Dataset Information

Fast Bootstrap Confidence Intervals for Continuous Threshold Linear Regression.

ABSTRACT: Continuous threshold regression is a common type of nonlinear regression that is attractive to many practitioners for its easy interpretability. More widespread adoption of thresh-old regression faces two challenges: (i) the computational complexity of fitting threshold regression models and (ii) obtaining correct coverage of confidence intervals under model misspecification. Both challenges result from the non-smooth and non-convex nature of the threshold regression model likelihood function. In this paper we first show that these two issues together make the ideal approach for making model-robust inference in continuous threshold linear regression an impractical one. The need for a faster way of fitting continuous threshold linear models motivated us to develop a fast grid search method. The new method, based on the simple yet powerful dynamic programming principle, improves the performance by several orders of magnitude.

SUBMITTER: Fong Y

PROVIDER: S-EPMC6713448 | biostudies-literature | 2019

REPOSITORIES: biostudies-literature

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Publications

Fast Bootstrap Confidence Intervals for Continuous Threshold Linear Regression.

Fong Youyi Y

Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America 20190213 2

Continuous threshold regression is a common type of nonlinear regression that is attractive to many practitioners for its easy interpretability. More widespread adoption of thresh-old regression faces two challenges: (i) the computational complexity of fitting threshold regression models and (ii) obtaining correct coverage of confidence intervals under model misspecification. Both challenges result from the non-smooth and non-convex nature of the threshold regression model likelihood function. I ...[more]

PMID: 31462887

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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.

Dataset Information

Fast Bootstrap Confidence Intervals for Continuous Threshold Linear Regression.

Publications

Fast Bootstrap Confidence Intervals for Continuous Threshold Linear Regression.

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