genes, each population has its own probability density function. The Student’s t statistic is used in one stage log-ratio models to identify differentially expressed genes. Similarly, Sg statistic proposed by Efron et al. (2001) is used in two-stage gene-by-gene models. In mixture probability density function models, differentially expressed genes are determined by the posterior odds which is a kind of Bayesian approach.
Finally, we consider the sample size based on the one-stage log-ratio models and the gene-by-gene models, respectively.
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Wu, Shu-Yu, and 吳書宇. "The Study of Sample Size Determination for Lower Confidence Limits for Estimating Multiple Product Characteristics Process Capability Indices." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/60773212374484460054.
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碩士<br>國立雲林科技大學<br>工業工程與管理研究所碩士班<br>90<br>The conventional process capability indices, such as Cp, Cpk, Cpm, have been proved as a useful tool to evaluate the process performance. Because the product complexity has been increased recently, the process capability analysis for process with multiple product characteristics becomes important. Some multivariate process capability indices have been developed for this purpose under the assumption of multivariate normal distribution. However, all these process capability indices are point estimators and will be affected by sampling errors. In order to resolve this problem, researchers have proposed the confidence interval for those process capability indices. In this paper, the sample number will be calculated under the condition of certain a risk, the fixed ratio of lower confidence interval and the value of the process indices MCp or the process indices MCpm. The tables of sample number for numerous a risk, the fixed ratio of lower confidence interval and the value of the process indices MCp or the process indices MCpm, and number of product characteristics are generated for the use of practicioners.
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Liu, Hsin-Yun, and 劉心筠. "Determination of Sufficient Sample Sizes in SEMvia ML-based Test Statistics." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/94366814442094351431.
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博士<br>國立臺灣大學<br>心理學研究所<br>99<br>The statistical theory of structural equation modeling (SEM) is based on large sample theory. Thus, determining a sufficient sample size is an important issue for application of the method. The commonly adopted approaches to the issue include absolute sample size, ratio of sample size to number of parameters, and power analysis via RMSEA (root mean squared error of approximation). Yet, there have been no comparative studies of these three approaches and no consensus concerning the optimal sample size determination with SEM has been reached. The present Monte Carlo study is designed to explore the appropriateness of the sample sizes suggested by these three approaches by examining the performance of maximum likelihood-based test statistics and fit indices. Distributions of variables, sample sizes, models of various sizes, and factor loadings were systematically manipulated. For variables of normal distribution, results showed that absolute minimum sample size and sample size suggested by power analysis via RMSEA were insufficient against large models (operationally defined by the number of estimated parameters). This, therefore, implicitly highlights the importance of considering sample size in relation to the number of parameters estimated (q). The findings suggested that N:q ≧ 10 seemed a plausible rule of thumb for sample size determination in SEM. For slightly nonnormally-distributed data, the results suggested that N:q ≧ 10 might also be a plausible rule of thumb. Moreover, the optimal N:q ratios needed to be larger in order to yield trustworthy test statistics as the degree of non-normality in the data increased. In addition, the behavior of fit indices could be considered acceptable with N:q ≧ 5, even for non-normally distributed variables.
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Wang, Hsien-Cheng, and 王獻正. "On Some Determinations of the Critical Values and Optimal Sample Sizes for the Process Capability Indices Cpm and Cpp." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/43876756311350292145.
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碩士<br>淡江大學<br>統計學系<br>90<br>In recent years, process capability indices (PCI’s) have been applied in the quality control by most practitioners, that are used to assess the ability of a production process whether is capable. However, these practitioners usually simply look at the value if the estimates calculate from the sample data and then make a conclusion on whether the given process meets the capability requirement. This approach is not appropriate, since sampling errors have been ignored and estimates of process indices are point estimates. However, a more appropriate estimate would be provided by a confidence interval. Therefore, estimates can be obtained by constructing the confidence interval.
In this paper, we use the approach of the non-central chi-square distribution, and the approximations that Patniak(1949), Zar(1978) and Wilson-Hilferty(1931) proposed. Under the condition of Alpa-risk and power, we apply interval estimation to derive the minimum critical values of the process indices Cpm and the maximum critical values of the process indices Cpp, and we also can determine the optimal sample sizes, respectively.
In most case, both mean and standard deviation are unknown. Therefore, in this paper, we use the range method and apply interval estimation to derive the minimum critical values of the process indices Cpm and the maximum critical values of the process indices Cpp, and we can determine the p-value, respectively. For this reason, the process is considered capable in connection with the test of hypothesis approach, to assess the process capability are more reliable.