Elsevier

Academic Radiology

Volume 9, Issue 3, March 2002, Pages 290-297
Academic Radiology

Estimation in Medical Imaging without a Gold Standard☆

https://doi.org/10.1016/S1076-6332(03)80372-0Get rights and content

Abstract

Rationale and Objectives

In medical imaging, physicians often estimate a parameter of interest (eg, cardiac ejection fraction) for a patient to assist in establishing a diagnosis. Many different estimation methods may exist, but rarely can one be considered a gold standard. Therefore, evaluation and comparison of different estimation methods are difficult. The purpose of this study was to examine a method of evaluating different estimation methods without use of a gold standard.

Materials and Methods

This method is equivalent to fitting regression lines without the x axis. To use this method, multiple estimates of the clinical parameter of interest for each patient of a given population were needed. The authors assumed the statistical distribution for the true values of the clinical parameter of interest was a member of a given family of parameterized distributions. Furthermore, they assumed a statistical model relating the clinical parameter to the estimates of its value. Using these assumptions and observed data, they estimated the model parameters and the parameters characterizing the distribution of the clinical parameter.

Results

The authors applied the method to simulated cardiac ejection fraction data with varying numbers of patients, numbers of modalities, and levels of noise. They also tested the method on both linear and nonlinear models and characterized the performance of this method compared to that of conventional regression analysis by using x-axis information. Results indicate that the method follows trends similar to that of conventional regression analysis as patients and noise vary, although conventional regression analysis outperforms the method presented because it uses the gold standard which the authors assume is unavailable.

Conclusion

The method accurately estimates model parameters. These estimates can be used to rank the systems for a given estimation task.

Section snippets

Materials and Methods

A variety of different parameters are estimated in medical imaging in an attempt to quantify an individual's health status. For example, the cardiac ejection fraction describes the fraction of the blood in the left ventricle that is pumped out during a given cycle. This parameter, which is used by physicians as an indicator of a patient's susceptibility to heart failure, can be estimated with use of ultrasound (US), magnetic resonance (MR), or gamma-ray imaging techniques (6, 7). When

Analysis of RWT

As stated, ML estimation is asymptotically efficient. Figure 3a shows that the RMSE, as given in Equation (5), decreases as the patient number increases. The variance of the noise σm was fixed for each modality in this experiment. In the limit of large patient numbers, the three different curves (each representing a different modality) tend to a minimum value σm/am (see Eqq [1] and [5]) in accordance with ML theory.

Figure 3b compares the performance of conventional regression analysis with that

Discussion

Arriving at a gold standard for a given estimation task is often difficult. Frequently, researchers in a given field do not agree on a gold standard, and even when such agreement occurs, the information can be difficult to obtain (eg, by means of postmortem examination). Indeed, if an accepted gold standard was easy to obtain, no other methods to ascertain the relevant information would be needed. Thus, a gold standard typically is not available.

In the absence of a gold standard, an alternate

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☆

Supported by National Institutes of Health grants P41 RR14304, KO1 CA87017-01, and RO1 CA 52643 and National Science Foundation grant 9977116.

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