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Showing papers on "Coverage probability published in 2007"


Journal ArticleDOI
TL;DR: A large simulation study of other influences on confidence interval coverage, type I error, relative bias, and other model performance measures found a range of circumstances in which coverage and bias were within acceptable levels despite less than 10 EPV.
Abstract: The rule of thumb that logistic and Cox models should be used with a minimum of 10 outcome events per predictor variable (EPV), based on two simulation studies, may be too conservative. The authors conducted a large simulation study of other influences on confidence interval coverage, type I error, relative bias, and other model performance measures. They found a range of circumstances in which coverage and bias were within acceptable levels despite less than 10 EPV, as well as other factors that were as influential as or more influential than EPV. They conclude that this rule can be relaxed, in particular for sensitivity analyses undertaken to demonstrate adequate control of confounding.

2,943 citations


Journal ArticleDOI
TL;DR: In this paper, the authors provide theoretical justification for some existing methods for constructing confidence intervals for the sum of coefficients in autoregressive models, and generalize the three valid methods to a larger class of statistics.
Abstract: The purpose of this paper is to provide theoretical justification for some existing methods for constructing confidence intervals for the sum of coefficients in autoregressive models. We show that the methods of Stock (1991), Andrews (1993), and Hansen (1999) provide asymptotically valid confidence intervals, whereas the subsampling method of Romano and Wolf (2001) does not. In addition, we generalize the three valid methods to a larger class of statistics. We also clarify the difference between uniform and pointwise asymptotic approximations, and show that a pointwise convergence of coverage probabilities for all values of the parameter does not guarantee the validity of the confidence set.

191 citations


Journal ArticleDOI
TL;DR: The results indicate that credible intervals will have approximately nominal coverage probability, on average, when the prior distribution used for sensitivity analysis approximates the sampling distribution of model parameters in a hypothetical sequence of observational studies.
Abstract: We consider Bayesian sensitivity analysis for unmeasured confounding in observational studies where the association between a binary exposure, binary response, measured confounders and a single binary unmeasured confounder can be formulated using logistic regression models. A model for unmeasured confounding is presented along with a family of prior distributions that model beliefs about a possible unknown unmeasured confounder. Simulation from the posterior distribution is accomplished using Markov chain Monte Carlo. Because the model for unmeasured confounding is not identifiable, standard large-sample theory for Bayesian analysis is not applicable. Consequently, the impact of different choices of prior distributions on the coverage probability of credible intervals is unknown. Using simulations, we investigate the coverage probability when averaged with respect to various distributions over the parameter space. The results indicate that credible intervals will have approximately nominal coverage probability, on average, when the prior distribution used for sensitivity analysis approximates the sampling distribution of model parameters in a hypothetical sequence of observational studies. We motivate the method in a study of the effectiveness of beta blocker therapy for treatment of heart failure.

172 citations


Journal ArticleDOI
TL;DR: In this paper, a test statistic is proposed for the existence of structural breaks in trends in mean non-stationary models, and simultaneous confidence bands with asymptotically correct nominal coverage probabilities are constructed.
Abstract: Summary. We consider statistical inference of trends in mean non-stationary models. A test statistic is proposed for the existence of structural breaks in trends. On the basis of a strong invariance principle of stationary processes, we construct simultaneous confidence bands with asymptotically correct nominal coverage probabilities. The results are applied to global warming temperature data and Nile river flow data. Our confidence band of the trend of the global warming temperature series supports the claim that the trend is increasing over the last 150 years.

166 citations


Journal ArticleDOI
TL;DR: This work presents approaches for estimating confidence intervals for the Youden index and corresponding optimal cut-point for normally distributed biomarkers and also those following gamma distributions, and provides confidence intervals using various bootstrapping methods.
Abstract: A global measure of biomarker effectiveness is the Youden index, the maximum difference between sensitivity, the probability of correctly classifying diseased individuals, and 1-specificity, the probability of incorrectly classifying healthy individuals. The cut-point leading to the index is the optimal cut-point when equal weight is given to sensitivity and specificity. Using the delta method, we present approaches for estimating confidence intervals for the Youden index and corresponding optimal cut-point for normally distributed biomarkers and also those following gamma distributions. We also provide confidence intervals using various bootstrapping methods. A comparison of interval width and coverage probability is conducted through simulation over a variety of parametric situations. Confidence intervals via delta method are shown to have both closer to nominal coverage and shorter interval widths than confidence intervals from the bootstrapping methods.

97 citations


Journal ArticleDOI
15 Mar 2007-Metrika
TL;DR: In this article, the problem of hypothesis testing and interval estimation of the reliability parameter in a stress-strength model involving two-parameter exponential distributions is considered, and a generalized variable approach is proposed.
Abstract: The problem of hypothesis testing and interval estimation of the reliability parameter in a stress–strength model involving two-parameter exponential distributions is considered. Test and interval estimation procedures based on the generalized variable approach are given. Statistical properties of the generalized variable approach and an asymptotic method are evaluated by Monte Carlo simulation. Simulation studies show that the proposed generalized variable approach is satisfactory for practical applications while the asymptotic approach is not satisfactory even for large samples. The results are illustrated using simulated data.

89 citations


Journal ArticleDOI
TL;DR: In this article, a new data-driven bandwidth selector is proposed based on heuristic arguments, which aims at minimizing the maximal deviation (L∞-distance) between and the estimator.
Abstract: Summary. Uniform confidence bands for densities f via non-parametric kernel estimates were first constructed by Bickel and Rosenblatt. In this paper this is extended to confidence bands in the deconvolution problem g=f*ψ for an ordinary smooth error density ψ. Under certain regularity conditions, we obtain asymptotic uniform confidence bands based on the asymptotic distribution of the maximal deviation (L∞-distance) between a deconvolution kernel estimator and f. Further consistency of the simple non-parametric bootstrap is proved. For our theoretical developments the bias is simply corrected by choosing an undersmoothing bandwidth. For practical purposes we propose a new data-driven bandwidth selector that is based on heuristic arguments, which aims at minimizing the L∞-distance between and f. Although not constructed explicitly to undersmooth the estimator, a simulation study reveals that the bandwidth selector suggested performs well in finite samples, in terms of both area and coverage probability of the resulting confidence bands. Finally the methodology is applied to measurements of the metallicity of local F and G dwarf stars. Our results confirm the ‘G dwarf problem’, i.e. the lack of metal poor G dwarfs relative to predictions from ‘closed box models’ of stellar formation.

59 citations


Journal ArticleDOI
TL;DR: A simple bias-reduction method is proposed to reduce the bias of the maximum likelihood estimators of a two-parameter Birnbaum-Saunders distribution using a Monte Carlo EM-algorithm.

53 citations


Journal ArticleDOI
TL;DR: Simulation studies demonstrate that the proposed approach can provide confidence intervals with satisfying coverage probabilities and can perform hypothesis testing with satisfying type-I error control even at small sample sizes, superior to the large sample approach.
Abstract: This paper proposes a novel approach for the confidence interval estimation and hypothesis testing of the common mean of several log-normal populations using the concept of generalized variable. Simulation studies demonstrate that the proposed approach can provide confidence intervals with satisfying coverage probabilities and can perform hypothesis testing with satisfying type-I error control even at small sample sizes. Overall, it is superior to the large sample approach. The proposed method is illustrated using two examples.

50 citations


Journal ArticleDOI
TL;DR: In this article, a generalized confidence region is derived using the concepts of generalized method based on the generalized p-value for the common mean vector of several multivariate normal populations when the covariance matrices are unknown and possibly unequal.

44 citations


Journal ArticleDOI
TL;DR: Some interesting relations between the exact test and the score test for a binomial proportion p are pointed out and approximate as well as exact methods of computing sample sizes required for the tests to attain a specified power are proposed.
Abstract: In this article, we point out some interesting relations between the exact test and the score test for a binomial proportion p. Based on the properties of the tests, we propose some approximate as well as exact methods of computing sample sizes required for the tests to attain a specified power. Sample sizes required for the tests are tabulated for various values of p to attain a power of 0.80 at level 0.05. We also propose approximate and exact methods of computing sample sizes needed to construct confidence intervals with a given precision. Using the proposed exact methods, sample sizes required to construct 95% confidence intervals with various precisions are tabulated for p = .05(.05).5. The approximate methods for computing sample sizes for score confidence intervals are very satisfactory and the results coincide with those of the exact methods for many cases.

Journal ArticleDOI
TL;DR: It is shown how the principle of preserving the null conditional rejection probability of the remainder of the trial at the time of each adaptive change may be extended to construct one-sided confidence intervals by applying the idea to a sequence of dual tests derived from the repeated confidence intervals (RCIs) proposed by Jennison and Turnbull.
Abstract: This paper proposes a method for computing conservative confidence intervals for a group sequential test in which an adaptive design change is made one or more times over the course of the trial. The key idea, due to Muller and Schafer (Biometrics 2001; 57:886-891), is that by preserving the null conditional rejection probability of the remainder of the trial at the time of each adaptive change, the overall type I error rate, taken unconditionally over all possible design modifications, is also preserved. We show how this principle may be extended to construct one-sided confidence intervals by applying the idea to a sequence of dual tests derived from the repeated confidence intervals (RCIs) proposed by Jennison and Turnbull (J. Roy. Statist. Soc. B 1989; 51:301-361). These adaptive RCIs, such as their classical counterparts, have the advantage that they preserve the desired coverage probability even if the pre-specified stopping rule is over-ruled. The statistical methodology is explored by simulations and is illustrated by an application to a clinical trial of deep brain stimulation for Parkinson's disease.

Journal ArticleDOI
TL;DR: In this article, the authors proposed two alternative confidence intervals, namely, Median t and Mad t, which are simple adjustments to the Student's t confidence interval, in order to compare the performance of these intervals, the following criteria are considered: (i) coverage probability; (ii) average width; and (iii) ratio of coverage to width.
Abstract: A number of methods are available in the literature to measure confidence intervals. Here, confidence intervals for estimating the population mean of a skewed distribution are considered. This note proposes two alternative confidence intervals, namely, Median t and Mad t, which are simple adjustments to the Student's t confidence interval. In order to compare the performance of these intervals, the following criteria are considered: (i) coverage probability; (ii) average width; and (iii) ratio of coverage to width. A simulation study has been undertaken to compare the performance of the intervals. The simulation study shows that for small sample size and moderate to highly skewed distributions, the proposed Median t performs the best in the sense of higher coverage, and the Mad t performs best in the sense of smaller confidence width. The proposed methods are very easy to calculate and are not overly computer-intensive, like Bootstrap confidence intervals. Some real-life examples have been considered that...

Journal ArticleDOI
TL;DR: In this article, a progressive Type-II right censored sample from Pareto distribution is considered and exact confidence region is derived for the parameters of the corresponding distribution under progressive censoring.
Abstract: In this article, progressive Type-II right censored sample from Pareto distribution is considered. Exact confidence region is derived for the parameters of the corresponding distribution under progressive censoring. Simulation study is performed to investigate the coverage probabilities of the proposed confidence region. Illustrative example is also given.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the coverage probability of an asymptotic and percentile bootstrap confidence interval with respect to the squared multiple correlation coefficient (Δρ2) associated with a variable in a regression equation.
Abstract: The increase in the squared multiple correlation coefficient (ΔR 2) associated with a variable in a regression equation is a commonly used measure of importance in regression analysis. The coverage probability that an asymptotic and percentile bootstrap confidence interval includes Δρ2 was investigated. As expected, coverage probability for the asymptotic confidence interval was often inadequate (outside the interval .925 to .975 for a 95% confidence interval), even when sample size was quite large (i.e., 200). However, adequate coverage probability for the confidence interval based on a bootstrap interval could typically be obtained with a sample size of 200 or less, and moreover, this accuracy was obtained with relatively small sample sizes (100 or less) with six or fewer predictors.

Journal ArticleDOI
TL;DR: For the assessment of agreement using probability criteria, the authors obtained an exact test, and for sample sizes exceeding 30, they gave a bootstrap-t test that is remarkably accurate, and illustrate their methodology with a real data set from the literature.

Journal Article
TL;DR: For the assessment of agreement using probability criteria, this paper obtained an exact test, and for sample sizes exceeding 30, they gave a bootstrap-t test that is remarkably accurate, and illustrate their methodology with a real data set from the literature.
Abstract: For the assessment of agreement using probability criteria, we obtain an exact test, and for sample sizes exceeding 30, we give a bootstrap- t test that is remarkably accurate. We show that for assessing agreement, the total deviation index approach of Lin [2000. Total deviation index for measuring individual agreement with applications in laboratory performance and bioequivalence. Statist. Med. 19, 255–270] is not consistent and may not preserve its asymptotic nominal level, and that the coverage probability approach of Lin et al. [2002. Statistical methods in assessing agreement: models, issues and tools. J. Amer. Statist. Assoc. 97, 257–270] is overly conservative for moderate sample sizes. We also show that the nearly unbiased test of Wang and Hwang [2001. A nearly unbiased test for individual bioequivalence problems using probability criteria. J. Statist. Plann. Inference 99, 41–58] may be liberal for large sample sizes, and suggest a minor modification that gives numerically equivalent approximation to the exact test for sample sizes 30 or less. We present a simple and accurate sample size formula for planning studies on assessing agreement, and illustrate our methodology with a real data set from the literature.

Journal ArticleDOI
TL;DR: This work constructs exact and optimal one-sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well-established optimality theory of Buehler.
Abstract: We construct exact and optimal one-sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well-established optimality theory of Buehler. Starting with five different approximate lower and upper limits, we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size. Exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use.

Journal Article
TL;DR: In this article, a methodology to compute the exact condence coecien t is proposed, where the point where the inm um of the coverage probabilities occurs, as well as the condence coefficient is precisely derived.
Abstract: Let X have a binomial distribution B(n; p). For a condence interval (L(X); U(X)) of a binomial proportion p, the coverage probability is a variable function of p. The condence coecien t of the condence interval is the inm um of the coverage probabilities, inf0 p 1 Pp(p 2 (L(X); U(X))). Usually, the exact condence coecien t is unknown since the inm um of the coverage probabilities may occur at any point p 2 (0; 1). In this paper, a methodology to compute the exact condence coecien t is proposed. With this methodology, the point where the inm um of the coverage probabilities occurs, as well as the condence coecien t, can be precisely derived.

Journal ArticleDOI
TL;DR: Concerning efficiency (required sample sizes) and robustness against the statistical anomalies commonly encountered in simulation studies, WASSP outperformed the Heidelberger-Welch procedure and compared favorably with ASAP3.
Abstract: A summary and an analysis are given for an experimental performance evaluation of WASSP, an automated wavelet-based spectral method for constructing an approximate confidence interval on the steady-state mean of a simulation output process such that the delivered confidence interval satisfies user-specified requirements on absolute or relative precision as well as coverage probability. The experimentation involved three difficult test problems, each with an output process exhibiting some combination of the following characteristics: a long warm-up period, a persistent autocorrelation structure, or a highly nonnormal marginal distribution. These problems were used to compare the performance of WASSP with that of the Heidelberger-Welch algorithm and ASAP3, two sequential procedures based respectively on the methods of spectral analysis and nonoverlapping batch means. Concerning efficiency (required sample sizes) and robustness against the statistical anomalies commonly encountered in simulation studies, WASSP outperformed the Heidelberger-Welch procedure and compared favorably with ASAP3.

Journal ArticleDOI
TL;DR: A novel method of generating a coverage probability matrix, that may be used to determine treatment margins and calculate uncertainties in dose, from this statistical shape model used to model the geometric uncertainties that accrue during the radiotherapy process.
Abstract: In this paper we describe a technique that may be used to model the geometric uncertainties that accrue during the radiotherapy process. Using data from in-treatment cone beam CT scans, we simultaneously analyse non-uniform observer delineation variability and organ motion together with patient set-up errors via the creation of a point distribution model (PDM). We introduce a novel method of generating a coverage probability matrix, that may be used to determine treatment margins and calculate uncertainties in dose, from this statistical shape model. The technique does not assume rigid body motion and can extrapolate shape variability in a statistically meaningful manner. In order to construct the PDM, we generate corresponding surface points over a set of delineations. Correspondences are established at a set of points in parameter space on spherically parameterized and canonical aligned outlines. The method is demonstrated using rectal delineations from serially acquired in-treatment cone beam CT image volumes of a prostate patient (44 image volumes total), each delineated by a minimum of two observers (maximum six). Two PDMs are constructed, one with set-up errors included and one without. We test the normality assumptions of the PDMs and find the distributions to be Gaussian in nature. The rectal PDM variability is in general agreement with data in the literature. The two resultant coverage probability matrices show differences as expected.

Journal ArticleDOI
TL;DR: Omitting an important balanced covariate lowers both coverage probability and study power, implying the need for thoughtful consideration of important covariates at the design as well as the analysis stages of a study.

Journal ArticleDOI
TL;DR: In this paper, a simple small sample corrected interval has been proposed to improve the coverage probability of a log-normal regression mean by replacing the quantile of the normal distribution by the appropriate quantile for Student t distribution.
Abstract: Large samples based confidence interval is frequently used by environmental scientists as an approximate data summary about the log-normal regression mean It has been shown by simulation that the coverage probability of such an interval is below the intended nominal level for small samples To overcome this difficulty, a complicated small sample corrected interval has been recently proposed in the literature which substantially improves the coverage probability In this paper, similar improvement are obtained by simply replacing the quantile of the normal distribution by the appropriate quantile of Student t distribution as will be demonstrated in this paper by simulation The advantage of our proposed interval is its simplicity and thus will be easier to use in applications As an illustration, we use the method to study the relationship between the flow and concentration of total phosphorous (TP) at four upstream/downstream sampling locations on the Fraser River of British Columbia Our interests in developing intervals for the mean TP level at each location as well as the ratio of the mean at a downstream location to that at an upstream location Such study is important in tracing the evolution of pollutants in an ecosystem and thus in setting policies for pollution control Copyright © 2006 John Wiley & Sons, Ltd

Journal ArticleDOI
TL;DR: In this paper, a modified large-sample approach and a generalized confidence interval (GCI) approach are proposed for constructing confidence intervals for intraclass correlation coefficients in a reliability study, where both subjects and raters are assumed to be random effects in a balanced two-factor design, including subject-by-rater interaction.

Journal ArticleDOI
TL;DR: Methods for obtaining estimates of percentiles and their associated confidence intervals when the results are log-normal and a fraction of the results is below the LOD are described.

Posted Content
TL;DR: This paper develops a new approach for computing the minimum sample size that does not require any approximation and overcomes the conservatism of existing rigorous sample size methods derived from Bernoulli's theorem or Chernoff bounds.
Abstract: It is a common contention that it is an ``impossible mission'' to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level. In this paper, we investigate such a very old but also extremely important problem and demonstrate that the difficulty for obtaining the exact solution is not insurmountable. Unlike the classical approximate sample size method based on the central limit theorem, we develop a new approach for computing the minimum sample size that does not require any approximation. Moreover, our approach overcomes the conservatism of existing rigorous sample size methods derived from Bernoulli's theorem or Chernoff bounds. Our computational machinery consists of two essential ingredients. First, we prove that the minimum of coverage probability with respect to a binomial parameter bounded in an interval is attained at a discrete set of finite many values of the binomial parameter. This allows for reducing infinite many evaluations of coverage probability to finite many evaluations. Second, a recursive bounding technique is developed to further improve the efficiency of computation.

Journal ArticleDOI
TL;DR: In this article, it is pointed out that the partial F test has in fact a naturally associated two-sided simultaneous confidence band, which is much more informative than the test itself, and a narrower and hence more efficient confidence band over a restricted region of the covariates should be used.

Journal ArticleDOI
TL;DR: For the one sample binomial confidence interval the Clopper-Pearson exact method has been regarded as definitive as it eliminates both overshoot and zero width intervals as discussed by the authors, and is unquestionably a better alternative to the Wald method Other viable alternatives include Wilson's Score, Agresti-Coull method, and Borkowf SAIFS-z.
Abstract: The construction of a confidence interval for a binomial parameter is a basic analysis in statistical inference Most introductory statistics textbook authors present the binomial confidence interval based on the asymptotic normality of the sample proportion and estimating the standard error - the Wald method For the one sample binomial confidence interval the Clopper-Pearson exact method has been regarded as definitive as it eliminates both overshoot and zero width intervals The Clopper-Pearson exact method is the most conservative and is unquestionably a better alternative to the Wald method Other viable alternatives include Wilson's Score, the Agresti-Coull method, and the Borkowf SAIFS-z

Journal ArticleDOI
TL;DR: In this article, the authors presented a direct adjustment of the estimative prediction limit to reduce the coverage error from a target value to third-order accuracy, which is asymptotically equivalent to those of Barndorff-Nielsen & Cox (1994, 1996) and Vidoni (1998).
Abstract: SUMMARY This note presents a direct adjustment of the estimative prediction limit to reduce the coverage error from a target value to third-order accuracy. The adjustment is asymptotically equivalent to those of Barndorff-Nielsen & Cox (1994, 1996) and Vidoni (1998). It has a simpler form with a plug-in estimator of the coverage probability of the estimative limit at the target value.

Journal ArticleDOI
TL;DR: Wald-type, logarithmic transformation, and Fieller-type statistics for the classical 2-sided equivalence testing of the rate ratio under matched-pair designs with a binary end point are compared.
Abstract: In this article, we compare Wald-type, logarithmic transformation, and Fieller-type statistics for the classical 2-sided equivalence testing of the rate ratio under matched-pair designs with a binary end point These statistics can be implemented through sample-based, constrained least squares estimation and constrained maximum likelihood (CML) estimation methods Sample size formulae based on the CML estimation method are developed We consider formulae that control a prespecified power or confidence width Our simulation studies show that statistics based on the CML estimation method generally outperform other statistics and methods with respect to actual type I error rate and average width of confidence intervals Also, the corresponding sample size formulae are valid asymptotically in the sense that the exact power and actual coverage probability for the estimated sample size are generally close to their prespecified values The methods are illustrated with a real example from a clinical laboratory study