Random measurement error in visual acuity measurement in clinical settings

Transcription

1 Random measurement error in visual acuity measurement in clinical settings Jaakko Leinonen, 1 Eero Laakkonen 2 and Leila Laatikainen 3 1 Department of Ophthalmology, Vaasa Central Hospital, Vaasa, Finland 2 Department of Teacher Education, University of Turku, Turku, Finland 3 Department of Ophthalmology, University of Helsinki, Helsinki, Finland ABSTRACT. Purpose: To estimate the random measurement error in visual acuity (VA) determination in the clinical environment in cataractous, pseudophakic and healthy eyes. Methods: The VAs of patients referred for cataract surgery or consultation by ophthalmic professionals were re-examined and the VA results for distance using projector acuity charts were compared. Refractive errors were also remeasured. A total of 99 eyes (41 cataractous, 36 pseudophakic and 22 healthy eyes) were examined. The healthy comparison group consisted of hospital staff. Only one eye of each person and eyes with Snellen VAs of (logmar 0.52 to 0.11) were included. The mean time interval between the first and second examinations was 45 days. Results: The estimated standard deviation of measurement error (SDME) of repeated VA measurements of all eyes was logmar Eyes with the lowest VA ( ) had the largest variability (SDME logmar 0.09), and eyes with VA 0.7 had the smallest (SDME logmar 0.04). The variability may be partly explained by the line size progression in lower VAs, partly by the difference in the remeasurement of the refractive error. The difference in the average VA between examinations 1 and 2 (logmar 0.15 versus 0.12) was considered to be of some interest because it indicates that some learning effect is possible. Conclusion: Visual acuity results in clinical settings have a certain degree of inherent variability. In this series variability ranged from SDME logmar 0.04 (eyes with good vision) to logmar 0.09 (in the lower vision group) in the Snellen VA range of Changes should be judged with caution, especially in cases of decreased VA. Key words: visual acuity variability cataract pseudophakia visual acuity charts refractive error Acta Ophthalmol. Scand. 2005: 83: Copyright # Acta Ophthalmol Scand setting, the results of the referring professional usually differ from those of the site of further examination. Physical, physiological and psychological factors may influence VA measurement (Michaels 1975). Different optotypes, projectors and charts, different numbers of optotypes per line, and different line size progressions can cause variation in the results of VA measurements (Gibson & Sanderson 1980; Van den Brom et al. 1995; Raasch et al. 1998). The results of refractive error measurements (REM) are also subject to variation and thus can cause variation in VA results. The variability diminishes the certainty of whether vision has changed or not (Bailey 1998; Siderov & Tiu 1999). The purpose of our study was to measure the test retest variability of VA in routine clinical environments where testing conditions, examiners and psychophysical conditions vary. Variation may differ depending on VA level and in various conditions. Therefore, the observations in this study were made on cataractous, pseudophakic and healthy eyes. doi: /j x Introduction Visual acuity (VA) is perhaps the most important single parameter influencing clinical ophthalmic decision making. It is also important in medical-legal decisions, such as those pertaining to driver s license eligibility or the definition of visual impairment. In a clinical Material and Methods The visual acuities and refractive errors of patients referred for cataract surgery to the ophthalmic ward of Vaasa Central Hospital, Vaasa, Finland, or for consultation at the first author s office were re-examined, and the best corrected VAs and refractive errors 328

2 ACTA OPHTHALMOLOGICA SCANDINAVICA 2005 obtained at both the initial and the second examinations were compared. The first examinations were performed by the referring ophthalmologist (n ¼ 19), optician (n ¼ 4) or the first author (n ¼ 76). There were eight different referring professionals, eight different examination sites, and six different distance acuity projectors (Rodavist 2 [Regen, Germany]; Rodamat [Regen, Germany]; Magnon CP 670 [Kamagori, Japan]; Magnon CP 600 [Kamagori, Japan]; Takagi [Nagano, Japan]; Topcon ACP 5 [Tokyo, Japan]). The first and second examinations were performed at different sites in 86/99 (87%) cases. Those involved in the second examination were masked to the results of the first examination. The VA projector charts had an examination distance of 6 metres. Acuities are reported here in Snellen decimal notation. When logmar is used, it is expressed as such. The eyes examined had cataract (41 eyes), were pseudophakic (36 eyes) or healthy (22 eyes). The persons with healthy eyes were hospital staff (nurses or office personal) who either gave written consent to participation and attended two examinations, or were referred by an optician for exclusion of eye disease (four persons). The data used here comprised routine patient data for clinical work. If the eyes of a patient were comparable, only the results of the right eye were included in the study. The total series included 99 eyes of 99 patients (Table 1). In the cataract group the comparisons were made between two preoperative examinations of the operated eye or between the initial (preoperative) examination and final examination of the cataractous, non-operated fellow eye. In both cases, the time interval between the two examinations was usually 1 2 months. The pseudophakic eyes included were the fellow eyes of patients who attended for second eye Table 1. Patient characteristics and time between examinations 1 and 2. Group n Age Time between first and second examinations (days) Median Range Median Range cataract surgery. Only eyes with VA 0.3 were included in this study. Visual acuities were recorded as correctly or partly correctly read lines. The line was recorded as correctly read if three-quarters of the optotypes of the line were correctly identified. If more than a quarter but less than three-quarters of the line was correctly read, the author used the expression partly read line, which in calculations received the mid value between partly correctly read line and one line below. Because variation in refractive error measurements was expected, all VA measurements were performed after refraction by retinoscopy and conventional subjective refraction (Michaels 1975). The acuity projectors used in this study had between three and five (average 4.0) optotypes per line in the VA range The line size progression varied between logmar and logmar The average was logmar The largest difference (logmar 0.125) in most charts was between lines 0.3 and 0.4. The average time between the first and second examinations was 45 days, with a total range of days (Table 1). In 10 cases, the second examination was performed more than 75 days after the first. The cataract and pseudophakic groups also had other ophthalmic diseases (Table 1), including macular degeneration, diabetic retinopathy without macular oedema, and glaucoma without central vision loss. Some of the pseudophakic eyes had mild posterior capsule opacities and in two cases laser capsulotomy had been performed. One of the seemingly healthy eyes had mild diabetic retinopathy without macular changes. The Snellen VA decimal values were converted mathematically to logmar values. Differences, averages and standard deviations were calculated in logmar units. Variability was Cataract Pseudophakia Healthy eyes All Other ophthalmic diseases; number of eyes calculated as the standard deviation for paired differences between measurements 1 and 2, as described by Bland & Altman (1986), Bland (1988a) and the MedCalc Manual (1999), and expressed as the estimated standard deviation of measurement error (SDME). Statistical calculations were made with SSPS Version The normalcy of distribution of the differences of paired measurements was tested for using the Shapiro Wilk test. Statistical significances were assumed at the p < 0.05 level. Differences in REM were calculated by the Harris matrix vector method (Harris 1990). A formula devised by Keating (1980) was used to convert the REM difference back to normal clinical notation. To estimate the effect of REM differences on VA, defocus equivalent (DE) was calculated according to Holladay et al. (1991) for each difference between paired REMs. Two groups of DE < 0.3 D and DE 0.3 D (maximum 0.75 D) were formed to study VA variability within these groups. The 0.3 D limit was arbitrarily selected because it represents the mid-point between the results of experimental studies of depth of focus in eyes with a 3-mm pupil (Ciuffreda 1998). Results The differences between examinations 1 and 2 in logmar units as plotted against the mean VA (logmar) in the two examinations are shown in Fig. 1. The differences were normally distributed (p ¼ 0.146) (Shapiro Wilk) (Fig. 2). The second examination gave logmar 0.04 higher VA values than the first one. The difference is significant (p < 0.05). The variability for all eyes was SDME logmar The highest variability (Table 2) was in the group with the lowest VA (VA , logmar 0.09) and smallest was in the group with the best (VA 0.7, logmar 0.04). In healthy eyes, the refractive error measurement was more uniform than in other groups. Only 2/22 had a REM difference expressed as DE 0.3 D. In addition, in the group where VA 0.7, there were only 10/59 (17%) eyes with DE 0.3 D. The total number of eyes with DE exceeding 329

3 Difference, logmar Examination 1 and 2, mean VA (logmar); (one point in axis 0.00 can represent 2 or more identical VA results) Fig. 1. Difference in VA in examinations 1 and 2 (logmar) % 25.0 % 20.0 % 15.0 % 10.0 % 5.0 % 0.0 % found frequency expected frequency Fig. 2. Found and expected frequencies (normal distribution) of difference (log MAR) in examinations 1 and D was 26/99 (27%), with the majority falling into the lower VA groups. In the whole series, the VA measurement error increased from logmar 0.05 (SDME) in DE < 0.3 D group (n ¼ 73/99) to logmar 0.09 (SDME) in DE 0.3 D (n ¼ 26/99) (Table 2). The mean difference in VA was smallest in the healthy eyes (both DE groups), logmar 0.01, and in the best seeing group (NS). The largest mean difference, logmar 0.08, was in the group where VA ¼ If the second examination was delayed by more than 75 days (10 eyes), the average VA was logmar 0.02 better in the latter examination. In the remaining 89 eyes that were re-examined sooner, the average VA was logmar 0.04 better in the latter examination. A difference of less than logmar 0.1 occurred in 72/99 (73%) eyes, with the group of cataractous eyes having the smallest percentage (63%). Exactly the same VA value was obtained in 23/ 99 eyes (23%; cataractous eyes 6/41, pseudophakic eyes 8/36 and healthy eyes 9/22). In 10/40 eyes (25%) in the VA group of , the first and second examination results fell on opposite sides of the Snellen value of 0.5, which is required for car driving in Europe. Of these 10 cases, nine eyes were cataractous and one was pseudophakic. In nine of them, VA was better in the second examination. Discussion Although VA measurement is perhaps the most common examination in ophthalmic practice, relatively few studies have dealt with random measurement error in VA measurement in clinical settings (Siderov & Tiu 1999). In controlled laboratory conditions, Arditi & Caganello (1993) found that VA may, with a 95% confidence limit, be ascertained within logmar 0.1 units in trained visually normal persons. In six different studies carried out with visually normal persons, using Sloan letters, with five letters per line and logmar 0.1 line size progression, the random measurement error varied between 0.4 and 1.2 lines (Raasch et al. 1998). Siderov & Tiu (1999) found that the 95% limits of agreement revealed logmar

4 ACTA OPHTHALMOLOGICA SCANDINAVICA 2005 Table 2. Characteristics of repeated measurements of visual acuity. Group n Visual acuity (logmar) SDME repeatability for patients with VA 0.1 with various refractive errors and various clinical conditions. Rosser et al. (2001) examined cataractous, pseudophakic and early-stage glaucoma eyes and found a Snellen acuity repeatability of logmar 0.24 (95% limits of agreement) when examined letter by letter and logmar 0.33 when expressed by lines. In these two studies, the Snellen VA varied from 0.1 (6/60) to normal. An earlier study (Gibson & Sanderson 1980) on cataractous eyes (VA of 6/9 or worse) found a difference of two lines or more in 13% of cases, which is somewhat more than in our study (3/41 eyes). Studies on random measurement error in VA testing using shorter examination protocols have recently been reported (McGraw et al. 2000; Camparini et al. 2001). These studies demonstrated that reducing the number of optotypes or using faster reading of lines above threshold values did not essentially diminish the random measurement error of VA testing. In our study, the SDME was logmar The SDME varied in different vision groups between logmar 0.04 and logmar This random measurement error is less than that found by Rosser et al. (2001), but VAs in our study were better, ranging from 0.3 to normal. In the study by Rosser et al. (2001), the ETDRS chart was taken as a gold standard, and statistics for the comparison of two methods were used, which gives a larger random measurement error. The Difference of < logmar 0.1 in exams 1 and 2 All /99 (73%) 0.04 DE < 0.3 D /73 DE 0.3 D /26 VA /59 (88%) 0.01 DE < 0.3 D /49 DE 0.3 D /10 VA /18 (56%) 0.08 DE < 0.3 D /13 DE 0.3 D /5 VA /22 (46%) 0.06 DE < 0.3 D /11 DE 0.3 D /11 SDME ¼ estimated standard deviation of the measurement error. DE ¼ defocus equivalent. Average of paired differences between measurements 1 and 2 variability observed in the present study was fairly similar to that reported by Siderov & Tiu (1999) for healthy eyes, and Van den Brom et al. 1995) for cataractous eyes. The dependence of refractive error measurement error on the VA in routine clinical practice has probably not been previously investigated. To elucidate the dependence of random measurement error on the VA, we categorized the eyes into two groups depending on defocus equivalents: DE < 0.3 D and DE 0.3 D. In empirical studies, quite a large variation exists for depth of field for a given pupil size: D for a 2- mm pupil and D for a 5-mm pupil (Ciuffreda 1998). It may be reasonable to assume that the depth of field in these eyes would be in the range of 0.3 D (Ciuffreda 1998) and the true value of refractive error in most cases is between the two obtained values. In accommodating eyes, the measurement error can be partly compensated for by accommodation. Thus, it can be concluded that REM differences in the group DE < 0.3 D have only a small effect on VA differences. We found that when the REM difference was greater (DE 0.3 D), the VA variability was greater (logmar 0.09 as compared to 0.05) in the group of nearly similar refractions (DE < 0.3 D). These eyes basically comprised those in the group with the poorest vision (VA ) with lower resolution. It is most likely that these eyes tolerate greater REM differences without effecting VA. Greater REM differences applied to only a minority of eyes: 27% of the total group. Thus it can be concluded that factors other than REM difference contributed to the major variation in VA results. The random measurement error for VA determination increased when the size progression between lines increased and when there were fewer optotypes per line (Vanden Bosch & Wall 1997; Raasch et al. 1998). Six different projectors were used in this study. The VA (in the first examination) varied between 0.3 and 1.3 (logmar 0.52 to 0.11) and in the VA charts the mean difference between lines was logmar (range logmar ). The mean size progression was thus smaller than in the ETDRS charts (logmar 0.1). The largest size difference (logmar 0.125) occurred in most cases between lines 0.3 and 0.4 and line 0.3 contained only the mean of 3.8 optotypes per line. Thus one letter had an average value of logmar 0.031, compared with 0.02 in ETDRS chart. The average VA value per letter in the vision range studied was 0.022, which is close to 0.02 in ETDRS chart. Because acuities were recorded only as correctly or partly correctly read lines, there were only two values per line, thus giving an average of logmar units per line. The measurement error thus increases by a factor of (0.044/0.02) 1/2 ¼ 1.48, as compared to an ETDRS chart read letter by letter (Bailey 1998). Some of the examinations in this study were carried out by reading numbers instead of letters. The recognizability of numbers, like that of letters, varies. However, the influence of readability of letters has a small influence on measurement error in acuity measurement (Raasch et al. 1998). Sloan letters give slightly better acuities than British Standard letters (logmar (Raasch et al. 1998). In our study, the use of British Standard letter charts and Sloan letter charts was fairly evenly distributed and therefore probably did not cause any systematic measurement error. The random measurement error estimated in this study was small, considering the fact that the charts were not ideal when compared with, for example, ETDRS charts. 331

5 Estimates of random measurement error of VA determination may vary considerably between sites, depending on clinical procedure. The outcome of the present study is in accordance with previous studies. Visual acuities in our study were somewhat better in the second examination than in the first, especially in poorly seeing eyes. In previous studies, the difference between the first and second examinations has usually not been significant (Klein et al. 1983; Elliott & Sheridan 1988; Siderov & Tiu 1999; Rosser et al. 2001). Few studies have been performed on cataractous or pseudophakic eyes. The differences between the results of examinations made within 75 days of one another were greater than when the time interval between examinations was longer. This difference may mean that patients exhibit some learning in VA testing. There are other possibilities, such as more vigorous VA testing during later examinations or patient psychological factors. These factors may be a reality in clinical work and may slightly alter results systematically. Because of the fairly rough half line assignment used, one might assume that the variability was not normally distributed, but that was not the case. One fourth of the measurements in the acuity group of were on different sides of the acuity value of 0.5 required for obtaining a driver s license in Finland. Both random errors and systematic errors such as learning may have an influence on the incorrect classification of car driving capability or visual handicap. A single testing of VA carried out when considering cataract extraction can also be misleading. Visual complaints are important in making decisions of whether or not there are indications for surgery, especially in borderline cases (Gibson & Sanderson 1980). In the group with the poorest vision (VA ), the SDME was logmar 0.09, which means that for a change in VA, in a single case, pthe ffi SDME for change is logmar 2*0.09 or 0.13 (Bland 1988b; difference of two random variables). Charts with a logarithmic progression of lines would increase the precision of VA measurements in clinical work. The lack of this did not, however, have any great influence on the results in the visual groups studied. It is likely that more variation would have occurred if groups with lower acuity than those used in this study had been measured. References Arditi A & Caganello R (1993): On the statistical reliability of letter chart visual acuity measurements. Invest Ophthalmol Vis Sci 34: Bailey IL (1998): Visual acuity. In: Benjamin WJ (ed). Borish s Clinical Refraction. Philadelphia: WB Saunders Company Bland M (1988a): An Introduction to Medical Statistics. Oxford: Oxford University Press 110. Bland M (1988b): Clinical measurement. In: An Introduction to Medical Statistics. Oxford: Oxford University Press Bland M & Altman D (1986): Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1: Camparini M, Cassinari P, Ferrigno L & Macaluso C (2001): ETDRS-fast: implementing psychophysical adaptive methods to standardized visual acuity measurement with ETDRS charts. Invest Ophthalmol Vis Sci 42: Ciuffreda KJ (1998): Accommodation, the pupil and presbyopia. In: Benjamin WJ (ed). Borish s Clinical Refraction. Philadelphia: WB Saunders Company Elliott DB & Sheridan M (1988): The use of accurate visual measurements in clinical anti-cataract formulation trials. Ophthalmic Physiol Opt 8: Gibson RA & Sanderson HF (1980): Observer variation in ophthalmology. Br J Ophthalmol 64: Harris WF (1990): Statistical inference on mean dioptric power: hypothesis testing and confidence regions. Ophthalmic Physiol Opt 10: Holladay JT, Lynn M, Waring GO III, Gemmill M, Keehn GC & Brooke F (1991): The relationship of visual acuity, refractive error and pupil size after radial keratotomy. Arch Ophthalmol 109: Keating MP (1980): An easier method to obtain the sphere, cylinder and axis from an off-axis dioptric power matrix. Am J Optom Physiol Optics 57: Klein R, Klein BE, Moss SE & DeMets D (1983): Inter-observer variation in refraction and visual acuity measurement using a standardized protocol. Ophthalmology 90: McGraw PV, Winn B, Gray LS & Elliott DB (2000): Improving the reliability of visual acuity measures in young children. Ophthalmic Physiol Opt 20: MedCalc Manual (1999): URL Michaels D (1975): Visual acuity. In: Visual Optics and Refraction, a Clinical Approach. Saint Louis, Missain: Mosby Raasch TW, Bailey IL & Bullimore MA (1998): Repeatability of visual acuity measurement. Optom Vis Sci 75: Rosser DA, Laidlaw DA & Murdoch IE (2001): The development of a reduced logmar visual acuity chart for use in routine clinical practice. Br J Ophthalmol 85: Siderov J & Tiu AL (1999): Variability of measurements of visual acuity in a large eye clinic. Acta Ophthalmol Scand 77: Van den Brom HJ, Kooijman AC, Blanksma JL & van Rij G (1995): Measurement of visual acuity with two different charts: a comparison of results and repeatability in patients with cataract. Doc Ophthalmol 90: Vanden Bosch ME & Wall M (1997): Visual acuity scored by the letter-by-letter or probit methods has lower retest variability than the line assignment method. Eye 11: Received on October 16th, Accepted on January 25th, Correspondence: Jaakko Leinonen MD Department of Ophthalmology Vaasa Central Hospital Hietalahdenkatu Vaasa Finland Tel: þ Fax: þ jaakko.leinonen@vshp.fi 332