共查询到20条相似文献，搜索用时 0 毫秒
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Li J Nordheim EV Zhang C Lehner CE 《Biometrical journal. Biometrische Zeitschrift》2008,50(1):110-122
The problem of finding confidence regions for multiple predictor variables corresponding to given expected values of a response variable has not been adequately resolved. Motivated by an example from a study on hyperbaric exposure using a logistic regression model, we develop a conceptual framework for the estimation of the multi-dimensional effective dose for binary outcomes. The k -dimensional effective dose can be determined by conditioning on k - 1 components and solving for the last component as a conditional univariate effective dose. We consider various approaches for calculating confidence regions for the multi-dimensional effective dose and compare them via a simulation study for a range of possible designs. We analyze data related to decompression sickness to illustrate our procedure. Our results provide a practical approach to finding confidence regions for predictor variables for a given response value. 相似文献
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There are many situations where it is desired to make simultaneous tests or give simultaneous confidence intervals for linear combinations (contrasts) of population or treatment means. Somerville (1997, 1999) developed algorithms for calculating the critical values for a large class of simultaneous tests and simultaneous confidence intervals. Fortran 90 and SAS‐IML batch programs and interactive programs were developed. These programs calculate the critical values for 15 different simultaneous confidence interval procedures (and the corresponding simultaneous tests) and for arbitrary procedures where the user specifies a combination of one and two sided contrasts. The programs can also be used to obtain the constants for “step‐down” testing of multiple hypotheses. This paper gives examples of the use of the algorithms and programs and illustrates their versatility and generality. The designs need not be balanced, multiple covariates may be present and there may be many missing values. The use of multiple regression and dummy variables to obtain the required variance covariance matrix is illustrated. Under weak normality assumptions the methods are “exact” and make the use of approximate methods or “simulation” unnecessary. 相似文献
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In the case of model I of linear regression there is derived a confidence interval for that xo where the “true line” will reach a given value yo. The interval can be given by the intersections between the line y = yo and the hyperbolas providing pointwise confidence intervals of the expectations of y. 相似文献
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John D. Spurrier 《Biometrical journal. Biometrische Zeitschrift》2002,44(7):801-812
The problem of finding exact simultaneous confidence bounds for differences in regression models for k groups via the union‐intersection method is considered. The error terms are taken to be iid normal random variables. Under an assumption slightly more general than having identical design matrices for each of the k groups, it is shown that an existing probability point for the multivariate studentized range can be used to find the necessary probability point for pairwise comparisons of regression models. The resulting methods can be used with simple or multiple regression. Under a weaker assumption on the k design matrices that allows more observations to be taken from the control group than from the k‐1 treatment groups, a method is developed for computing exact probability points for comparing the simple linear regression models of the k‐1 groups to that of the control. Within a class of designs, the optimal design for comparisons with a control takes the square root of (k‐1) times as many observations from the control than from each treatment group. The simultaneous confidence bounds for all pairwise differences and for comparisons with a control are much narrower than Spurrier's intervals for all contrasts of k regression lines. 相似文献
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This paper provides asymptotic simultaneous confidence intervals for a success probability and intraclass correlation of the beta‐binomial model, based on the maximum likelihood estimator approach. The coverage probabilities of those intervals are evaluated. An application to screening mammography is presented as an example. The individual and simultaneous confidence intervals for sensitivity and specificity and the corresponding intraclass correlations are investigated. Two additional examples using influenza data and sex ratio data among sibships are also considered, where the individual and simultaneous confidence intervals are provided. 相似文献
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Summary . Capture–recapture methods are widely adopted to estimate sizes of populations of public health interest using information from surveillance systems. For a two-list surveillance system with a discrete covariate, a population is divided into several subpopulations. A unified framework is proposed in which the logits of presence probabilities are decomposed into case effects and list effects. The estimators for the whole population and subpopulation sizes, their adjusted versions, and asymptotic standard errors admit closed-form expressions. Asymptotic and bootstrap individual and simultaneous confidence intervals are easily constructed. Conditional likelihood ratio tests are used to select one from three possible models. Real examples are investigated. 相似文献
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Michael Daniel Lucagbo Thomas Mathew 《Biometrical journal. Biometrische Zeitschrift》2023,65(3):2100180
Reference intervals are widely used in the interpretation of results of biochemical and physiological tests of patients. When there are multiple biochemical analytes measured from each subject, a multivariate reference region is needed. Because of their greater specificity against false positives, such reference regions are more desirable than separate univariate reference intervals that disregard the cross-correlations between variables. Traditionally, under multivariate normality, reference regions have been constructed as ellipsoidal regions. This approach suffers from a major drawback: it cannot detect component-wise extreme observations. In the present work, procedures are developed to construct rectangular reference regions in the multivariate normal setup. The construction is based on the criteria for tolerance intervals. The problems addressed include the computation of a rectangular tolerance region and simultaneous tolerance intervals. Also addressed is the computation of mixed reference intervals that include both two-sided and one-sided limits, simultaneously. A parametric bootstrap approach is used in the computations, and the accuracy of the proposed methodology is assessed using estimated coverage probabilities. The problem of sample size determination is also addressed, and the results are illustrated using examples that call for the computation of reference regions. 相似文献
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Jiayang Sun 《Biometrical journal. Biometrische Zeitschrift》2001,43(5):627-643
When there are many parameters of interest (finitely large or infinite), standard multiple comparison procedures for a finite number of parameters (called discrete‐domain approaches) may lead to a simultaneous confidence region (SCR) too conservative to be useful. Such cases often arise in locating disease genes, detecting changes in image data and examining shapes and patterns in growth curves; or generally, in quantifying uncertainty in an estimate of a regression function (as one entity). In these cases, procedures designed for a continuous domain must be used. Scheffe's method is a classical example of continuous‐domain approaches. It provides an SCR for a regression function when errors are iid Gaussian and the predictor space is unconstrained, i.e. the domain of interest is the q dimensional Euclidean space. In practice, however, functions defined on finite intervals or other constrained domains are often of interest and data may not be Gaussian. Thus, Scheffe's SCR becomes either too conservative or inadequate. In this paper, we introduce and survey a modern‐type continuous‐domain approach, and explore a connection between some discrete‐ and continuous‐domain multiple comparison procedures. We show that, in some cases, even for a small number of parameters, it is still better to use a continuous‐domain multiple comparison procedure. The main ideas behind the continuous‐domain procedures are shown. A new procedure for comparing a finite number of contrasts about k regression curves is developed. Relevant software is provided. 相似文献
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This paper proposes a general approach for handling multiple contrast tests for normally distributed data in the presence of heteroscedasticity. Three candidate procedures are described and compared by simulations. Only the procedure with both comparison-specific degrees of freedom and a correlation matrix depending on sample variances maintains the alpha-level over all situations. Other approaches may fail notably as the variances differ more. Furthermore, related approximate simultaneous confidence intervals are given. The approach will be applied to a toxicological experiment. 相似文献
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Summary Suppose that we are interested in making joint inferences about a set of constrained parameters. Confidence regions for these parameters are often constructed via a normal approximation of the distribution of a consistent estimator for a transformation of the parameters. In this article, we utilize the confidence distribution, a frequentist counterpart to the posterior distribution in Bayesian statistics, to obtain optimal confidence regions for the parameters. Members of such a region can be generated efficiently via a standard Markov chain Monte Carlo algorithm. We then apply this technique to draw inferences about the temporal profile of the survival function with censored observations. We illustrate the new proposal with the survival data from the well‐known Mayo primary biliary cirrhosis study and show that the volume of the new 0.95 confidence region is only one thirty‐fourth of that of the conventional confidence band. 相似文献
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Paul Somerville Tetsuhisa Miwa Wei Liu Anthony Hayter 《Biometrical journal. Biometrische Zeitschrift》2001,43(5):533-542
Lee and Spurrier (1995) present one‐sided and two‐sided confidence interval procedures for making successive comparisons between ordered treatments. Their procedures have important applications for problems where the treatments can be assumed to satisfy a simple ordering, such as for a sequence of increasing dose‐levels of a drug. The two‐sided procedure provides both upper and lower bounds on the differences between successive treatments, whereas the one‐sided procedure only provides lower bounds on these differences. However, the one‐sided procedure allows sharper inferences regarding which treatments can be declared to be better than their previous ones. In this paper we apply the results obtained in Hayter , Miwa , and Liu (2000) to develop a new procedure which combines the good aspects of both the one‐sided and the two‐sided procedures. This new procedure maintains the inferential sensitivity of the one‐sided procedure while also providing both upper and lower bounds on the differences between successive treatments. Some new critical points are needed which are tabulated for the balanced case where the sample sizes are all equal. The application of the new procedure is illustrated with an example. 相似文献
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Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describe simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth of the results. For the analyses we use the R add-on package multcomp, which provides a convenient interface to the general approach adopted here. 相似文献
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Summary . Functional principal component regression (FPCR) is a promising new method for regressing scalar outcomes on functional predictors. In this article, we present a theoretical justification for the use of principal components in functional regression. FPCR is then extended in two directions: from linear to the generalized linear modeling, and from univariate signal predictors to high-resolution image predictors. We show how to implement the method efficiently by adapting generalized additive model technology to the functional regression context. A technique is proposed for estimating simultaneous confidence bands for the coefficient function; in the neuroimaging setting, this yields a novel means to identify brain regions that are associated with a clinical outcome. A new application of likelihood ratio testing is described for assessing the null hypothesis of a constant coefficient function. The performance of the methodology is illustrated via simulations and real data analyses with positron emission tomography images as predictors. 相似文献
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J. B. Smaers F. J. Rohlf 《Evolution; international journal of organic evolution》2016,70(5):1145-1149