Properties of Staircase Procedures for Estimating Thresholds in Automated Perimetry

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1 Investgatve Ophthalmology & Vsual Scence. Vol. 33. No. 10. September 1992 Copyrght Assocaton for Research n Vson and Ophthalmology Propertes of Starcase Procedures for Estmatng Thresholds n Automated Permetry Chrs A. Johnson,* Balwanrray C. Chouhaaf and Lonel fv Shapro*:): The propertes of the starcase procedure as appled n automated permetry were examned. Two computer smulaton models were used to vary dfferent test- and patent-related parameters n clncal permetry. One model was based on the KKAKEN computer smulaton program; the other computer smulaton was based on stmulus-response data sets from 11 normal subjects. The results were analyzed n terms of effcency and accuracy. It was found that: (1) n general, there was an effcencyaccuracy trade-off; (2) ncreases n responsefluctuatonproduced substantally greater errors n threshold estmates; (3) lttle or no mprovements n accuracy were acheved by ncreasng the number of reversals; (4) the startng poston of the starcase relatve to the threshold nfluenced the effcency of threshold determnatons but not ther accuracy; (5) a sngle-response error reduced the effcency of starcases; (6) the poston of a sngle-response error n a starcase sequence nfluenced the accuracy and effcency of the threshold determnaton; and (7) more than one response error durng a starcase sequence always resulted n a marked reducton n accuracy and/or effcency. Current pcrmctrc strateges appear to be at or near optmal levels, and therefore, strategcs n the future may need to depart from a starcase-style procedure to acheve a sgnfcant ncrease n both accuracy and effcency. Computer smulaton studes can provde an effectve means of evaluatng permetrc test procedures and defnng optmum strateges, whch then can be verfed clncally by subsequent testng n patent populatons. Invest Ophthalmol Vs Sc 33: , 1992 The statstcal propertes of starcase procedures used n psychophyscal studes have been well documented. 1 " 3 However, these analyses examned starcases n whch trals or presentatons were used to establsh sngle threshold values. In clncal vsual feld testng wth automated permetry, sngle thresholds are estmated at locatons. As a result of tme constrants, abbrevated starcase procedures that requre four to ten presentatons per locaton are used. Although automated permetry s accepted wdely as the standard n vsual feld testng, From the *Optcs and Vsual Assessment Laboratory. Department of Ophthalmology. School of Medcne. Unversty of Calforna, Davs. Calforna: the tdcpartmcnl of Ophthalmology. Dalhouse Unversty. Halfax, Nova Scota; and the JDepartment of Cogntve Scence. School of Socal Scences, Unversty of Calforna, Irvne. Calforna. Supported n part by Natonal Eye Insttute (Bcthcsda. MD) research grant EY (CAJ), an unrestrcted research support grant from Research to Prevent Blndness, Inc. (New York. NY. CAJ and LRS). and research grant MT from the Medcal Research Councl of Canada (Ottawa, Canada. BCC). Presented n part at the Annual Meetng of the Assocaton for Research n Vson and Ophthalmology, Sarasota, Florda. May Submtted for publcaton: November 7, 1991; accepted March Reprnt requests: Chrs A. Johnson, PhD, Optcs and Vsual Assessment Laboratory, Department of Ophthalmology, School of Medcne. Unversty of Calforna, Davs, Davs, CA our current knowledge of starcase procedures n permetry s lmted. 4 " 6 We provded a more comprehensve evaluaton of the propertes of starcases n automated permetry usngcomputersmulaton technques. 7 In 1972, a computersmulaton was reported n an deal patent. 4 Several parameters were examned, ncludng target locaton spacng, step sze, response fluctuaton, response error rate, and overall vsual feld depresson. Ths procedure conssted of four phases: (1) use of a coarse target grd of 7.5 spacng; (2) followed by a fne grd of 3 spacng wth alternatng stmulus values (one half above and one half below expected thresholds); (3) retestng questonable ponts and applcaton of a starcase procedure to suspected scotomas; and (4) applcaton of a correcton factor to remanng ponts (nonscotoma locatons). Ths procedure requred approxmately 800 presentatons, equvalent to a test tme of mn. Although a comprehensve analyss of all parameters was not reported to examne potental nteractons, ths study poneered the applcaton of computer smulaton n permetry. It was the bass for establshng a sold theoretc and emprc foundaton to develop and refne automated permetry test strateges for threshold estmaton. In a later study, 5 both smulatons and actual tests were used on fve normal subjects and eght glaucoma 2966

2 No. 10 STAIRCASES IN PEPJMETRY / Johnson er ol 2967 suspects and patents to evaluate strateges n automated permetry. In smulatons, the reproducblty of results was hghest usng a strategy where thresholds were estmated frst n four "seed" locatons usng a three-reversal starcase, followed by an abbrevated starcase for the remanng locatons. In patents, a three-reversal starcase appled to all locatons yelded the hghest reproducblty. Lttle f any parametrc manpulatons were appled to the smulatons to examne the procedures under varyng condtons. We reported smulaton results from a comparson of two permetrc procedures under a lmted selecton of varyng condtons. 6 The two procedures conssted of a smple starcase, such as the one used n the full threshold programs of the Humphrey Feld Analyzer (Humphrey, Inc., San Leandro, CA) and a modfed bnary search (MOBS) procedure 8 adapted for permetrc testng purposes. Comparsons were made across three varables: response fluctuaton, false-postve errors, and false-negatve errors. Interactons were not addressed n ths study. The KRAKEN smulaton program 7 was used to test 80 normal and 80 abnormal vsual felds. We found MOBS to be more accurate but less effcent compared wth the conventonal starcase procedure. Prevous studes 4 " 6 examned (to a lmted extent) the nfluence of test- and patent-related parameters on the dynamcs of starcase procedures n clncal permetry. Before researchers develop newer permetrc strateges, there s a need to understand the propertes of starcases fully n clncal permetry. Research nto new procedures requre a well-defned "standard" to whch comparsons can be made objectvely on a condton-by-condton bass. Clncally, there are two mportant components of automated permetry that are related to the test strategy: (1) the degree to whch test results represent vsualfeldsenstvty (accuracy); and (2) the amount of tme requred to do the test (effcency). In ths analyss, the accuracy and effcency of starcase procedures were examned for both test parameters and patentresponse characterstcs. KRAKEN s a computer smulaton program for permetry that allows test parameters (such as response fluctuaton, number of stmul, and response "errors") to be manpulated n smulaton runs. 7 In each seres of starcase smulaton runs, the followng condtons were specfed. For lest parameters (Fg. 1), we used (1) the startng poston of the starcase relatve to threshold (10 db below to 10 db above threshold); (2) the sze of the ntal starcase step (3-8 db); (3) the sze of the fnal starcase step (2-4 db); and (4) the number of starcase reversals at the fnal step sze (one to three). For patent response characterstcs, we used: (1) the amount of response fluctuaton (standard devaton. 0-6 db); (2) the number of response errors for each starcase (zero to two); and (3) the poston of response errors n the starcase procedure. In ths experment, a dstncton was drawn between response fluctuatons and response errors. In a typcal psychophyscal study, the subject makes a "yes/no" or forced-choce response for each tral. However, n automated permetry, the subject only provdes yes responses; the automated permeter supples a no response based on whether the subject responded n a prescrbed tme perod after stmulus presentaton. The subject's reacton tme, the stmulus duraton, the nterstmulus nterval, the presentaton sequence, and the response tmng crtera all nfluence the decson process. Thus, a slow reacton tme can result n an nadvertent no response; a rhythmc presentaton pattern may nduce an unntentonal yes answer. In addton, an especally long response delay can produce an nadvertent no response to the current stmulus and an nadvertent yes response to the next one. These types of response anomales are not necessarly related to the probablstc nature of detecton and, therefore, are treated separately and referred to as response errors n the analvss. tme > Materals and Methods We conducted two experments n ths study. In the frst, we used the KRAKEN smulaton program 7 and. n the second, stmulus-response data sets from normal subjects to evaluate the propertes of starcases n automated permetry. Experment 1: Smulaton wth KRAKEN Fg. I. Schema of the starcase procedures used n ths study. A. Startng poston of starcase relatve to threshold; B. sze of ntal starcase step sze; C. sze of fnal starcase step sze; and D. number of reversals at the fnal step sze.

3 INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / Seprember 1992 Vol. 33 A total of 50 starcases were done for each combnaton of test condtons evaluated. Each starcase began wth the stmulus value at the predetermned startng poston. Experment 2: Smulaton Wth Stmulus-Response Data From Normal Subjects The subjects were clncally normal volunteers (age range, yr; mean, yr). All subjects had a vsual acuty of 20/25 or better, a spectacle correcton not exceedng ± 3.00 D (equvalent sphere), and a pupl dameter of at least 3 mm. One eye of each subject was selected randomly for testng. Informed consent was obtaned from all subjects. We tested fve retnal locatons (coordnates n degrees, [0, 30]; [0, 15]; [0, 0]; [0, -15]; and [0, -30]) usng the Tbnger permeter (Oculus, Wetzlar, Germany) to obtan our stmulus-response data sets. The order of the tested locatons was randomzed, and only one locaton per sesson was tested. Each subject frst underwent a 5-mn learnng perod. The threshold at the tested locaton then was estmated. After ths, stmul rangng 15 db (n 1-dB steps) and centered on the estmated threshold were presented ten tmes n a predetermned random order. Thus the stmulus-response data set for each locaton and subject contaned 150 observatons. All fve locatons were tested the same day. The stmulus-response data sets for each subject and locaton were used n the smulatons. We programmed a computer to test the varous starcase procedures and smulated the subject's responses based on the data. Because these computer smulaton studes were based on stmulus-response data sets from actual subjects, varables such as response fluctuaton and response errors were ncorporated nto the stmulus-response data sets. Therefore, we were able to create a realstc permetrc model to evaluate the starcases. A total of 50 trals were done for starcase, locaton, and subject. Because experments 1 and 2 were complementary and addressed smlar ssues from dfferent but parallel approaches, fndngs from each experment are nterspersed throughout the Results secton. Results The number of threshold determnatons (effcency) and the error n threshold estmates (accuracy) for fve dfferent starcase procedures usng ntal step szes of 4,6, or 8 db and fnal step szes of 2, 3, or 4 db are shown as a functon of response fluctuaton n Fgure 2. These results were obtaned from experment 1 n whch the data ponts represent the means of 50 threshold estmates usng each starcase at each of 11 startng postons of the starcase (10 db above to 10 db below threshold n 2-dB ntervals). For each condton, the end-pont crteron for termnatng the starcase conssted of one reversal at the fnal step sze. No response "errors" were ntroduced durng the starcase for ths part of the analyss. There were large dfferences n the effcency of the fve starcase condtons. The 4-4 strategy (4 db ntal step and 4 db fnal step) was the most effcent, wth a mean of less then three presentatons requred to estmate threshold (Fg. 2, left). By contrast, the 8-2 strategy was the least effcent, revealng nearly a twofold ncrease n the mean number of presentatons n comparson wth the 4-4 strategy. Other strateges had effcences between these extremes. Assumng a corn- Fg. 2. (A) Mean number of presentatons and (B) mean error n threshold estmate of the fve starcase procedures as a functon of response fluctuaton n Experment 1. Each data pont n the (A) and (B) curves represents the mean number of presentatons and the mean error n threshold estmate, respectvely, of 50 starcase runs at each of 11 startng postons (10 db above to 10 db below threshold n 2-dB steps). FLUCTUATION (db)

4 No. 10 STAIRCASES IN PERIAAETRY / Johnson er ol 2969 bned stmulus duraton and nterstmulus nterval of 2 sec for threshold estmates at 76 vsual feld locatons (smlar to the test procedures used by many automated permeters), the correspondng range of test tmes would be 7-16 mn. Increasng the response fluctuaton from 0 to 6 db had a mnmal effect on the effcency of the 4-4 strategy and modest (10-20%) nfluences on the other strateges. As expected, the most effcent starcase condtons had the greatest average error n threshold estmates (poorest accuracy) and vce versa (Fg. 2, rght). The magntude of dfferences among the fve starcase condtons was, however, only approxmately 0.5 db. Contrary to the effcency results, changes n the amount of response fluctuaton had a large nfluence on the accuracy of the starcases. For every 2-dB ncrease n response fluctuaton, there was approxmately a 1-dB ncrease n the mean error of threshold estmates. Comparable results from experment 2 showed that there was a sgnfcant relatonshp (P < 0.001) between the average number of threshold determnatons (effcency) and the average error n threshold estmates (accuracy) for the fve starcase condtons examned (Fg. 3). The regresson slope was, however, only db/step, suggestng that only small ncreases n accuracy could be attaned by usng the more accurate (but less effcent) strateges. Ths relatonshp was consstent over a wder range of accuracy and effcency measurements. 9 Thus, both smulatons show a trade-off between accuracy and effcency for dfferent test strateges. For the K.RAKEN smulaton used n experment 1, ncreasng the number of reversals at the fnal step sze requred a larger number of presentatons to estmate threshold, especally for larger amounts of response fluctuaton (Fg. 4, left). Each addtonal reversal added one to two extra presentatons, wth the largest dfferences n the number of presentatons occurrng at the hgher levels of response fluctuaton. Wth no response fluctuaton present, neglgble dfferences were found for the accuracy of one, two, and three starcase reversals at the fnal step sze. Other levels of response fluctuaton demonstrated a small ncrease n accuracy (approxmately, db per addtonal starcase reversal). The effcency and accuracy data from experment 2 showed that ncreasng the number of reversals at the fnal step sze ncreased the mean number of presentatons wthout producng a notceable reducton on the mean error n the threshold estmate (Fg. 5; slope, db/step; P = 0.878). In addton, ncreasng the number of reversals dd not decrease the varance of the error n threshold estmates (P = by Bartlett-Box F test). Although we present nformaton usng only the 6-3 strategy, smlar results were found for the other starcase condtons. At frst glance, we mght assume there s a dscrepancy between the data n Fgures 4 and 5. However, the nformaton n Fgure 4 ncludes a more extensve range of fluctuaton levels (explctly controlled n the smulaton program to vary between 0-6 db); the data n Fgure 5 (based on a normal populaton set and not explctly vared by the smulaton program) reflect the range of values ^ 3 CQ Fg. 3. Mean error n threshold estmate as a functon of mean number of presentatons for the fve starcase procedures n Experment 2. Each data pont represents the mean number of presentatons and the mean error n threshold estmate n 50 runs for each subject and locaton. The regresson slope ( db/stcp) was hghly sgnfcant (/' < 0.001), ndcatng an nverse relatonshp between mean error n threshold estmate and mean number of presentatons. The correlaton coeffcent was (agan. P< 0.001). n 2 Q o (/) CC X z CC o CC CC.A * A S 1. «V PROCEDURE 8-2 o * 8-4 A MEAN NUMBER OF PRESENTATIONS

5 2970 INVESTIGATIVE OPHTHALMOLOGY 6 VISUAL SCIENCE / Seprember 1992 Vol. 33 to FLUCTUATION (db) Fg. 4. (A) Mean number of presentatons and (B) mean error n threshold estmate of the 6-3 starcase procedure as a functon of response fluctuaton n Experment I usng one. two, and three reversals at the fnal step sze. Each data pont n the (A) and (B) curves represents the mean number of presentatons and the mean error n threshold estmate respectvely of 50 starcase runs at each of 11 startng postons (10 db above to lodb below threshold n 2-dB steps). between 0 and 2 db of Fgure 4. Wthn a comparable range (0-2 db), the data n Fgures 4 and 5 generally are smlar. The mean number of presentatons and mean error n threshold estmates forfvestarcase procedures are plotted as a functon of the startng poston of the starcase relatve to threshold n Fgures 6 and 7, respectvely. In experment 1, the effcency of the 4-4 strategy depended on the startng poston (Fg. 6, left). The ncrease n the number of presentatons occurred for startng postons > 4 db greater than or less than threshold. Other strateges were nfluenced ether moderately (8-2 and 4-2) or not at all (6-3 and 8-4) by the startng poston. In experment 2, we found that the effcency of all strateges depended on the startng poston of the starcase (Fg. 6, rght). The 4-2 and 4-4 strateges showed generally that the number of presentatons ncreased wth ncreasng devaton from threshold; the 8-2 and 8-4 strateges showed that the effcency was poorest when the startng poston was at or close to threshold. In both experments, there appeared to be no clear relatonshp between the error n threshold estmates (accuracy) and the startng poston of the fve starcase procedures (Fg. 7). There were large varatons n each curve; some starcase condtons had snuso- Fg. 5. Mean error n threshold estmate as a functon of mean number of presentatons of the 6-3 starcase procedure n Experment 2 usng one, two, and three reversals at the fnal step sze. Each data pont represents the mean number of presentatons and the mean error n threshold estmate n 50 runs for each subject and locaton. The regresson slope (0.003 db/stcp) was not sgnfcant (/ J = 0.878), ndcatng ncreasng the number of reversals had no effect on the accuracy of the threshold estmate MEAN NUMBER OF PRESENTATIONS

6 No. 10 STAIRCASES IN PERIMETRY / Johnson er ol 2971 Fg. 6. Mean number of presentatons of the fve starcase procedures as a functon of the startng poston of the starcase relatve to threshold n Experment 1 (left) and Experment 2 (rght). Each data pont n Experment I represents the mean number of presentatons of 50 starcase runs usng a response fluctuaton of 4 db, whereas each data pont n Experment 2 represents the mean number of presentatons of 50 starcase runs n each subject and locaton STARTING POSITION OF STAIRCASE RELATIVE TO THRESHOLD (db) dal curves that appeared to be a functon of the fnal step sze. No meanngful dfferences were observed among the fve strateges. Interactons between response fluctuatons and response errors, n conjuncton wth ther combned nfluence on the mean number of stmulus presentatons and the mean error n threshold estmates, are presented n Fgure 8 for results obtaned n experment I. Two starcase procedures (8-2 and 6-3) were evaluated for 0, 2, and 4 db of response fluctuaton combned wth ether 0 or I response errors. For both starcases, a sngle-response error ncreased the mean number of presentatons, but addtonal response fluctuatons dd not ncrease the mean number of presentatons (Fg. 8, left). When no response errors were present, there was an ncrease n the mean number of presentatons wth ncreases n response fluctuaton level. As a consequence, there was a dfference of approxmately one presentaton between the no-response and one-response error condtons when a 0- db response fluctuaton was present. As the response fluctuaton ncreased to 4 db, the dfference between the no-response and one-response error condtons became neglgble. At all response-fluctuaton levels, a sngle-response error ncreased the mean error n threshold estmate by db (Fg. 8, rght). Smlarly, n the absence or presence of a response error, both starcases dsplayed a 0.5-dB ncrease n the mean error n threshold estmates for every I db of response fluctuaton. Thus, Fg. 7. Mean error n threshold estmate of the fve starcase procedures as a functon of the startng poston of the starcase relatve to threshold n Experment I (left) and Experment 2 (rght). Each data pont n Experment I represents the mean error n threshold estmate of 50 starcase runs usng a response fluctuaton of 4 db, whereas each data pont n Experment 2 represents the mean error n threshold estmate of 50 starcase runs n each subject and locaton. EXPERIMENT 1 m 4 s P 3 a o jj 2 h- VN ERROR OF EXPERIMENT2 PROCEDURE 8-2 o f u ' 2 n STARTING POSITION OF STAIRCASE RELATIVE TO THRESHOLD (db)

7 2972 INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / September 1992 Vol FLUCTUATION (db) Fg. 8. (A) Mean number of presentatons and (B) mean error n threshold estmate of the 8-2 and 6-3 starcase procedures as a functon of response fluctuaton n Experment I wth 0 or I response errors. Ffty starcase runs were performed for each startng poston relatve to threshold, and response errors postoned at ether the frst, second, thrd, or fourth presentaton n the starcase. Each data pont n the (A) and (B) curves represents the mean of all trals for each startng value and response error poston combnaton. both response errors and response fluctuatons decreased the accuracy of threshold estmates, and ther effects appeared to be addtve. The nfluence of the poston of a response error n the starcase (eg, frst presentaton or second presentaton) n experment I s shown n Fgure 9 for the 4-2 starcase strategy (top graphs) and the 8-2 starcase strategy (bottom graphs) wth 0 db (left graphs) and 2 db (rght graphs) of response fluctuaton. The mean number of presentatons and the mean error n threshold estmates for the no-response error condton also are shown for comparson. For all condtons shown 4-2 PROCEDURE OdB FLUCTUATION 4-2 PROCEDURE 2 db FLUCTUATION uj 6 a u. O OC c Ul m 1 S o \ \\ >r > 0 X X \ X \.» \_ x x Xv/ " POSITION OF ERROR IN STAIRCASE 8-2 PROCEDURE 0 db FLUCTUATION PRESENTATIONS ERROR 8-2 PROCEDURE 2 db FLUCTUATION Fg. 9. Mean number of presentatons and mean error n threshold estmate curves for the 4-2 (top) and 8-2 (bottom) starcase condtons wth OdB (left) and 2 db (rght) response fluctuaton n Experment 1 as a functon of the poston of response error n the starcase. Data for the no response error condton arc shown for comparson. Q»» \ 1 X» % \ POSITION OF ERROR IN STAIRCASE

8 No. 10 STAIRCASES IN PEIXIMETRY / Johnson er ol 2973 n Fgure 9, t was clear that the specfc poston of the response error n the starcase procedure affected both the accuracy and effcency of the starcase. Wth the excepton of one condton, the addton of a response error at any poston n the starcase always produced a reducton n both the accuracy and effcency of the threshold estmate. In addton, recprocty between accuracy and effcency was evdent for response errors placed at specfc locatons n the starcase. As a general rule, the accuracy and effcency curves tended to resemble a mrror mage of each other (e, an ncrease n one was accompaned by a decrease n the other). Smlar results were obtaned for other starcase strateges and dfferent numbers of reversals at the fnal step sze. We examned the nfluence of two or more response errors n several starcase condtons. For all combnatons of two or more response errors evaluated, there was always a marked ncrease n the mean number of presentatons, the mean error n threshold estmates, or both, rrespectve of the type of starcase strategy, the amount of response fluctuaton, the startng poston of the starcase, or the number of reversals of the starcase. Dscusson In our study, we dd comprehensve computer smulaton experments to evaluate the propertes of starcase procedures n automated permetry usng two dfferent types of smulaton models. Our fndngs may be summarzed as follows. Frst, for all starcase condtons, there was a recprocal relatonshp between accuracy and effcency. Second, ncreases n response fluctuaton requred a slghtly greater number of presentatons to estmate thresholds but produce substantally greater errors. Thrd, ncreasng the number of reversals at the fnal step sze necesstated a larger number of presentatons and caused no mprovement n accuracy at lower levels of response fluctuaton, although a modest ncrease n accuracy was observed at hgher levels of fluctuaton. There was also no decrease n the varablty of threshold estmates wth an ncrease n the number of reversals. Fourth, the effcency of a starcase generally depended on the startng poston of the starcase relatve to the threshold. Some strateges requred more presentatons when the startng poston was at or close to threshold; n others, the reverse was true. The accuracy of a starcase dd not appear to depend on the startng poston although the strateges vared consderably. Ffth, a sngle-response error reduced the effcency of starcases, especally when response fluctuatons were low. Accuracy also was dmnshed by the presence of a sngle-response error, and these effects appeared to be addtve to those produced by response fluctuatons. Sxth, the poston of a sngleresponse error n a starcase nfluenced the accuracy and effcency of the threshold estmate. Last, more than one response error n the starcase always resulted n a marked reducton n accuracy and/or effcency. Our general fndngs probably are applcable to starcases used for clncal psychophyscal test procedures other than automated permetry (eg, the tradeoff between accuracy and effcency). However, threshold determnatons n automated permetry dffer from other psychophyscal procedures n several respects (eg, the small number of stmulus presentatons per starcase, the use of nformaton from neghborng regons to determne startng values and ntate retests, and many other factors). Therefore, a drect applcaton of the optmum starcase parameters defned for automated permetry may not be approprate for other tests (eg, contrast senstvty functons). Our two smulaton models operated on dfferent prncples; however, the results obtaned from them generally agreed. The most remarkable dfference between the two experments was n the effcency obtaned as a functon of the startng poston relatve to the threshold (Fg. 6). These dfferences probably were caused by the excessve range of response fluctuaton (up to 6 db) used by the KRAKEN smulatons. In the stmulus-response data sets, the response fluctuaton was ncorporated as a result of the data set used and could not be calculated readly. Typcal fluctuaton levels for normal observers are generally 1-3 db. We beleve, however, that usng both smulaton models we obtaned complementary results that allowed us to conduct experments n whch both test and patent-related parameters could be modulated n realstc test stuatons. The fnal determnant of performance for automated permetry test strateges requres clncal valdaton by means of comparatve evaluatons of patents wth normal and abnormal vsualfelds.ths cauton s partcularly noteworthy for experment 2 because only data sets from normal observers were used for the smulaton studes. Nonetheless, computer smulaton can be an effectve means of dentfyng the most promsng test strateges to evaluate n formal clncal trals. Several conclusons may be drawn from our study. The best accuracy-effcency compromse (consderng all starcase condtons and patent-response parameters) appeared to be a starcase wth an ntal step sze of 6 db, a fnal step sze of 3 db,and a sngle reversal at the fnal step sze. Exstng starcase procedures for automated permetry appeared to be at or near optmal levels for varous clncal condtons en-

9 2974 INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / Seprember 1992 Vol. 33 countered durng routne testng. Thus, further refnements of starcase threshold determnaton procedures are unlkely to produce sgnfcant mprovements n accuracy, reductons n testng tme, or mprovements n test-retest relablty. 6 It should be noted that MOBS. 8 a specal varant of the standard starcase procedure, was adapted to automated permetry and compared n computer smulaton studes wth the starcase strategy typcally used n automated permetry. 6 The results of ths study ndcated that the MOBS procedure mproved accuracy by approxmately 10% over the starcase, but there was a 5-7% ncrease n the number of stmulus presentatons. Thus, the accuracy-effcency trade-off appeared to be a general lmtaton of all starcase procedures used for automated permetry. To provde addtonal advances n these areas, t wll be necessary to explot heurstc technques that have been optmzed for permetrc stuatons. Such work s ongong n our laboratory and presently s undergong refnement. Key words: automated permetry. vsual felds, starcases accuracy, effcency, computer smulaton References 1. Comswcct TN: The starcase-method n psyche-physcs. Am J Psychol 75:485, Fccny S. Kaser PK. and Thomas JP: An analyss of data gathered by the starcase-method. Am J Psychol 79:652, Rose RM, Teller DY, and Rcndlcman P: Statstcal propertes of starcase estmates. Percepton and Psychophyscs 8:199, Frankhauscr F. Koch P. and Rouler A: On automaton of permetry. Gracfcs Arch Gn Exp Ophthalmol 184:126, Hcjl A: Computer test logcs for automated permetry. Acta Ophthalmol (Copcnh) 55: Johnson CA and Shapro LR: A comparson of MOBS (modfed bnary search) and starcase test procedures n automated permetry. In Nonnvasvc Assessment of the Vsual System Techncal Dgest Scres. Vol 7, 1989, p Shapro LR. Johnson CA. and Kennedy RL: KRAKEN: A computer smulaton procedure for statc, knetc, suprathrcshold statc and heurstc pcrmctry. /// Permetry Update 1988/ 89: Proceedngs of the Vlllth Internatonal Pcrmctry Socety Meetng. Hcjl A. edtor. Amsterdam. Kuglcr & Ghcdn. 1989, p Tyrrell RA and Owens DA: A rapd technque to assess the restng states of the eyes and other threshold phenomena: The modfed bnary search (MOBS). Behavor Research Methods. Instruments, and Computers 20: House PH and Chauhan BQThrcsholdngstrateges n conventonal and hgh-pass resoluton permetry. ARVO Abstracts. Invest Ophthalmol Vs Sc 32(Suppl):l

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