**Purpose**:
To introduce a new method (ARBON) for decreasing the test time of psychophysical procedures and examine its application to perimetry.

**Methods**:
ARBON runs in parallel with an existing psychophysical procedure injecting occasional responses of seen or unseen into that procedure. Using computer simulation to mimic human responses during perimetry, we assess the performance of ARBON relative to an underlying test procedure and a version of that procedure truncated to be faster. Simulations used 610 normal eyes (age 20 to 80 years) and 163 glaucoma eyes (median mean deviation = −1.81 dB, 5th percentile = +2.14 dB, 95th percentile = −22.55 dB). Outcome measures were number of presentations and mean absolute error in threshold estimation. We also examined the probability distribution of measured thresholds.

**Results**:
ARBON and the Truncated procedure reduced presentations by 16% and 18%, respectively. Mean error was increased by 8% to 10% for the Truncated procedure but decreased by 5% to 7% for ARBON. The probability distributions of measured thresholds using ARBON overlapped with the Underlying procedure by over 80%, whereas the Truncated procedure overlapped by 50%.

**Conclusions**:
ARBON offers a principled method for reducing test time. ARBON can be added to any existing psychophysical procedure without requiring any change to the logic or parameters controlling the procedure, resulting in distributions of measured thresholds similar to those of the underlying procedure.

**Translational Relevance**:
ARBON can be added to a perimetry test procedure to speed up the test while largely preserving the distribution of returned sensitivities, thus producing normative data similar to the data for the original, underlying perimetric test.

^{1}Dynamic strategy,

^{2}and GATE

^{3}); Bayesian procedures (for example, variants of the ZEST procedure

^{4}

^{–}

^{6}); hybrids of the two (such as the SITA family of algorithms

^{7}

^{–}

^{10}); and other approaches (for example, PASS

^{11}and TOP

^{12}). All of these algorithms have governing parameters that determine things such as when the test terminates, what order the locations in the visual field are tested, and the luminance level of stimuli presented. The selection of these parameters controls the trade-off between precision and accuracy of threshold estimation and test time. Usually, altering the parameters to make testing faster will reduce the precision and accuracy of the threshold measurements. For example, a key difference between the SITA Standard test procedure and SITA Fast is an alteration to the termination parameter (ERF - error-related factor),

^{9}which results in decreased test time for SITA Fast but also some differences in the distributions of the returned threshold estimates.

^{13}

^{14}

^{,}

^{15}In particular, the procedure stops when the standard deviation of its probability distribution of likely thresholds at a location drops below 2.0 dB, with a maximum of 10 presentations allowed. The exact details of the procedure generating the specific decision tree are not particularly important for this manuscript; this underlying algorithm serves to illustrate the ARBON method, which can be applied to any psychophysical algorithm. This particular tree would require further testing and engineering before it could be used in perimetry. We refer to it hereafter as the Underlying procedure.

^{16}The red nodes in Figure 1 show the Underlying ZEST procedure if the stopping standard deviation is raised to 2.5 dB rather than 2.0 dB. As can be seen, paths in the tree are shorter, so the number of presentations to determining a threshold is smaller. For example, if the subject responds “seen” to 25 dB on the first presentation and “seen” to 29 dB on the second presentation, the shorter procedure stops and reports a threshold of 31 dB, whereas the original presents one more stimulus of 31 dB before returning either 30 or 32 dB. We refer to this shorter procedure as Truncated.

*range of possible thresholds*(ROPT) of a node in the tree to be the range of all the possible final thresholds that could be reached from the node. Throughout, we use the standard Cartesian coordinate notation (

*x*,

*y*) to refer to nodes in the tree of Figure 1, and the notation [

*a*,

*b*] to indicate a range of values that includes both

*a*and

*b*. As an example of ROPT, the node in Figure 1 at (8, 27) can lead to threshold values 26, 28, and 31, so the ROPT is [26, 31]. Similarly, the root node (0, 25) has a ROPT of [0, 32]. Further, we define the ROPT of a group of nodes as the range of their individual possible ranges. That is, the ROPT of a group of ROPTs [

*a*

_{1},

*b*

_{1}], [

*a*

_{2},

*b*

_{2}], …, [

*a*,

_{n}*b*] is [min(

_{n}*a*

_{1},

*a*

_{2}, …,

*a*), max(

_{n}*b*

_{1},

*b*

_{2}, …,

*b*)].

_{n}- 1. ROPT_Yes is the ROPT at the end of the Yes branch from the node representing the range of final thresholds that would be possible if a Yes response was recorded at this location.
- 2. ROPT_No is the ROPT at the end of the No branch from the node representing the range of final thresholds that would be possible if a No response was recorded at this location.
- 3. ROPT_Close is the ROPT of all the ROPT_Yes and ROPT_No ranges of the neighboring locations at this stage in the test giving the range of the possible final thresholds of all the neighbors of the location under consideration.

- • Check Rule 1. If ROPT_Yes is a subset of ROPT_Close and ROPT_No does not overlap either ROPT_Yes or ROPT_Close, then inject an artificial Yes response at this location.
- • Check Rule 2. If ROPT_No is a subset of ROPT_Close and ROPT_Yes does not overlap ROPT_No or ROPT_Close, then inject an artificial No response at this location.

^{1}For this pattern, there can be about a 1 dB difference in thresholds between adjacent neighbors simply due to the eccentricity of the test locations relative to each other. Thus, when making the comparisons in the Check Rules, we adjusted thresholds by an appropriate factor before being aggregated to form the ROPT values. This factor was taken from a Hill of Vision model in figure 12 of Pricking et al.

^{17}

*delta*dB) in the ROPTs, or expansion of supersets to satisfy the ARBON rules for injecting artificial responses. By increasing

*delta*, we get more artificial responses and thus a faster test, but threshold values are smoothed to be more like their neighbors. In the experiments discussed below, we used a

*delta*value of 1.0 dB.

^{17}which gives a single decibel value at any location in the visual field for an eye of a particular age. To generate threshold values for an eye of a given age, we first choose a general height in the form of probability

*q*between 0.0001 and 0.9999 then take the

*q*th quantile from the normal distributions with means given by the model at each location and standard deviation of 1. To these sampled values at each location, we add a small perturbation (uniform random in the range of −0.5 to 0.5) and finally round the value to a whole decibel. This approach preserves the general shape of the normal hill of vision but introduces fluctuations for the whole eye (

*q*value) and some individual location differences (±0.5 dB before rounding). Using this approach, we generated 610 normal eyes with the 24-2 pattern, 10 of each age from 20 to 80 inclusive.

^{4}Visual field damage in this dataset ranged from mild to severe visual field damage (median mean deviation [MD] = −1.81 dB; 5th percentile = +2.14 dB; 95th percentile = −22.55 dB).

^{18}In this model, the probability of seeing a stimulus of

*x*dB is given by

*p*and

*n*are the false-positive and false-negative rates, respectively;

*t*is the assumed true threshold of the simulated location, and Φ(

*x*,

*m*,

*s*) is the cumulative normal distribution with mean

*m*and standard deviation

*s*. We simulated with two error conditions: reliable, where

*p*=

*n*= 0%, and typical, where

*p*= 10% and

*n*= 3%.

^{7}These commence by testing four primary locations, one in each quadrant. One consequence of this approach is that locations must have their threshold determination completed before related locations can begin any presentations. An alternative approach is to propagate the response to each stimulus to its neighboring locations, perhaps with weighting factor such as in the SWeLZ

^{19}or TOP

^{12}approaches. Both of these approaches embed the spatial logic as an integral component of the testing procedure; hence, any tweaking of parameters or alteration of the logic effectively creates a variant of the procedure that may result in a different distribution of threshold values being returned.

**A. Turpin**, iCare Finland OY (F);

**A.M. McKendrick**, iCare Finland OY (F)

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*x*,

*t*) be the probability of seeing stimulus

*t*with true threshold

*t*. One could use the same equation as used for the simulations above for Ψ assuming some representative values of

*p*and

*n*. Let

*T*be a decision tree for some location and some test procedure (like that in Fig. 1). For some given true threshold value

*t*, we can compute the probability of following a branch in

*T*from Ψ and thus the probability of arriving at any leaf as the product of the probability of following the branches that lead to the leaf. Thus, we can compute the expected measured threshold (EMT) for true threshold

*t*using tree

*T*as

*P*(

*t*) = probability of the population having true threshold

*t*, then the mean threshold observed for population

*P*for tree

*T*will be

*M*′ using EMT′, and the difference between

*M*′ and

*M*becomes the correction to apply to the final threshold.