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The direct integral method for confidence intervals for the ratio of two location parameters.

ABSTRACT: In a relative risk analysis of colorectal caner on nutrition intake scores across genders, we show that, surprisingly, when comparing the relative risks for men and women based on the index of a weighted sum of various nutrition scores, the problem reduces to forming a confidence interval for the ratio of two (asymptotically) normal random variables. The latter is an old problem, with a substantial literature. However, our simulation results suggest that existing methods often either give inaccurate coverage probabilities or have a positive probability to produce confidence intervals with infinite length. Motivated by such a problem, we develop a new methodology which we call the Direct Integral Method for Ratios (DIMER), which, unlike the other methods, is based directly on the distribution of the ratio. In simulations, we compare this method to many others. These simulations show that, generally, DIMER more closely achieves the nominal confidence level, and in those cases that the other methods achieve the nominal levels, DIMER has comparable confidence interval lengths. The methodology is then applied to a real data set, and with follow up simulations.

SUBMITTER: Wang Y

PROVIDER: S-EPMC4575252 | biostudies-literature | 2015 Sep

REPOSITORIES: biostudies-literature

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The direct integral method for confidence intervals for the ratio of two location parameters.

Wang Yanqing Y Wang Suojin S Carroll Raymond J RJ

Biometrics 20150501 3

In a relative risk analysis of colorectal caner on nutrition intake scores across genders, we show that, surprisingly, when comparing the relative risks for men and women based on the index of a weighted sum of various nutrition scores, the problem reduces to forming a confidence interval for the ratio of two (asymptotically) normal random variables. The latter is an old problem, with a substantial literature. However, our simulation results suggest that existing methods often either give inaccu ...[more]

PMID: 25939421

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Project description:In the analysis of networks we frequently require the statistical significance of some network statistic, such as measures of similarity for the properties of interacting nodes. The structure of the network may introduce dependencies among the nodes and it will in general be necessary to account for these dependencies in the statistical analysis. To this end we require some form of Null model of the network: generally rewired replicates of the network are generated which preserve only the degree (number of interactions) of each node. We show that this can fail to capture important features of network structure, and may result in unrealistic significance levels, when potentially confounding additional information is available.We present a new network resampling Null model which takes into account the degree sequence as well as available biological annotations. Using gene ontology information as an illustration we show how this information can be accounted for in the resampling approach, and the impact such information has on the assessment of statistical significance of correlations and motif-abundances in the Saccharomyces cerevisiae protein interaction network. An algorithm, GOcardShuffle, is introduced to allow for the efficient construction of an improved Null model for network data.We use the protein interaction network of S. cerevisiae; correlations between the evolutionary rates and expression levels of interacting proteins and their statistical significance were assessed for Null models which condition on different aspects of the available data. The novel GOcardShuffle approach results in a Null model for annotated network data which appears better to describe the properties of real biological networks.An improved statistical approach for the statistical analysis of biological network data, which conditions on the available biological information, leads to qualitatively different results compared to approaches which ignore such annotations. In particular we demonstrate the effects of the biological organization of the network can be sufficient to explain the observed similarity of interacting proteins.

Project description:This work seeks to develop exact confidence interval estimators for figures of merit that describe the performance of linear observers, and to demonstrate how these estimators can be used in the context of x-ray computed tomography (CT). The figures of merit are the receiver operating characteristic (ROC) curve and associated summary measures, such as the area under the ROC curve. Linear computerized observers are valuable for optimization of parameters associated with image reconstruction algorithms and data acquisition geometries. They provide a means to perform assessment of image quality with metrics that account not only for shift-variant resolution and nonstationary noise but that are also task-based.We suppose that a linear observer with fixed template has been defined and focus on the problem of assessing the performance of this observer for the task of deciding if an unknown lesion is present at a specific location. We introduce a point estimator for the observer signal-to-noise ratio (SNR) and identify its sampling distribution. Then, we show that exact confidence intervals can be constructed from this distribution. The sampling distribution of our SNR estimator is identified under the following hypotheses: (i) the observer ratings are normally distributed for each class of images and (ii) the variance of the observer ratings is the same for each class of images. These assumptions are, for example, appropriate in CT for ratings produced by linear observers applied to low-contrast lesion detection tasks.Unlike existing approaches to the estimation of ROC confidence intervals, the new confidence intervals presented here have exactly known coverage probabilities when our data assumptions are satisfied. Furthermore, they are applicable to the most commonly used ROC summary measures, and they may be easily computed (a computer routine is supplied along with this article on the Medical Physics Website). The utility of our exact interval estimators is demonstrated through an image quality evaluation example using real x-ray CT images. Also, strong robustness is shown to potential deviations from the assumption that the ratings for the two classes of images have equal variance. Another aspect of our interval estimators is the fact that we can calculate their mean length exactly for fixed parameter values, which enables precise investigations of sampling effects. We demonstrate this aspect by exploring the potential reduction in statistical variability that can be gained by using additional images from one class, if such images are readily available. We find that when additional images from one class are used for an ROC study, the mean AUC confidence interval length for our estimator can decrease by as much as 35%.We have shown that exact confidence intervals can be constructed for ROC curves and for ROC summary measures associated with fixed linear computerized observers applied to binary discrimination tasks at a known location. Although our intervals only apply under specific conditions, we believe that they form a valuable tool for the important problem of optimizing parameters associated with image reconstruction algorithms and data acquisition geometries, particularly in x-ray CT.

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The direct integral method for confidence intervals for the ratio of two location parameters.

Publications

The direct integral method for confidence intervals for the ratio of two location parameters.

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