Nonparametric signal detectability evaluation using an exponential transformation of the FROC curve

3D printed phantom with 12 000 submillimeter lesions to improve efficiency in CT detectability assessment

BACKGROUND

The detectability performance of a CT scanner is difficult to precisely quantify when nonlinearities are present in reconstruction. An efficient detectability assessment method that is sensitive to small effects of dose and scanner settings is desirable. We previously proposed a method using a search challenge instrument: a phantom is embedded with hundreds of lesions at random locations, and a model observer is used to detect lesions. Preliminary tests in simulation and a prototype showed promising results.

PURPOSE

In this work, we fabricated a full-size search challenge phantom with design updates, including changes to lesion size, contrast, and number, and studied our implementation by comparing the lesion detectability from a nonprewhitening (NPW) model observer between different reconstructions at different exposure levels, and by estimating the instrument sensitivity to detect changes in dose.

METHODS

Designed to fit into QRM anthropomorphic phantoms, our search challenge phantom is a cylindrical insert 10 cm wide and 4 cm thick, embedded with 12 000 lesions (nominal width of 0.6 mm, height of 0.8 mm, and contrast of -350 HU), and was fabricated using PixelPrint, a 3D printing technique. The insert was scanned alone at a high dose to assess printing accuracy. To evaluate lesion detectability, the insert was placed in a QRM thorax phantom and scanned from 50 to 625 mAs with increments of 25 mAs, once per exposure level, and the average of all exposure levels was used as high-dose reference. Scans were reconstructed with three different settings: filtered-backprojection (FBP) with Br40 and Br59, and Sinogram Affirmed Iterative Reconstruction (SAFIRE) with strength level 5 and Br59 kernel. An NPW model observer was used to search for lesions, and detection performance of different settings were compared using area under the exponential transform of free response ROC curve (AUC). Using propagation of uncertainty, the sensitivity to changes in dose was estimated by the percent change in exposure due to one standard deviation of AUC, measured from 5 repeat scans at 100, 200, 300, and 400 mAs.

RESULTS

The printed insert lesions had an average position error of 0.20 mm compared to printing reference. As the exposure level increases from 50 mAs to 625 mAs, the lesion detectability AUCs increase from 0.38 to 0.92, 0.42 to 0.98, and 0.41 to 0.97 for FBP Br40, FBP Br59, and SAFIRE Br59, respectively, with a lower rate of increase at higher exposure level. FBP Br59 performed best with AUC 0.01 higher than SAFIRE Br59 on average and 0.07 higher than FBP Br40 (all P < 0.001). The standard deviation of AUC was less than 0.006, and the sensitivity to detect changes in mAs was within 2% for FBP Br59.

CONCLUSIONS

Our 3D-printed search challenge phantom with 12 000 submillimeter lesions, together with an NPW model observer, provide an efficient CT detectability assessment method that is sensitive to subtle effects in reconstruction and is sensitive to small changes in dose.

A novel regression method for the analysis of multireader multicase-free-response receiver operating characteristics studies

In diagnostic radiology, the multireader multicase (MRMC) design and the free-response receiver operating characteristics (FROC) method are often used in combination. The cross-correlated data generated by the MRMC-FROC study leads to difficulties in the corresponding analysis, and the need to include covariates in the model further complicates the subsequent analysis. In this paper, we propose a regression approach based on three new measures with good interpretability. The correlation structure of the original test results is taken directly into account in the estimation procedure. The proposed method also allows the inclusion of continuous or discrete covariates. Consistent and asymptotically normal estimators are derived for the new measures. Simulation studies are conducted to evaluate the performance of the proposed approach. The simulation results show that the regression approach performs well under a wide range of scenarios. We also apply the proposed regression approach to a diagnostic study of computer-aided diagnosis in lung cancer.

Rapid measurement of the low contrast detectability of CT scanners

PURPOSE

Low contrast detectability (LCD) is a metric of fundamental importance in computed tomography (CT) imaging. In spite of this, its measurement is challenging in the context of nonlinear data processing. We introduce a new framework for objectively characterizing LCD with a single scan of a special-purpose phantom and automated analysis software. The output of the analysis software is a "machine LCD" metric which is more representative of LCD than contrast-noise ratio (CNR). It is not intended to replace human observer or model observer studies.

METHODS

Following preliminary simulations, we fabricated a phantom containing hundreds of low-contrast beads. These beads are acrylic spheres (1.6 mm, net contrast ~10 HU) suspended and randomly dispersed in a background matrix of nylon pellets and isoattenuating saline. The task was to search for and localize the beads. A modified matched filter was used to automatically scan the reconstruction and select candidate bead localizations of varying confidence. These were compared to bead locations as determined from a high-dose reference scan to produce free-response ROC curves. We compared iterative reconstruction (IR) and filtered backpropagation (FBP) at multiple dose levels between 40 and 240 mAs. The scans at 60, 120, and 180 mAs were performed three times each to estimate uncertainty.

RESULTS

Experimental scans demonstrated the feasibility of our technique. Our metric for machine LCD was the area under the exponential transform of the FROC curve (AUC). AUC increased monotonically from 0.21 at 40 mAs to 0.84 at 240 mAs. The sample standard deviation of AUC was approximately 0.02. This measurement uncertainty in AUC corresponded to a change in tube current of 4% to 8%. Surprisingly, we found that AUCs for IR were slightly worse than AUCs for FBP. While the phantom was sufficient for these experiments, it contained small air bubbles and alternative fabrication methods will be necessary for widespread utilization.

CONCLUSIONS

It is feasible to measure machine LCD using a search task on a phantom with hundreds of beads and to obtain tight error bars using only a single scan. Our method could facilitate routine quality assurance or possibly enable comparisons between different protocols and scanners.

Evaluation of diagnostic accuracy in free-response detection-localization tasks using ROC tools

Diagnostic systems designed to detect possibly multiple lesions per patient (e.g. multiple polyps during CT colonoscopy) are often evaluated in “free-response” studies that allow for diagnostic responses unconstrained in their number and locations. Analysis of free-response studies requires extensions of the traditional receiver operating characteristic (ROC) analysis, which are termed free-response ROC (FROC) methodology. Despite substantial developments in this area, FROC tools and approaches are much more cumbersome than traditional ROC methods. Alternative approaches that use well-known ROC tools (e.g. ROI-ROC) require defining and physically delineating regions of interest (ROI) and combine FROC data within ROIs. We propose an approach that allows analyzing FROC data using conventional ROC tools without delineating the actual ROIs or reducing data. The design parameters of FROC study are used to make FROC data analyzable using ROC tools and to calibrate the corresponding FROC and ROC curves on both conceptual and numerical levels. Differences in the performance indices of the nonparametric FROC and the new approach are shown to be asymptotically negligible and typically rather small in practice. Data from a large multi-reader study of colon cancer detection are used to illustrate the new approach.

The Reproducibility of Changes in Diagnostic Figures of Merit Across Laboratory and Clinical Imaging Reader Studies

RATIONALE AND OBJECTIVES

In this paper we examine which comparisons of reading performance between diagnostic imaging systems made in controlled retrospective laboratory studies may be representative of what we observe in later clinical studies. The change in a meaningful diagnostic figure of merit between two diagnostic modalities should be qualitatively or quantitatively comparable across all kinds of studies.

MATERIALS AND METHODS

In this meta-study we examine the reproducibility of relative measures of sensitivity, false positive fraction (FPF), area under the receiver operating characteristic (ROC) curve, and expected utility across laboratory and observational clinical studies for several different breast imaging modalities, including screen film mammography, digital mammography, breast tomosynthesis, and ultrasound.

RESULTS

Across studies of all types, the changes in the FPFs yielded very small probabilities of having a common mean value. The probabilities of relative sensitivity being the same across ultrasound and tomosynthesis studies were low. No evidence was found for different mean values of relative area under the ROC curve or relative expected utility within any of the study sets.

CONCLUSION

The comparison demonstrates that the ratios of areas under the ROC curve and expected utilities are reproducible across laboratory and clinical studies, whereas sensitivity and FPF are not.

On the meaning of the weighted alternative free-response operating characteristic figure of merit

PURPOSE

The free-response receiver operating characteristic (FROC) method is being increasingly used to evaluate observer performance in search tasks. Data analysis requires definition of a figure of merit (FOM) quantifying performance. While a number of FOMs have been proposed, the recommended one, namely, the weighted alternative FROC (wAFROC) FOM, is not well understood. The aim of this work is to clarify the meaning of this FOM by relating it to the empirical area under a proposed wAFROC curve.

METHODS

The weighted wAFROC FOM is defined in terms of a quasi-Wilcoxon statistic that involves weights, coding the clinical importance, assigned to each lesion. A new wAFROC curve is proposed, the y-axis of which incorporates the weights, giving more credit for marking clinically important lesions, while the x-axis is identical to that of the AFROC curve. An expression is derived relating the area under the empirical wAFROC curve to the wAFROC FOM. Examples are presented with small numbers of cases showing how AFROC and wAFROC curves are affected by correct and incorrect decisions and how the corresponding FOMs credit or penalize these decisions. The wAFROC, AFROC, and inferred ROC FOMs were applied to three clinical data sets involving multiple reader FROC interpretations in different modalities.

RESULTS

It is shown analytically that the area under the empirical wAFROC curve equals the wAFROC FOM. This theorem is the FROC analog of a well-known theorem developed in 1975 for ROC analysis, which gave meaning to a Wilcoxon statistic based ROC FOM. A similar equivalence applies between the area under the empirical AFROC curve and the AFROC FOM. The examples show explicitly that the wAFROC FOM gives equal importance to all diseased cases, regardless of the number of lesions, a desirable statistical property not shared by the AFROC FOM. Applications to the clinical data sets show that the wAFROC FOM yields results comparable to that using the AFROC FOM.

CONCLUSIONS

The equivalence theorem gives meaning to the weighted AFROC FOM, namely, it is identical to the empirical area under weighted AFROC curve.

Optimal Joint Detection and Estimation That Maximizes ROC-Type Curves

Combined detection-estimation tasks are frequently encountered in medical imaging. Optimal methods for joint detection and estimation are of interest because they provide upper bounds on observer performance, and can potentially be utilized for imaging system optimization, evaluation of observer efficiency, and development of image formation algorithms. We present a unified Bayesian framework for decision rules that maximize receiver operating characteristic (ROC)-type summary curves, including ROC, localization ROC (LROC), estimation ROC (EROC), free-response ROC (FROC), alternative free-response ROC (AFROC), and exponentially-transformed FROC (EFROC) curves, succinctly summarizing previous results. The approach relies on an interpretation of ROC-type summary curves as plots of an expected utility versus an expected disutility (or penalty) for signal-present decisions. We propose a general utility structure that is flexible enough to encompass many ROC variants and yet sufficiently constrained to allow derivation of a linear expected utility equation that is similar to that for simple binary detection. We illustrate our theory with an example comparing decision strategies for joint detection-estimation of a known signal with unknown amplitude. In addition, building on insights from our utility framework, we propose new ROC-type summary curves and associated optimal decision rules for joint detection-estimation tasks with an unknown, potentially-multiple, number of signals in each observation.

Evaluation of computer-aided detection and diagnosis systems

Computer-aided detection and diagnosis (CAD) systems are increasingly being used as an aid by clinicians for detection and interpretation of diseases. Computer-aided detection systems mark regions of an image that may reveal specific abnormalities and are used to alert clinicians to these regions during image interpretation. Computer-aided diagnosis systems provide an assessment of a disease using image-based information alone or in combination with other relevant diagnostic data and are used by clinicians as a decision support in developing their diagnoses. While CAD systems are commercially available, standardized approaches for evaluating and reporting their performance have not yet been fully formalized in the literature or in a standardization effort. This deficiency has led to difficulty in the comparison of CAD devices and in understanding how the reported performance might translate into clinical practice. To address these important issues, the American Association of Physicists in Medicine (AAPM) formed the Computer Aided Detection in Diagnostic Imaging Subcommittee (CADSC), in part, to develop recommendations on approaches for assessing CAD system performance. The purpose of this paper is to convey the opinions of the AAPM CADSC members and to stimulate the development of consensus approaches and "best practices" for evaluating CAD systems. Both the assessment of a standalone CAD system and the evaluation of the impact of CAD on end-users are discussed. It is hoped that awareness of these important evaluation elements and the CADSC recommendations will lead to further development of structured guidelines for CAD performance assessment. Proper assessment of CAD system performance is expected to increase the understanding of a CAD system's effectiveness and limitations, which is expected to stimulate further research and development efforts on CAD technologies, reduce problems due to improper use, and eventually improve the utility and efficacy of CAD in clinical practice.

Reducing radiation dose to the female breast during CT coronary angiography: a simulation study comparing breast shielding, angular tube current modulation, reduced kV, and partial angle protocols using an unknown-location signal-detectability metric

PURPOSE

The authors compared the performance of five protocols intended to reduce dose to the breast during computed tomography (CT) coronary angiography scans using a model observer unknown-location signal-detectability metric.

METHODS

The authors simulated CT images of an anthropomorphic female thorax phantom for a 120 kV reference protocol and five "dose reduction" protocols intended to reduce dose to the breast: 120 kV partial angle (posteriorly centered), 120 kV tube-current modulated (TCM), 120 kV with shielded breasts, 80 kV, and 80 kV partial angle (posteriorly centered). Two image quality tasks were investigated: the detection and localization of 4-mm, 3.25 mg/ml and 1-mm, 6.0 mg/ml iodine contrast signals randomly located in the heart region. For each protocol, the authors plotted the signal detectability, as quantified by the area under the exponentially transformed free response characteristic curve estimator (ÂFE), as well as noise and contrast-to-noise ratio (CNR) versus breast and lung dose. In addition, the authors quantified each protocol's dose performance as the percent difference in dose relative to the reference protocol achieved while maintaining equivalent ÂFE.

RESULTS

For the 4-mm signal-size task, the 80 kV full scan and 80 kV partial angle protocols decreased dose to the breast (80.5% and 85.3%, respectively) and lung (80.5% and 76.7%, respectively) with ÂFE=0.96, but also resulted in an approximate three-fold increase in image noise. The 120 kV partial protocol reduced dose to the breast (17.6%) at the expense of increased lung dose (25.3%). The TCM algorithm decreased dose to the breast (6.0%) and lung (10.4%). Breast shielding increased breast dose (67.8%) and lung dose (103.4%). The 80 kV and 80 kV partial protocols demonstrated greater dose reductions for the 4-mm task than for the 1-mm task, and the shielded protocol showed a larger increase in dose for the 4-mm task than for the 1-mm task. In general, the CNR curves indicate a similar relative ranking of protocol performance as the corresponding ÂFE curves, however, the CNR metric overestimated the performance of the shielded protocol for both tasks, leading to corresponding underestimates in the relative dose increases compared to those obtained when using the ÂFE metric.

CONCLUSIONS

The 80 kV and 80 kV partial angle protocols demonstrated the greatest reduction to breast and lung dose, however, the subsequent increase in image noise may be deemed clinically unacceptable. Tube output for these protocols can be adjusted to achieve a more desirable noise level with lesser breast dose savings. Breast shielding increased breast and lung dose when maintaining equivalent ÂFE. The results demonstrated that comparisons of dose performance depend on both the image quality metric and the specific task, and that CNR may not be a reliable metric of signal detectability.

A brief history of free-response receiver operating characteristic paradigm data analysis

In the receiver operating characteristic paradigm the observer assigns a single rating to each image and the location of the perceived abnormality, if any, is ignored. In the free-response receiver operating characteristic paradigm the observer is free to mark and rate as many suspicious regions as are considered clinically reportable. Credit for a correct localization is given only if a mark is sufficiently close to an actual lesion; otherwise, the observer's mark is scored as a location-level false positive. Until fairly recently there existed no accepted method for analyzing the resulting relatively unstructured data containing random numbers of mark-rating pairs per image. This report reviews the history of work in this field, which has now spanned more than five decades. It introduces terminology used to describe the paradigm, proposed measures of performance (figures of merit), ways of visualizing the data (operating characteristics), and software for analyzing free-response receiver operating characteristic studies.

A nonparametric procedure for comparing the areas under correlated LROC curves

In contrast to the receiver operating characteristic (ROC) assessment paradigm, localization ROC (LROC) analysis provides a means to jointly assess the accuracy of localization and detection in an observer study. In a typical multireader, multicase (MRMC) evaluation, the data sets are paired so that correlations arise in observer performance both between readers and across the imaging conditions (e.g., reconstruction methods or scanning parameters) being compared. Therefore, MRMC evaluations motivate the need for a statistical methodology to compare correlated LROC curves. In this work, we suggest a nonparametric strategy for this purpose. Specifically, we find that seminal work of Sen on U-statistics can be applied to estimate the covariance matrix for a vector of LROC area estimates. The resulting covariance estimator is the LROC analog of the covariance estimator given by DeLong et al. for ROC analysis. Once the covariance matrix is estimated, it can be used to construct confidence intervals and/or confidence regions for purposes of comparing observer performance across imaging conditions. In addition, given the results of a small-scale pilot study, the covariance estimator may be used to estimate the number of images and observers needed to achieve a desired confidence interval size in a full-scale observer study. The utility of our methodology is illustrated with a human-observer LROC evaluation of three image reconstruction strategies for fan-beam x-ray computed tomography (CT).