was predicted using the above formula (8), with subtraction of the electrode configuration length of 17 mm.
Multi-Dimensional Linear Regression Insertion Model
The anatomical measurements, e.g., four diameters (or eight radii) of the cochleas, were considered as anatomical input parameters in a prediction model. These input parameters were first further analyzed. For this purpose the cochleas were also clustered into 3 cochlear size clusters (small, medium and large) based on the sum of the four diameters, with the K-sample clustering procedure of SPSS (SPSS 17.0 for Windows; SPSS Inc., Chicago, IL, USA). The relation between surgical insertion (LE16), cochlear size clusters and insertion depth was analyzed using one-way analysis of variance (ANOVA) and multiple linear regression analyses. The surgical insertion LE16 was combined with one or more of the cochlear diameters and radial distances in order to predict the insertion depth (θ E1) using general linear regression modeling.
Model Validation
The described models produce an estimated surgical insertion distance (L’E16) based on a target angle. Using the post-operative data set it is possible to do a validation of the models by inserting the actual insertion angle θE1 of a patient and thereby predicting the surgical insertion distance (L’E16). The difference between the actual recorded surgical insertion distance (LE16) and the predicted one is a measure for the accuracy. A second estimator of accuracy used the surgical insertion distance (LE16) and the model to estimate the insertion angle θ’E1. This served the purpose of illustrating the variance in the target angles if the ‘prescribed surgical insertion distance’ would have been used (and achieved) by the surgeon. For this purpose the two insertion models were inverted.
Validation using Bootstrapping
Finally, the prediction model with the highest R-squared, defining the explained variance by the model (R2), was further analyzed. To assess the risk of ‘overfitting’, i.e., using too
many parameters in the prediction model, resulting in predictions from the model that do not generalize to new patients outside the sample, the model was internally validated with bootstrapping as described in Steyerberg ‘Clinical Prediction Models’ (Steyerberg, 2009). This was performed for 1000 samples with the ‘validate.ols function’ of the ‘rms package’
by F.E. Harrell Jr. in R statistical software (R version 2.15.0; R Foundation for Statistical Computing, Vienna, Austria). The average performance of these bootstrap samples was used to quantify the ‘optimism’, i.e., the difference between ‘apparent’ performance in the bootstrap samples and true performance in the original sample. This optimism of the prediction model is subtracted from the original estimate of R2 to obtain the optimism-corrected R2, which
represents the estimate of the performance in future cases.
Figure 2. A. Relation between surgical insertion distance (LE16) and frequency mismatch (∆F). B: Rela-
tion between insertion depth (θE1) and frequency mismatch (∆F). Lines represent the fitted
quadratic functions with calculated R-squared and the cochlear cluster sizes are marked by color (blue=small, green=medium, red=large). The black line represents the fitted function of the total population.
Table I. Relation between frequency mismatch and surgical insertion distance
Group a b c LE16(min) R2
Total population (N=222) 0.43 -5.78 23.91 6.7 0.56
Small cluster (N=117) 0.48 -5.92 23.14 6.2 0.64
Medium cluster (N=171) 0.42 -5.70 23.42 6.8 0.60
5
RESULTS
Frequency Mismatch
The cochleas were clustered into 3 cochlear size groups (‘small’ N:117, ‘medium’ N:171,
‘large’ N:74), with mean D1=8.5 mm, 8.9 mm and 9.4 mm, respectively. In Figure 2 the
overall frequency mismatch (∆F) is plotted as a function of surgical insertion distance (Figure 2A) and as function of the insertion depth (Figure 2B). The black line shows the quadratic fit of the total population and the colored lines show the fits of the cochlear size clusters.
The mean frequency mismatch for the studied electrode array type was 6.3 semitones (N=222). The data shows the expected U-shape described in the introduction, as illustrated by the fitted quadratic functions. The fitted quadratic function between frequency mismatch and surgical insertion distance (Figure 2A) was given by;
∆F= a∙ (LE16)2+b ∙ (L
E16) + c (9).
Table I shows the values of the coefficients, the R2 and the surgical insertion distance that
gives the minimum frequency mismatch (LE16(min)) for the total population and cluster size groups separately. The fitted quadratic function of the total population (N=222) showed an R2 of 0.56 (p<0.01).
The correlation function between frequency mismatch and insertion depth was defined by; ∆F=d ∙ (θ E1)2 + e ∙ (θ
E1) + f, (10)
and the total population yielded an R2 of 0.86 (p<0.01). Table II shows the values of the
coefficients, the R2 and the insertion depth belonging to the minimum of the quadratic
functions (θ E1(min)) for the total population and cluster size groups. The minimum mismatch in frequency for this electrode design is found to be at a surgical insertion distance of 6.7 mm (Figure 2A) and an insertion depth of 484˚ (Figure 2B).
Table II. Relation between frequency mismatch and insertion depth
Group d e f θE1(min) R2
Total population (N=222) 0.000519 -0.50 125.24 484 0.86
Small cluster (N=117) 0.000565 -0.56 141 496 0.90
Medium cluster (N=171) 0.000530 -0.51 127 481 0.86
An additional analysis, however, could not demonstrate any significant correlation (p= 1.0) between the frequency mismatch and final phoneme scores (average scores for 65dB SPL and 75dB SPL between 1 and 2 years after implantation). This analysis was performed in the subsample of postlingually deaf adults (N=123), analyzed for a previous study by Van der Marel et al. (2015), for which frequency mismatch data and long-term follow-up data were available.
Influence of Cochlear Size on Insertion Depth
In Figure 3 the relation between surgical insertion distance (LE16) and insertion depth (θ E1) is shown, with different cochlear size clusters marked by colors. The mean insertion depth (θ E1) was 480˚ and the mean surgical insertion distance (LE16) was 6.5 mm (N=362). The mean surgical insertion distance (LE16) per cluster was 6.4 mm for ‘small’ cochleas, 6.6 mm for ‘medium’ cochleas and 6.5 mm for ‘large’ cochleas. This mean surgical insertion distance did not significantly differ between the cochlear cluster size groups as determined by one-way ANOVA (F(2,359) =0.241, p =0.79).
Linear regression lines were calculated per group, and within group correlations turned out to be highly significant (R2=0.76 (p<0.01) for ‘small’, R2=0.74 (p<0.01) for ‘medium’ and
R2=0.76 (p<0.01) for ‘large’ cochleas). Furthermore, these regression lines were significantly
Figure 3.
Relation between surgical insertion distance (LE16) and insertion depth (θ E1), with cochlear cluster siz-
es marked by color (blue=small, green=medium, red=large). Straight lines represent the fitted linear regression fits with calculated R-squared per cluster. The horizontal and vertical dashed reference lines represent the mean values for each cochlear cluster size.