Supplemental Digital Content: Description of the notch detecting algorithm
The simple notch-detection algorithm relies on a few parameters that allow for variations in the notch shape and location. The specifics of the algorithm are described with the aid of Fig.
2 in the manuscript, which shows algorithm parameters along with features of a PR difference curve (the difference between an individual PR response and the mean PR of normal ears) for an SCD ear. First, the algorithm searches for a local minimum in the PR difference curve within a specified notch frequency range (underlined italics refer to parameters that can be optimized), and designates this minimum point as the location of a potential notch (indicated by a star in Fig. 2). Next, the algorithm finds the maxima on each side of the notch occurring within the notch frequency range (marked as crosses in Fig. 2). The notch depth (italics without underline refer to computed values) is computed as the difference between the lower of the two
surrounding maxima and the minimum value in the notch (Fig. 2 is an example of the case where the upper-frequency maxima is used to calculate the notch depth, illustrated by a vertical barred line). Once the notch depth is computed, it is compared to the minimum notch depth to determine if the notch meets the threshold depth criteria. Notches that are too wide are eliminated by comparisons to the maxima found within a designated notch frequency range.
Finally, the algorithm checks whether the identified minimum value of the V-shaped notch is sufficiently less than the average of the difference curve over a specified frequency range below the notch frequency. Specifically, the average value of the PR difference curve is
computed over a baseline range comprising frequencies from 1.5 to 0.5 octaves below the notch frequency. (The average over the baseline range is shown as a thick horizontal bar in Fig. 2).
This low-frequency “baseline” controls for variations in the low-frequency PR in different ears.
The difference between this low-frequency average value and the value of the curve at the minimum “notch” point is defined as the notch size (the example shown in Fig. 2 has a notch
size of 0.294), and the minimum notch size parameter can be optimized. Both notch depth and notch size were necessary for detection because the notch depth can be calculated from either the low-frequency or the high-frequency maxima (as in the example of fig. 2) and senses only whether this “notch” is deep and narrow enough in a specific frequency range. On the other hand, notch size describes the depth of the notch with respect to a low-frequency baseline value, which was useful in optimizing notch identification in ears with SCD. We also tested for
correlations between notch size, SCD size and air-bone gap (discussed in a subsequent section).
We were able to adjust the three parameters (notch frequency range, minimum notch depth, minimum notch size) to distinguish between SCD and normal ears with high sensitivity and moderately high specificity. Detection thresholds of the above parameters were originally determined based on optimization around a subset of the data (26/40 ears) together with the normal population of 58 ears. The parameters were adjusted iteratively, and after each iteration, the sensitivity and specificity were evaluated and optimized. In defining notch frequency range the mean frequency of the SCD notch was used as the center, and the width around this center was widened until all of the SCD notches were present within this range. This resulted in a fixed notch frequency range between 585 and 1876 Hz. The effect of variations in minimum notch depth and minimum notch size on sensitivity and specificity were then evaluated by first setting one of these parameters to a fixed level. For example, before looking at the sensitivity and selectivity associated with variations in notch size, we fixed the minimum notch size, and all PR curves with notch sizes smaller than the minimum were assigned notch depths of zero. This exercise was repeated for the full collection of the 40 SCD ears with respect to the 58 normal control ears, resulting in the same optimized parameters, thereby demonstrating the strength of the selected parameter values. Fig. 3 A & B of the manuscript show receiver operating
characteristic (ROC) curves calculated for the 40 SCD ears and 58 normal ears for parameter variations. In Figure 3A, we compare the use of notch size as a decision variable after first applying two different minimum notch depths. In Figure 3B we look at the use of notch depth as
a decision variable after first applying a minimum notch size. A minimum notch size on the order 0.1 and a minimum notch depth between 0.05 and 0.1 were found to separate most SCD ears from normals.
