Threshold Estimating Algorithms

Threshold sensitivity is determined by a staircase algorithm, which is a psychophysical technique. A compromise between the test duration, accuracy and reproducibility is made when estimating the threshold sensitivity. Variability occurs depending on the

accuracy of the threshold estimation algorithm used. Scatter in the data is present, due to the measurement of differential light threshold (Flammer et al. 1984b).

Supra-threshold and threshold are the two static examination strategies which may be used in perimetry. The supra-threshold strategy presents stimuli at an intensity above threshold and is used for rapid screening purposes in the determination of normality, to give an approximation of the visual field. Threshold strategies determine the threshold for each point in the visual field and are used for more accurately determining visual field loss. The most common threshold estimating algorithms for threshold strategies are described here.

The Full Threshold strategy on the HFA employs a 4-2 double reversal staircase procedure to determine the threshold sensitivity at each test location. The initial step size is 4dB, which is reduced to 2dB after initially crossing the threshold (reversal). The threshold is recorded as the last seen stimulus after the 2dB step size has crossed the threshold again. Such an algorithm is sometimes referred to as a double reversal algorithm. The Full Threshold strategy measures the central 30° field in around 12 minutes in normal subjects and may take as long as 20 minutes in glaucoma patients (Anderson & Patella 1992). This older algorithm employs a greater number of reversals, which produces longer testing staircase sequences. Consequently the examinations are longer, leading to fatigue to the detriment of the test reliability. The FASTPAC program was developed with the aim of decreasing test duration. This strategy of threshold estimation uses 3dB steps and crosses the threshold only once (Flanagan et al. 1993a). FASTPAC was demonstrated to reduce test duration by 36- 40% compared to the Full Threshold strategy (Flanagan et al. 1993b; Mills et al. 1994) but yielded an increased SF (Flanagan et al. 1993a,b; Mills et al. 1994). Contradictory findings have been reported regarding the ability of FASTPAC to detect visual field defects. Erroneous underestimation (Flanagan et al. 1993b) and overestimation (O’Brien et al. 1994) of defect severity by the FASTPAC algorithm have been

observed. No significant difference of FASTPAC from Full Threshold strategy, in criteria based defect detection has also been noted (Mills et al. 1994). Nevertheless, the FASTPAC algorithm increases the number of patients capable of performing reliable threshold perimetry (O’Brien et al. 1994).

Figure 1-4. Full Threshold and FASTPAC algorithms

The next generation of algorithms, Swedish Interactive Threshold Algorithms (SITA), were created with the intent of minimising test duration whilst maintaining the quality of data comparable to the Full Threshold strategy (Bengtsson et al. 1997b). SITA operates using a probability model of the threshold value constructed from databases of known normal and glaucomatous visual fields. Prior to the start of visual field testing, models of normal and glaucomatous visual fields are constructed. These include information about the age-corrected normal values at each stimulus location (Heijl et al. 1987a), the frequency-of-seeing curves and the correlations between threshold values at different stimulus locations (Bengtsson et al. 1997b). A higher correlation exists between adjacent test points than stimuli situated further apart and points depressed due to glaucomatous field loss mostly occur in clusters corresponding

Full Threshold 4-2 dB FASTPAC 3 dB Threshold error Threshold error

to the shape of the retinal nerve fibre layer (Bengtsson et al. 1997b). Initially, thresholds are determined at four seed locations by the standard 4-2dB staircase sequence with two reversals. The seed locations are then used to calculate the starting threshold estimates at adjacent points. Patient responses to stimuli and the known distribution models are used to calculate posterior probability distributions, an approach used in Bayesian statistics (Bengtsson et al. 1997b). The posterior probability of a threshold occurring is the conditional probability that is assigned after previous responses and information from the models are taken into account. Posterior probability functions are recalculated following each stimulus presentation and continuously change shape with more responses, facilitating new threshold estimates and continuation of the staircase. The values from the known models gradually exert less influence on the threshold estimates with more response data added to the models. Testing is stopped once the measurement error estimates reach a predetermined limit of accuracy, the error related factor (ERF). ERF values were established based on computer simulation of visual field assessment (Bengtsson et al. 1997b). If the estimated value is greater than 12dB from the initial predicted value, SITA repeats the staircase, as opposed to the Full Threshold strategy, which repeats the staircase if the estimated value is greater than 4dB from the initial value (Bengtsson & Heijl 1998a; Turpin et al. 2003). As well as the advent of a new threshold estimating algorithm, SITA incorporated novel processes for timing and the estimation of false answers. The timing algorithm is repeatedly adjusted based on each response throughout testing. Like older threshold estimating algorithms, false negatives are measured using catch trials, however false positive answers are detected during periods when no responses are expected, rather than performing separate catch trials. A post processing step is implemented in SITA, which recalculates all threshold values taking into account the influence of the patient reaction times and the frequencies of false answers on the probability curves used in threshold estimation (Bengtsson et al. 1997b). As a result of the more efficient threshold estimating algorithm, the elimination

of catch trials for false positives and the more effective timing algorithm, SITA reduced the examination duration of older algorithms, whilst maintaining reproducibility comparable to Full Threshold strategy (Bengtsson et al. 1998; Bengtsson & Heijl 1998b). SITA Standard was reported to take approximately half the time of the Full Threshold strategy and 84-85% of the time of FASTPAC, in normal subjects (Bengtsson et al. 1998) and glaucoma patients (Bengtsson & Heijl 1998b). Furthermore, the number of stimuli presented was decreased by 29% in normals and 26% in glaucoma patients (Bengtsson et al. 1997b).

SITA Standard and SITA Fast are the two algorithms available on the HFA, which correspond to Full Threshold and FASTPAC algorithms, respectively. The threshold estimation in SITA Fast interrupts the stimulus sequence earlier than in SITA Standard, by increasing the limit of the ERF, such that a diminished accuracy of test results is accepted and thus fewer stimuli are presented (Bengtsson & Heijl 1998a). SITA Fast was reported to present 30-34% fewer stimuli than FASTPAC in normal and glaucomatous visual field tests (Bengtsson & Heijl 1998a). SITA algorithms have reduced between-subject variability, compared to Full Threshold and FASTPAC algorithms, therefore narrowing confidence limits for definition of normality (Bengtsson & Heijl 1999a; Wild et al. 1999). In normal subjects, SITA MS values have been reported to be around 1dB higher when compared to Full Threshold values (Artes et al. 2002; Shirato et al. 1999; Wild et al. 1999). Moreover, the normal hill of vision was noted to be slightly higher and flatter than the Full Threshold algorithm (Bengtsson & Heijl 1999a). This bias between algorithms has been hypothesised to be caused by a reduced fatigue effect when using the briefer SITA examinations (Bengtsson & Heijl 1999b), however it has been argued that factors other than fatigue are responsible for the difference (Artes et al. 2002; Shirato et al. 1999; Turpin et al. 2003). It has been suggested that the magnitude of the bias is related to the size of the ERF (Artes et al. 2002). The difference in threshold values between the Full Threshold and SITA

strategies were found to vary in a nonlinear pattern with sensitivity in glaucoma patients (Artes et al. 2002). In glaucomatous visual fields, the SITA algorithms detected a greater number of pattern deviation defects than the Full Threshold algorithm despite producing similar MD values (Bengtsson & Heijl 1999b). Normal individuals naïve to perimetry were also observed to have more significantly depressed pattern deviation points when tested with SITA standard compared to Full Threshold strategies (Schimiti et al. 2002). A limitation in the performance of SITA was recognised in a study using computer simulations of visual field testing (Turpin et al. 2003). When response errors were made by simulated patients, the accuracy and precision of sensitivity estimates were poor when the initial estimate of threshold was not close to the true threshold (Turpin et al. 2003).