All analyses were performed with commercial software (MatLab; The Mathworks, Natick, MA). Pupil size was normalized to the mean value of a trend line through the 240 seconds of pupil diameter data of each test. Thus, the multifocal responses were relative responses compared with a normalized diameter of 1 (dimensionless). For convenience, normalized data were multiplied by 3.5 mm, the mean pupil size of the subjects. The resulting peak scaled response amplitudes are referred to as standardized amplitudes (AmpStd).
The data produced by the TrueField device are effectively the mean response to the transient stimuli presented at each test region (e.g.,
Fig. 2). The response waveforms were fitted to the log-normal function
A exp[–(ln(
t/
t p)/σ
2)], where
A is the peak amplitude,
t p is the time to peak (PeakTime), and σ defines the width of the response. The direct and consensual responses for each test region resulted in 44 × 2 × 2 = 176 response waveforms per test.
Diagnostic power was assessed by receiver operator characteristic (ROC) plots, summarized as the area under the curve (AUC). Standard errors in the AUCs were also calculated.
37 The ROC analysis was based on regional deviations from the normative data, not unlike the total deviations (TDs) of a perimeter. The steps in computing these deviations were:
-
Select the parameter to be analyzed (e.g., standardized amplitude).
-
Pool the direct and consensual visual field data. Pooling was achieved by selecting the direct or consensual field with the largest median z-score (i.e., the more reliably measured field of the two).
-
Compute the normative data via a multivariate linear model that fitted the means for every field location of the normal subjects (including a constant offset for the women).
-
Subtract the fields of all subjects from the normative data to create deviations from normal at each field location.
-
Optionally, compute the visual field asymmetry between eyes by replacing the deviations with the absolute value of the differences between left and right eye field locations.
-
Optionally, repeat steps 1 to 5 for a second parameter (e.g., PeakTime), creating a second set of deviations. Then form a linear combination, or deviation score, of the two forms of deviations based on a Fisher's linear discriminant function
38 which best separated the normal subjects and patients. This method defines a two-element vector with coefficients
w i =
S –1(m 1 – m 2), where the
mi are the means of the parameters, and
S is the 2 × 2 pooled covariance matrix. The scores are then the dot product
w ·
xi , where
xi is a two-element vector containing each pairing of deviations for each field location.
-
Transform the final deviations to z-scores, permitting transformation to probabilities that individual field locations differ from the normative data. For step 7, the final deviations were transformed into equivalent probabilities according to the empiric distribution of deviation values over the normative data, separately for each visual field region. The transformation was achieved by interpolation of the mapping from empiric distribution of normative values to equivalent standard normal quantiles, with linear extrapolation, and then mapping to equivalent probability values.
Figure 3 illustrates the outcome of this process for one subject. Two analyses were performed for
Figure 3: one in which at step 2 only the left pupil data were used (
Figs. 3A,
3B), and a second using only the right pupil data (
Figs. 3C,
3D). In this particular subject, the median
z-score at step 2 was 2.67 for the left pupil and 2.57 for the right; therefore, in the usual analysis the fields from the left pupil would have been selected for ROC analysis. It may be supposed that taking the mean across pupils would be more reliable; however, most of the noise is on the efferent pathways and therefore is correlated between the pupils, and so averaging fields across pupils adds no value. One advantage is that only one functional pupil is required.