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Approximating statistical functions by using fractional polynomial regression 用分数多项式回归逼近统计函数
The Statistician : journal of the Institute of Statisticians Pub Date : 1997-09-01 DOI: 10.1111/1467-9884.00093
P. Royston, D. Altman
{"title":"Approximating statistical functions by using fractional polynomial regression","authors":"P. Royston, D. Altman","doi":"10.1111/1467-9884.00093","DOIUrl":"https://doi.org/10.1111/1467-9884.00093","url":null,"abstract":"SUMMARY In statistics it is common to require a simple approximating equation for a smooth relationship between Yand X. The exact mathematical form may be known (but complicated) or unknown. We show that fractional polynomials are particularly good at providing concise and accurate formulae for representing such relationships. We give several examples, including the approximation of the 5% point of a statistic used in the analysis of means and of an unbiasing factor for calculating the standard deviation from a doubly censored normal sample.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"2 1","pages":"411-422"},"PeriodicalIF":0.0,"publicationDate":"1997-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89905654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 93
Power and sample size considerations for detecting deviations from secular trends in surveillance surveys 监测调查中检测偏离长期趋势的功率和样本量考虑
The Statistician : journal of the Institute of Statisticians Pub Date : 1997-09-01 DOI: 10.1111/1467-9884.00094
Philip J. Smith
{"title":"Power and sample size considerations for detecting deviations from secular trends in surveillance surveys","authors":"Philip J. Smith","doi":"10.1111/1467-9884.00094","DOIUrl":"https://doi.org/10.1111/1467-9884.00094","url":null,"abstract":"SUMMARY On-going public health surveillance is essential to the detection and monitoring of epidemics. We present statistical methods for determining the sample size that is required to detect unacceptable deviations from existing secular trends in prevalence with specified power. Between 1958 and 1969, a large study was conducted for providing surveillance of the prevalence of infection for a well-known disease. Data from this study indicated that the prevalence of infection in the mid-1960s increased significantly over previous secular trends among important demographic groups tested. These data are used to illustrate the statistical methods that we propose for detecting departures from existing temporal trends, estimating the year in which the changepoint occurred and specifying sample sizes for on-going active surveillance studies.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"13 1","pages":"423-432"},"PeriodicalIF":0.0,"publicationDate":"1997-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87136135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The asymptotically optimal tests 渐近最优检验
The Statistician : journal of the Institute of Statisticians Pub Date : 1997-09-01 DOI: 10.1111/1467-9884.00087
J. Rayner
{"title":"The asymptotically optimal tests","authors":"J. Rayner","doi":"10.1111/1467-9884.00087","DOIUrl":"https://doi.org/10.1111/1467-9884.00087","url":null,"abstract":"This paper reviews the asymptotically optimal tests: the likelihood ratio, score and Wald tests, with emphasis on the score and Wald tests. These tests are also given after a linear transformation of the parameter space. Use of this approach often simplifies the calculations involved, especially when multiple tests are to be derived.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"46 1","pages":"337-345"},"PeriodicalIF":0.0,"publicationDate":"1997-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77641175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Confidence limits and log‐odds ratios 置信限和对数优势比
The Statistician : journal of the Institute of Statisticians Pub Date : 1997-09-01 DOI: 10.1111/1467-9884.00095
D. E. Walters
{"title":"Confidence limits and log‐odds ratios","authors":"D. E. Walters","doi":"10.1111/1467-9884.00095","DOIUrl":"https://doi.org/10.1111/1467-9884.00095","url":null,"abstract":"A very simple application of Bayes's theorem provides a flexible, adaptable and reliable method of deriving confidence limits for nominated functions of several binomial random variables. Tables of confidence coefficients are presented to illustrate the reliability of the method when the functions represent log-odds ratios.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"65 1","pages":"433-438"},"PeriodicalIF":0.0,"publicationDate":"1997-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79096460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sample size for estimating species lists in vegetation surveys 在植被调查中估计物种列表的样本量
The Statistician : journal of the Institute of Statisticians Pub Date : 1997-07-01 DOI: 10.1111/1467-9884.00081
T. Sparks, J. Mountford, S. Manchester, P. Rothery, J. Treweek
{"title":"Sample size for estimating species lists in vegetation surveys","authors":"T. Sparks, J. Mountford, S. Manchester, P. Rothery, J. Treweek","doi":"10.1111/1467-9884.00081","DOIUrl":"https://doi.org/10.1111/1467-9884.00081","url":null,"abstract":"SUMMARY The vegetation communities of fields, e.g. those of unimproved grassland, can be very complex. Many factors influence the composition of these communities including current and historical management, drainage, soil properties and climate. In the current competitive research environment, vegetation surveys need to be carried out in a cost-effective manner. This paper uses computer simulation to suggest appropriate samples sizes for vegetation surveys in a wide range of conditions.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"19 1","pages":"253-260"},"PeriodicalIF":0.0,"publicationDate":"1997-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73344180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Power and sample size requirements for tests of differences between two Poisson rates 检验两个泊松率之间差异的功率和样本量要求
The Statistician : journal of the Institute of Statisticians Pub Date : 1997-07-01 DOI: 10.1111/1467-9884.00078
H. Thode
{"title":"Power and sample size requirements for tests of differences between two Poisson rates","authors":"H. Thode","doi":"10.1111/1467-9884.00078","DOIUrl":"https://doi.org/10.1111/1467-9884.00078","url":null,"abstract":"SUMMARY The statistic (y-x)/(y + X)1/2 is often used as an approximate test for comparing two Poisson observations. When x and y come from different sized sampling frames, a uniformly most powerful unbiased (UMPU) test is obtained using the binomial distribution of the conditional distribution of y given x + y. Shiue and Bain showed that a test based on the normal approximation of the binomial distribution is nearly as powerful as the UMPU test and presented power and sample size formulae. Here we present an alternative test and show that, when the Poisson rate is greater for the larger sampling frame, it has higher power than the Shiue and Bain test. Power and sample size formulae are given.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"6 1","pages":"227-230"},"PeriodicalIF":0.0,"publicationDate":"1997-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83739714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 25
On some sample size formulae for controlling both size and power in clinical trials 临床试验中控制样本量和功率的一些公式
The Statistician : journal of the Institute of Statisticians Pub Date : 1997-07-01 DOI: 10.1111/1467-9884.00080
Wei Liu
{"title":"On some sample size formulae for controlling both size and power in clinical trials","authors":"Wei Liu","doi":"10.1111/1467-9884.00080","DOIUrl":"https://doi.org/10.1111/1467-9884.00080","url":null,"abstract":"Suppose that observations are taken from a population with normal distribution N(μ, σ 2 ) where both μ and σ 2 are unknown parameters. Our goal is to design a two-sided test of H 0 : μ = 0 against H a : μ ¬= 0 which has, at least approximately, size a and power β at |μ| = d > 0, where a, β and d are three preassigned constants. The classical solution is Stein's two-stage procedure, which tends to oversampling, however. Three new procedures are proposed and studied in this paper. They all have both size and power very close to the target values α and β and require only a few more observations than the necessary sample size to achieve our goal if σ 2 had been completely known.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"2 1","pages":"238-251"},"PeriodicalIF":0.0,"publicationDate":"1997-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85197752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Sample size determination : a review 样本量测定:综述
The Statistician : journal of the Institute of Statisticians Pub Date : 1997-07-01 DOI: 10.1111/1467-9884.00082
C. Adcock
{"title":"Sample size determination : a review","authors":"C. Adcock","doi":"10.1111/1467-9884.00082","DOIUrl":"https://doi.org/10.1111/1467-9884.00082","url":null,"abstract":"This paper is concerned with methods of sample size determination. The approach is to cover a small number of simple problems, such as estimating the mean of a normal distribution or the slope in a regression equation, and to present some key techniques. The methods covered are in two groups: frequentist and Bayesian. Frequentist methods specify a null and alternative hypothesis for the parameter of interest and then find the sample size by controlling both size and power. These methods often need to use prior information but cannot allow for the uncertainty that is associated with it. By contrast, the Bayesian approach offers a wide variety of techniques, all of which offer the ability to deal with uncertainty associated with prior information.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"33 1","pages":"261-283"},"PeriodicalIF":0.0,"publicationDate":"1997-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85447731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 275
Bayesian sample size determination for normal means and differences between normal means 正态均值和正态均值之差的贝叶斯样本量测定
The Statistician : journal of the Institute of Statisticians Pub Date : 1997-07-01 DOI: 10.1111/1467-9884.00077
L. Joseph, P. Belisle
{"title":"Bayesian sample size determination for normal means and differences between normal means","authors":"L. Joseph, P. Belisle","doi":"10.1111/1467-9884.00077","DOIUrl":"https://doi.org/10.1111/1467-9884.00077","url":null,"abstract":"SUMMARY Several criteria for Bayesian sample size determination based on lengths and coverages of posterior credible intervals have recently appeared in the literature. Some but not all of these have been applied to estimating sample sizes for normal distributions. In this paper, these criteria are applied to find sample sizes for single normal means and differences between two normal means, both when the variances are known and when they are unknown. Fully Bayesian approaches as well as mixed Bayesian-likelihood approaches are considered. In the case of the difference between two normal means, situations with equal and unequal variances of the two distributions are considered. In addition to the rule that assumes equally sized groups, optimal solutions are determined which allow the sizes drawn from the two populations to differ while minimizing their sum. Exact closed form solutions are available for many of the situations, whereas numerical algorithms are described for others.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"395 1","pages":"209-226"},"PeriodicalIF":0.0,"publicationDate":"1997-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85013312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 114
Bayesian double‐sampling plans with normal distributions 正态分布的贝叶斯双抽样计划
The Statistician : journal of the Institute of Statisticians Pub Date : 1997-07-01 DOI: 10.1111/1467-9884.00076
L. Yeh, L. Van
{"title":"Bayesian double‐sampling plans with normal distributions","authors":"L. Yeh, L. Van","doi":"10.1111/1467-9884.00076","DOIUrl":"https://doi.org/10.1111/1467-9884.00076","url":null,"abstract":"In this paper, a Bayesian double-variable sampling plan is studied. Assume that the variable measured for each item in a batch has a normal distribution with known variance and unknown mean which has a normal prior distribution. Assume further that the loss function is a polynomial. An explicit expression for the Bayes risk is derived. Then a finite algorithm is suggested for determining an optimal double-sampling plan in a finite number of searching steps. A sensitivity study and a robustness analysis are also conducted.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"62 1","pages":"193-207"},"PeriodicalIF":0.0,"publicationDate":"1997-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81342354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
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