SAP Visual Field Simulation Results using Barramundi

A. Turpin, A.M. McKendrick, C.A. Johnson, and A.J. Vingrys.

This site accompanies a manuscript submitted for publication in January 2002. Once the manuscript appears in press, full experimental results will be added to this site. For now the page contains information that a reviewer of the manuscript may find helpful, but due to word limitations could not be incorporated in the original manuscript.

Contents

  1. Derivation of ERF constants
  2. References

1. Derivation of ERF constants

The termination of the SITA algorithm is controlled both by the staircase, which stops after two reversals, and the Error Related Factor (ERF) of the probability functions maintained during the test. ERF is defined as [BOHR97]

    ERF(P) = a + b * sqrt(variance) - c * threshold
    where If the ERF of either normal or abnormal probability function falls below 0.69 then SITA terminates[BOHR97].

    Unfortunately the values for a, b and c are proprietary information. What is known, however, is that "Low ERF values are associated with small threshold variance and high threshold light intensity, while large ERF values accept larger variance and lower light intensity" [B99], and that linear regression was employed on clinical data to derive a, b and c [B99].

    In this study, a, b and c were derived by assuming

    1. that it is acceptable for a procedure to report a threshold of 35 dB with a 95% confidence of the threshold being in the range 31 to 39 dB;
    2. that it is acceptable for a procedure to report a threshold of 0 dB with a 95% confidence of the threshold being in the range -1 to 2 dB; and
    3. that the 95% confidence limit of a threshold can be read from the probability distribution as two times the standard deviation about the mean.
    Assumption 1 implies that for a threshold value of 35dB, a standard deviation of 2dB is acceptable, hence a variance of 4dB. Assumption 2 implies that for a threshold value of 0dB, a standard deviation of 0.5dB is acceptable, hence a variance of 0.25dB. Assumption 3 allows us to also interpolate that a threshold value of 20dB has a variance of 1.84dB.

    Using the ERF equation and a value of 0.69, we have the 3 equations

    0.69 = a + b * sqrt(4.00) - c * 35
    0.69 = a + b * sqrt(1.84) - c * 20
    0.69 = a + b * sqrt(0.25) - c * 0
    and three unknowns.

    Solving these equations yields

    which are the values used in the simulations of algorithm SQ.

    Whether these values are even close to the true values used by SITA is a little academic as we tuned our stopping ERF for maximum performance of SQ, and the behaviour of algorithm SQ matches the behaviour of SITA as it is reported in all simulation and clinical studies. The fact that our stopping ERF turned out to be 0.70 as opposed to the 0.69 reported in the SITA literature suggests that these values are at least in the right proportions.

    2. References

    [B99] B Bengtsson 1999. "Improved computerized perimetric threshold strategies." Doctoral dissertation, Department of Ophthalmology, Malmo University Hospital, Malmo, Sweden.

    [BOHR97] B Bengtsson, J Olsson, A Heijl and H Rootzen. "A new generation of algorithms for computerized threshold perimetry, SITA." Acta Op. Scandinavica 1997: 75. Pages 368-375.

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    Created 9 Jan 2003 by Andrew Turpin

    Last updated Thu Jan 9 15:00:21 WST 2003