Reappraisal of the glycerol test in patients with suspected Menière's disease

Abstract

Background: Recent advances in magnetic resonance imaging make it possible to visualize the presumed pathophysiologic correlate of Menière's disease: endolymphatic hydrops. As traditional diagnostic tests can provide only indirect evidence, they are hardly competitive in this respect and need to be rethought. This is done here for the glycerol test.

Methods: The data of a previous retrospective analysis of the glycerol test in patients with suspected Menière's disease are reinterpreted using a simple model. The mean threshold reduction (MTR) in the frequency range from 125 to 1500 Hz (calculated from audiograms obtained immediately before and four hours after the glycerol intake) is used as the test statistic. The proposed model explains the frequency distribution of the observed MTR by the convolution of a Gaussian probability density function (representing measurement errors) with a template representing the frequency distribution of the true MTR. The latter is defined in terms of two adjustable parameters. After fitting the model to the data, the performance of the test is evaluated using receiver operating characteristic (ROC) analysis.

Results: The cumulative frequency distribution of the observed MTR can be explained almost perfectly by the model. According to the ROC analysis performed, the capability of the currently used audiometric procedure to detect a glycerol-induced threshold reduction corresponds to a diagnostic test of rather high accuracy (area under the ROC curve greater than 0.9). Simulations show that methodological improvements could further enhance the performance.

Conclusions: Owing to their ability to reveal functional aspects without an obvious morphological correlate, traditional test for Menière's disease could be decisive for defining the stage of the disease. A distinctive feature of the glycerol test is that it is capable of determining, with high accuracy, whether the pathophysiologic condition of the inner ear is partially reversible. Prospectively, this could help to estimate the chances of specific therapies.

Figure 1

Correlation between mean threshold reduction (MTR) and aggregate threshold reduction (ATR). Both the MTR and the ATR can assume only a limited number of values. As a consequence, there are generally multiple occurrences for each combination of these measures so that a standard scatter plot would be problematic. The problem was solved by plotting a circle for each MTR-ATR combination and adjusting the radius so that the area of the circle is proportional to the number of occurrences. The two dotted lines (one horizontal, the other vertical) represent criteria that generally lead to consistent decisions as to the presence of a glycerol induced effect. The few exceptions are marked by filled circles: Blue indicates that the MTR is equal to or greater than the associated criterion value while the ATR falls short of the corresponding threshold. Red indicates that the situation is just the other way round.

Figure 2

Model for the distribution of the “true” MTR (i.e., the MTR that would be obtained if thresholds were estimated without errors). (a) Basic idea. A first model parameter corresponds to the proportion of patients without a glycerol-induced threshold reduction (represented by the arrow), whereas a second one scales the MTR distribution of the patients showing an effect. (b) Discretized and smoothed version of the upper model.

Figure 3

Analysis of the measurement error. The histogram on the left shows the MTR distribution estimated from the data, whereas the histogram on the right is based on a Monte Carlo simulation in which the investigator was assumed to be partially biased. The superimposed solid curves show normal distributions with zero mean and standard deviations corresponding to those calculated from the (measured or simulated) data. The normal distribution shown as a dotted curve in the right panel refers to the measurement error in the unbiased model.

Figure 4

Comparison between data and model for three groups of patients: (a) all patients, (b) the poor candidates for the glycerol test, and (c) the good candidates. Convolving the theoretical frequency distribution shown on the left with the probability density function of the measurement error yields the observed frequency distribution shown in the middle (histogram representing the MTR values obtained from the data, curve representing the model). The corresponding cumulative frequency distributions are shown on the right.

Figure 5

Cumulative distribution functions for the true MTR. These functions were derived from the cumulative distribution functions on the right of Figure 4 (which would be obtained in the absence of measurement errors). The solid curve represents all patients, whereas the other two curves represent the poor (dotted) and the good candidates (dashed).

Figure 6

False-positive rate (1 - specificity) versus true-positive rate (sensitivity). The bold curve was obtained on the basis of all patients, whereas the curves above and below were obtained for the good and the poor candidates, respectively. Approximately halving the standard deviation of the measurement error yielded the dotted curves. By increasing the threshold of the assumed “gold standard” method from 2 dB to 5 dB, the bold curve turned into the curve bounding the gray area in the background.