June 2011
Volume 52, Issue 7
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Clinical and Epidemiologic Research  |   June 2011
A Comparison of Standard Scoring versus Rasch Scoring of the Visual Function Index-14 in Patients with Cataracts
Author Affiliations & Notes
  • Carlota Las Hayas
    From the Research Unit, Hospital Galdakao-Usansolo, CIBER Epidemiology and Public Health (CIBERESP), Usansolo, Bizkaia, Spain; and
  • Amaia Bilbao
    the Basque Foundation for Health Innovation and Research (BIOEF), CIBER Epidemiology and Public Health (CIBERESP), Sondika, Bizkaia, Spain.
  • Jose M. Quintana
    From the Research Unit, Hospital Galdakao-Usansolo, CIBER Epidemiology and Public Health (CIBERESP), Usansolo, Bizkaia, Spain; and
  • Susana Garcia
    From the Research Unit, Hospital Galdakao-Usansolo, CIBER Epidemiology and Public Health (CIBERESP), Usansolo, Bizkaia, Spain; and
  • Iratxe Lafuente
    From the Research Unit, Hospital Galdakao-Usansolo, CIBER Epidemiology and Public Health (CIBERESP), Usansolo, Bizkaia, Spain; and
  • Corresponding author: Carlota Las Hayas, CIBER Epidemiology and Public Health, Research Unit, 9th Floor, Hospital de Galdakao, Usansolo, B° Labeaga s/n, 48960 Galdakao, Vizcaya, Spain; carlota.lashayasrodriguez@osakidetza.net
  • Footnotes
    3  Members of the IRYSS Cataract Group are listed in Appendix B.
Investigative Ophthalmology & Visual Science June 2011, Vol.52, 4800-4807. doi:10.1167/iovs.10-6132
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      Carlota Las Hayas, Amaia Bilbao, Jose M. Quintana, Susana Garcia, Iratxe Lafuente, ; A Comparison of Standard Scoring versus Rasch Scoring of the Visual Function Index-14 in Patients with Cataracts. Invest. Ophthalmol. Vis. Sci. 2011;52(7):4800-4807. doi: 10.1167/iovs.10-6132.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose.: To compare the discriminatory ability and sensitivity to change of the standard summative score of the Visual Function Index (VF)-14 with two alternative Rasch-based scoring systems.

Methods.: A total of 4335 prospective patients with cataracts completed the VF-14 before surgery and 3 months after surgery. Rasch analysis was applied to the VF-14 patient responses before surgery and the VF-14 joint patient responses before and after surgery. To study the discriminatory ability, the VF-14 patient responses were grouped according to the preoperative visual acuity (VA) and the presence of ocular morbidities besides cataracts. For analysis of the sensitivity to change, the overall mean change in VF-14 scores was calculated after surgery, and the patients were grouped according to the presence of other ocular morbidities, postoperative VA gain, and satisfaction with the surgical outcome. The relative precision (RP) index and the effect size were used to compare the different scoring systems.

Results.: Rasch analysis confirmed the unidimensional structure of the VF-14. All items and scales adjusted well to the model (fit indices range, 0.71–1.34). The RP index for discrimination by ocular morbidity was 0.82 and by preoperative VA level, 1.02. Regarding sensitivity to change, the RP was 2.68 based on ocular morbidity and 1.78 with samples grouped by postoperative VA gain.

Conclusions.: For longitudinal studies in which change is the relevant outcome, Rasch scores should be used, rather than the traditional score. However, for cross-sectional studies, both scoring systems were similarly precise.

Auseful approach for assessing visual disability is questioning patients about their level of functioning. 1 Such assessments are usually based on questionnaires, in which the patient reports his or her level of ability to perform a range of different vision-related activities. 2 Since 1981, 3 a dozen visual function questionnaires have been developed, among which the Visual Function Index (VF)-14 is the one used most extensively to measure disability, especially in patients with cataracts. 4,5 This index is a measure of perceived visual function based on an itemized list of 14 everyday activities that may be affected by cataracts. It requires patients to rate the difficulty of each activity on a scale of 0 (no difficulty) to 4 (unable to do the activity). 
The VF-14 in its native form and scored with simple summative scoring has been used extensively in research. 6 8 Nevertheless, some 5,9 11 have questioned the validity of its summative scoring method based on the classical test theory. This summative scoring procedure presents various problems (i.e., there is no justification for how numerical values are assigned to response categories or for how a series of scores should be added to produce an overall score). 5 In addition, instruments such as the VF-14 are based on ordinal levels of measurement, such that, although it may be possible to determine whether change has occurred, it is difficult to estimate the degree of the change. An alternative model of questionnaire development is based on item response theory (IRT). 12 Rasch analysis is a statistical procedure within IRT that calculates item difficulty in relation to personal ability and weights the overall scores accordingly. The resulting scores are on a linear scale, allowing easy comparison of measures and easy interpretation of changes in scores. Previous studies have applied Rasch methodology to the VF-14 to shorten the questionnaire 9,13 and explore its psychometric properties. 
The purpose of the present study was to determine whether there were any empiric advantages in scoring precision when using an aggregate measure for the VF-14 based on the Rasch IRT model versus the traditional summative scoring model. 
Methods
Participants
Data for this analysis were derived from a multisite longitudinal study of patients scheduled for cataract surgery. Over 10 months, 17 Spanish public hospitals invited patients to participate if they were scheduled for phacoemulsification during the recruitment period, aged 18 years or older, and had signed an informed consent form. Exclusion criteria were patients having severe comorbidities (cancer or a terminal illness), serious psychiatric conditions, and corneal dystrophy. 
The study complied with the Declaration of Helsinki and was approved by the local human research ethics committee at each hospital. Personal data were collected to track patients before and after surgery. All data remained confidential. 
Materials
The VF-14 4 asks patients to rate their subjective functional limitations in performing 14 vision-dependent activities of daily living, even with glasses. As mentioned above, each question had five response categories (0–4). The scores are added and standardized to range from 0 (unable to perform any applicable activities) to 100 (can perform all applicable activities without difficulty). The VF-14 was translated into Spanish, adapted, and validated and shows good validity, reliability, and sensitivity to clinical changes. 14  
Procedures
At the time of the preoperative visit and approximately 12 weeks after cataract removal, patients received the VF-14 and additional questions about their ocular disease and level of surgical satisfaction by post. To increase the response rate to the questionnaire, up to two reminder letters were sent at predetermined times to nonresponders. During the preoperative visit and approximately 6 weeks after surgery, ophthalmologists and nurses collected demographic and clinical data, such as the visual acuity (VA) in the surgical eye recorded in decimal notation and ocular pathologies. 
Postoperative change scores in the VF-14 were calculated by subtracting total postoperative from the total preoperative scores. A VA gain was calculated by subtracting the postoperative from the preoperative VA. If the resulting difference was more than 0.5, it was equivalent to a gain in VA of >5 Snellen lines. On the contrary, if the difference was equal to or less than 0.5, it meant that the VA of the patient had increased by ≤5 lines after surgery. In the present study, the patients were classified into the following categories: those with a preoperative VA of 6/12 or less versus those with VA of more than 6/12, since there is evidence in the literature that a VA of more than 6/12 allows most activities to be performed without difficulty 4,15,16 ; a postoperative VA gain >5 Snellen lines versus a postoperative gain of ≤5, since evidence from past research 17 supports this categorization; simple cataracts (cataracts with no other ocular pathologies that may affect visual prognosis) versus cataracts and other ocular pathologies that may affect visual prognosis (retinopathies, maculopathies, vasculopathies, neuropathies, corneal opacity, or corneal dystrophies, except Fuchs' dystrophy), since patients with ocular morbidities other than cataracts show lower levels of functioning before surgery than patients with simple cataracts 4 and report lower gains in functioning after cataract surgery 18 ; and patients reporting that they are “very satisfied” or “somewhat satisfied” with the surgery versus those who were “dissatisfied” or “very dissatisfied.” 19 Finally, with the intention of creating two unequivocally different groups of patients to compare the discriminatory capacity and sensitivity of the two VF-14 scoring systems, summative-based versus Rasch-based approaches, we (1) divided the sample as follows: patients with a preoperative VA lower than 6/60 versus those with a preoperative VA higher than 6/12, and (2) compared the mean gain on the VF-14 after surgery between those who increased their VA ≤1 Snellen line after surgery versus those who increased their VA ≥9 Snellen lines after surgery. 
Statistical Analysis
The patient was the unit of study. When a participant underwent two interventions during the study period, we included only the first. Descriptive statistics included frequency tables and data expressed as means and standard deviations. 
Rasch Analysis.
The Rasch model assumes unidimensionality, which means that one trait drives participant responses to the items 20 and requires that individuals with greater ability obtain higher ratings for an item than those with less ability. 21 The Rasch method was applied to the VF-14, using the polytomous rating scale model because our response scales were ordinal. 22  
The functioning of the rating scale categories was examined for the VF-14 items to assess monotonicity, 23 in accordance with the criteria proposed by Linacre 24 to assess adequate functioning. Unidimensionality was assessed by the mean square infit and outfit statistics, with values between 0.7 and 1.3 indicating good fit, 25 and through principal components analysis of the residuals extracted from the Rasch model. 26 If in addition to the first factor, other factors had eigenvalues exceeding 3, it was considered to be a violation of unidimensionality. 27 To detect the presence of differential item functioning (DIF), which occurs when items are functioning in a different manner in various subgroups of subjects, 28 the different levels of the trait were compared in terms of ocular pathology (simple cataract versus cataract with other ocular morbidities), the preoperative VA level (VA ≤ 6/12 vs. VA > 6/12) and time (preoperative versus postoperative) in the stacked data (that is, data from the two time points combined, see below). Again, we followed the criteria of Linacre to assess DIF. 27 Residual correlations between items within a scale were examined for local dependency. 29 Correlations greater than 0.5 indicate that responses to one item may be dependent on the responses to another. Assessment of adequate stratification of visual functioning was examined by item and person separation indices. 30 A value of 2.0 or greater for this statistic is comparable to a reliability of 0.80 and was considered acceptable. 
To assess the constancy of difficulties with given items over time (assertion of constancy 31 ), we applied the Rasch analysis separately to the dataset of VF-14 responses before surgery and after surgery. Preoperative item difficulties were then plotted against those obtained after surgery including confidence intervals based on the calibration error. If an item was outside the confidence intervals, the item was regarded as having changed over time. 31,32 A compromise set of calibrations (assertion of compromise 33 ) can be obtained from joint analysis of the data from two time points combined (stacked data). 34 This approach provides a common average frame of reference for information from both time points. 
Standard Summative-Based Scoring versus Rasch-Based Scoring.
The standard summative-based scoring was calculated by adding the patient's ratings for all 14 items. The Rasch separate score was calculated using the scores obtained from the Rasch analysis applied to the preoperative sample. The Rasch stacked score then was calculated using the scores obtained from the Rasch analysis applied to the stacked data. Both Rasch scores also were standardized to range from 0 to 100. If fewer than 50% of the VF-14 items were missing, a person-specific estimate was inserted by averaging the available item responses and substituting this value for the missing items. If more than 50% of the items were missing, no scale score was calculated. 
The methods used to compare best performance between different scoring procedures were the relative precision (RP) and the effect size (ES) indices. 35 The former indicates how much more or less precise a new scoring method (in this case, the Rasch-based score) is relative to the standard (here, the summative-based score) in distinguishing groups expected to differ. 31 RP is calculated as the ratio of pairwise F statistics (the Rasch score F statistic divided by the summative-based score F statistic). Specifically, we examined the RP of the Rasch scoring method versus the summative-based scoring method to discriminate patient groups with known levels of functional limitations (i.e., patients classified by preoperative VA and ocular pathology) and to determine sensitivity to the relative magnitude of change after surgery in selected patient groups (i.e., patients classified by VA changes after surgery, ocular pathology, and postoperative satisfaction level). The ES index is a common measure of sensitivity (ability to detect differences between groups) and responsiveness (ability of a scale to detect changes). The formula and thresholds for calculating and interpreting ES values taken from the literature 36 categorize effect sizes of 0.2 to 0.5 as small differences, 0.5 to 0.8 as moderate differences, and 0.8 or higher as large differences. 
P < 0.05 was considered significant. The WinSteps software (version 3.69.1.4) 37 was used to conduct the Rasch analysis. All other statistical analyses were performed with commercial software (SAS for Windows, ver. 9.1; SAS Institute Inc., Cary, NC). 
Results
A total of 7438 patients scheduled for cataract extraction were identified. Of these, 907 were excluded for not meeting the inclusion criteria or for not having ophthalmic clinical data. A total of 4335 (66.3%) patients responded to the VF-14 posted to them 3 months after surgery, met inclusion criteria, and had the required clinical data. The mean age of these patients was 73.4 years (SD 8.8), and 58.2% were women. 
Rasch Analysis
Table 1 shows item difficulty, measurement error, and mean square fit indices for preoperative and postoperative samples. The items were similarly ranked in both samples. The only item with a fit index slightly above the recommended threshold was item 14, nighttime driving. Figure 1 displays the item and person map for the preoperative VF-14 scores, and Figure 2 shows the item difficulties estimated before surgery (baseline) plotted against those estimated after surgery (follow-up). Only five items fell within the 95% confidence intervals, indicating that most items were not constant over time. We stacked the data from both time points in the same dataset and performed Rasch analysis again. Results from the third Rasch analysis resulted in a calibration of item difficulties between the preoperative and postoperative data calibrations (fit indices range, 0.71–1.34; Fig. 3), but the calibrations were almost identical with the preoperative ranking. The size of the first contrast when performing the PCA of the residuals was 2.3. The first dimension explained 69.5% of the variance and the greatest contribution of a potential additional dimension was 5%. These results enabled further components to be ignored. In the three Rasch analyses, the functioning of the rating scale categories was adequately monotonic for every item; DIF was not detected, except for item 12, watching TV, in relation to time; no local dependence was found between any item; and the person and item separation indices exceeded the required value of 2.0, thereby indicating a reliability higher than 0.80. 
Table 1.
 
Indices Resulting from Rasch Analysis for Preoperative and Postoperative Samples
Table 1.
 
Indices Resulting from Rasch Analysis for Preoperative and Postoperative Samples
Item Preoperative* Postoperative†
n (%) Item Difficulty SE Infit MNSQ Outfit MNSQ n (%) Item Difficulty SE Infit MNSQ Outfit MNSQ
14 961 (22.17) 1.80 0.05 1.33 1.32 839 (19.35) 1.79 0.02 1.36 1.43
1 4050 (93.43) 1.70 0.02 1.23 1.24 3982 (91.86) 1.94 0.02 1.15 1.21
2 3956 (91.26) 1.14 0.02 0.93 0.91 3918 (90.38) 1.31 0.03 0.94 0.86
7 3821 (88.14) 0.90 0.02 1.01 0.99 3674 (84.75) 1.19 0.03 0.95 0.93
8 4012 (92.55) 0.10 0.02 0.91 0.87 3952 (91.16) 0.49 0.03 0.96 0.89
13 1014 (23.39) −0.02 0.04 1.16 1.10 943 (21.75) −0.45 0.07 1.19 1.03
12 4198 (96.84) −0.03 0.02 0.95 1.03 4176 (96.33) −0.54 0.03 1.01 1.16
6 3976 (91.72) −0.16 0.02 1.02 1.05 4044 (93.29) −0.51 0.03 0.99 0.97
3 4030 (92.96) −0.55 0.02 1.07 1.04 4012 (92.55) −0.49 0.03 1.20 0.95
5 4200 (96.89) −0.57 0.02 1.02 1.07 4178 (96.38) −0.60 0.03 1.05 1.16
10 3452 (79.63) −0.77 0.02 0.82 0.81 3507 (80.90) −0.71 0.04 0.87 0.71
9 2735 (63.09) −0.83 0.03 0.77 0.70 2817 (64.98) −0.71 0.04 0.89 0.72
4 4197 (96.82) −1.29 0.02 1.11 1.12 4184 (96.52) −1.58 0.04 1.11 0.99
11 3351 (77.30) −1.43 0.03 0.88 0.85 3342 (77.09) −1.11 0.04 1.06 1.01
Figure 1.
 
Item-person map of the VF-14 for preoperative data (n = 4335). Both individuals and items are presented on the same logit scale.
Figure 1.
 
Item-person map of the VF-14 for preoperative data (n = 4335). Both individuals and items are presented on the same logit scale.
Figure 2.
 
Comparison of item difficulties (n = 4335).
Figure 2.
 
Comparison of item difficulties (n = 4335).
Figure 3.
 
Item difficulty scores based on separate and stacked Rasch analysis.
Figure 3.
 
Item difficulty scores based on separate and stacked Rasch analysis.
Summative scores, preoperative and stacked Rasch scores, and the corresponding standardized 0 to 100 scores are shown in Appendix A, to facilitate use of the VF-14 by practitioners and researchers. 
RP and Clinical Discrimination
Comparisons of the RPs and ES values of the three scoring methods for discriminating between clinical groups differing in ocular morbidity and preoperative VA are presented in Table 2. Patients with simple cataracts had higher mean preoperative VF-14 scores than patients with cataracts and other ocular morbidities (P < 0.0001). These results were replicated for all three scoring systems. Nevertheless, the summative score showed advantages over either of the Rasch scores for discriminating between patients based on ocular pathology (Rasch separate and Rasch stacked versus summative RP were 0.83 and 0.82, respectively; summative ES = 0.23, Rasch separate ES = 0.21; Rasch stacked ES = 0.21) and extreme preoperative VA groups (Rasch separate and Rasch stacked versus summative RP were 0.87 and 0.86, respectively; summative ES = 0.76, Rasch separate ES = 0.70; Rasch stacked ES = 0.70). 
Table 2.
 
Comparisons of the RP and ES Values of the Three Scoring Methods for Discriminating between Clinical Groups differing in Ocular Morbidity and Preoperative VA
Table 2.
 
Comparisons of the RP and ES Values of the Three Scoring Methods for Discriminating between Clinical Groups differing in Ocular Morbidity and Preoperative VA
Scoring System Simple Cataract Cataract with Comorbidities Difference between Groups F RP ES
Ocular Pathology
n 3197 969
Summative 62.34 (0.39) 57.09 (0.75) 5.25 (0.82) 41.01 1.00 0.23
Rasch separate 59.79 (0.26) 56.66 (0.48) 3.13 (0.54) 34.03 0.83 0.21
Rasch stacked 59.28 (0.26) 56.17 (0.48) 3.11 (0.54) 33.63 0.82 0.21
Preoperative VA
VA ≤6/12 >6/12
n 3933 201
Summative 60.75 (0.36) 68.83 (1.39) 8.09 (1.62) 24.97 1.00 0.36
Rasch separate 58.82 (0.23) 64.16 (0.96) 5.33 (1.06) 25.45 1.02 0.36
Rasch stacked 58.31 (0.23) 63.64 (0.97) 5.33 (1.06) 25.38 1.02 0.36
Extreme Preoperative VA
VA <6/60 >6/12
n 484 201
Summative 49.99 (1.22) 68.83 (1.39) 18.85 (2.09) 81.04 1.00 0.76
Rasch separate 51.81 (0.86) 64.16 (0.96) 12.35 (1.47) 70.32 0.87 0.70
Rasch stacked 51.38 (0.86) 63.64 (0.97) 12.26 (1.47) 69.84 0.86 0.70
Scoring systems were also compared according to their ability to discriminate groups in relation to the gains in VF-14 scores. Table 3 shows the mean change scores in VF-14 according to ocular morbidities, postoperative VA gain, extreme postoperative VA gain, and satisfaction with the surgical outcome. The Rasch scoring methods were better at distinguishing between these four patient groups. Specifically, the Rasch stacked scoring was almost three times more effective than the summative scoring method for detecting gains in visual function in patients with simple cataracts than in patients with other ocular morbidities. The Rasch stacking method was also 78% better at discriminating between gains according to VA change, 51% better at discriminating between gains according to extreme groups, and 12% more able to discriminate between satisfaction groups. 
Table 3.
 
Mean Score Change Based on Ocular Pathology, Change in VA, and Satisfaction
Table 3.
 
Mean Score Change Based on Ocular Pathology, Change in VA, and Satisfaction
Scoring System Simple Cataract Cataract with Comorbidities Mean Difference between Groups F RP ES
Ocular Pathology
n 3070 936
Summative 24.62 (0.43) 21.51 (0.83) 3.11 (0.90) 11.92 1.00 0.13
Rasch separate 20.31 (0.34) 16.36 (0.63) 3.95 (0.71) 31.09 2.52 0.21
Rasch stacked 20.52 (0.34) 16.49 (0.63) 4.03 (0.71) 31.90 2.68 0.21
VA Change (Snellen Lines Gained)
VA ≤5 >5
n 2182 1572
Summative 22.47 (0.51) 26.56 (0.60) 4.10 (0.79) 26.88 1.00 0.17
Rasch separate 17.82 (0.40) 22.12 (0.48) 4.30 (0.62) 47.64 1.77 0.23
Rasch stacked 18.00 (0.40) 22.34 (0.48) 4.35 (0.63) 47.96 1.78 0.23
Extreme VA Change (Snellen Lines Gained)
VA ≤1 Line ≥9 Lines
n 365 193
Summative 14.08 (1.37) 31.99 (1.71) 17.92 (2.26) 62.84 1.00 0.71
Rasch separate 10.61 (1.03) 27.20 (1.32) 16.59 (1.71) 93.72 1.49 0.86
Rasch stacked 10.71 (1.04) 27.48 (1.33) 16.77 (1.72) 94.88 1.51 0.87
Postoperative Satisfaction
Satisfied Dissatisfied
n 3126 345
Summative 27.96 (0.41) 1.55 (1.34) 26.40 (1.31) 409.31 1.00 1.09
Rasch separate 22.99 (0.32) 1.19 (0.94) 21.81 (1.02) 456.19 1.11 1.15
Rasch stacked 23.23 (0.33) 1.22 (0.94) 22.01 (1.03) 458.00 1.12 1.15
RP and Sensitivity to Change
Table 4 shows the within-group comparison for the preoperative and 3-month postoperative scores according to the three scoring methods, their RP indices, and ES values. Of the five within-group comparisons, the RP gains with Rasch scoring compared with the summative scoring procedure ranged from 1% for changes in patients with cataracts and other ocular comorbidities to 10% for the changes in patients who gained >5 Snellen lines in postoperative VA. The ES values were also higher for the Rasch-based scorings than for the summative-based scoring for all within-group comparisons. 
Table 4.
 
Mean Score Based on Ocular Pathology, Change in VA, and Satisfaction
Table 4.
 
Mean Score Based on Ocular Pathology, Change in VA, and Satisfaction
Scoring System Preoperative Mean (SD) Postoperative Mean (SD) Change Mean (SE) F RP ES
Overall
    Summative 61.53 (22.21) 85.42 (17.82) 23.90 (0.38) 3913.75 1.00 1.08
    Rasch separate 59.32 (14.46) 78.71 (16.84) 19.39 (0.30) 4158.96 1.06 1.34
    Rasch stacked 58.81 (14.47) 78.39 (17.04) 19.58 (0.30) 4177.04 1.07 1.35
Ocular pathology
    Simple cataract
        Summative 62.81 (21.76) 87.44 (15.59) 24.62 (0.43) 3310.85 1.00 1.13
        Rasch separate 60.10 (14.28) 80.41 (15.82) 20.31 (0.34) 3560.51 1.08 1.42
        Rasch stacked 59.58 (14.31) 80.11 (16.03) 20.52 (0.34) 3576.04 1.08 1.43
    Cataract with comorbidities
        Summative 57.31 (23.16) 78.82 (22.49) 21.51 (0.83) 665.64 1.00 0.93
        Rasch separate 56.77 (14.76) 73.13 (18.77) 16.36 (0.63) 674.44 1.01 1.11
        Rasch stacked 56.27 (14.73) 72.76 (18.92) 16.49 (0.63) 677.04 1.02 1.12
Change in VA (Snellen lines gained)
    ≤0.5
        Summative 61.01 (22.30) 83.48 (19.45) 22.47 (0.51) 1936.88 1.00 1.01
        Rasch separate 59.07 (14.53) 76.89 (17.45) 17.82 (0.40) 1991.84 1.03 1.23
        Rasch stacked 58.56 (14.54) 76.56 (17.63) 18.00 (0.40) 2000.77 1.03 1.24
    >0.5
        Summative 62.11 (22.01) 88.68 (14.11) 26.56 (0.60) 1933.36 1.00 1.21
        Rasch separate 59.63 (14.11) 81.75 (15.40) 22.12 (0.48) 2119.68 1.10 1.57
        Rasch stacked 59.12 (14.13) 81.46 (15.63) 22.34 (0.48) 2127.05 1.10 1.58
Discussion
The purpose of this study was to determine whether there were potential gains from improved measurement of outcomes on the VF-14 by using Rasch scoring over the standard raw summative scoring. To do so, we performed a new Rasch analysis of the VF-14. The results showed that the VF-14 measures only one construct (i.e., functioning), each rating scale is monotonic, items are locally independent, and the test does not present differential item functioning. The Rasch method has been applied to the Visual Function Index 9,13,21,38 40 in other studies and to other cataract related questionnaires such as the Refractive Status and Vision Profile. 41 We again applied the Rasch method to the VF-14 in our study because we had access to a very large sample of subjects with cataracts (n = 4335). They were all Spanish and so the results were easily generalizable within the culture. Thus, we believed that this research would provide valuable information. Comparing our results with other studies, the items identified by Rasch analysis as easier and more difficult in our sample were similar to those identified in previous Rasch analyses. 13,21,38,40 Overall, the easiest items were related to cooking and recognizing people nearby, and the most difficult were reading small print, such as labels on medicine bottles, telephone books, and food labels, and nighttime driving. Compared with other studies, the current Rasch results showed better unidimensionality of the VF-14, given that only nighttime driving showed a slight misfit. Other studies 21,39,42 also reported difficulties with the same item, arguing that night driving may be impaired by cataract-induced glare, and patients may have difficulty with nighttime driving without having difficulty with other activities on the VF-14. 42 In addition, in many countries, including Spain, it is common that older patients do not drive. 21 To evaluate whether this misfitting item (driving at night) could reduce the discriminative ability of the Rasch version we repeated the analysis excluding that item. The resulting RP indices were almost identical with those obtained including the item (results not shown). 
Once we obtained a satisfactory Rasch analysis of the VF-14, we compared two alternative Rasch-based scoring systems with summative-based scoring to assess cross-discrimination and sensitivity to change. Our results showed some gains in precision over summative-based scoring using the Rasch scoring in discriminating between patient groups expected to differ in the extent of change because of ocular comorbidities, the amount of postoperative VA gain, or the retrospective level of surgical satisfaction. Of the two Rasch scoring methods, the second, derived from stacked data, generated consistently greater RP gains in distinguishing groups defined by both clinical and patient-based criteria. A study by Garamendi et al., using a cross-sectional design, 41 also showed a 10% gain in RP index for the Rasch version of the Refractive Status and Vision Profile questionnaire over the standard summative version. 
A study by Gothwal et al. 39 presents significant similarities with ours. Particularly, they also examined whether Rasch-based scoring of the VF-14 measured cataract surgery outcome more precisely than the Likert-based scoring. Furthermore, they stacked their data (n = 51) before and after surgery (6 months after surgery) and performed a Rasch analysis, using Winsteps software. They demonstrated an unequivocal advantage of using Rasch-based scoring of the VF-14 for assessing cataract surgery outcomes. On the other hand, there are differences between the two studies. The main purpose of their study was to determine the best version of the VF-14 for assessing the change in visual functioning after cataract surgery. So they used the Rasch method to develop two shorter versions: the VF-11R and the VF-8R. Indeed, the RP indices that they provided point to a better precision being obtained with the short forms of the VF-14 in comparison to the original VF-14. On the contrary, in our study, we assessed the RP of the comprehensive and original versions of the VF-14, using either Likert or Rasch-based scoring. Compared to our results, Gothwal et al. 39 found higher RP indices for detecting change in visual function after surgery. Whereas their VF-11R version gained 98% precision over the original VF-14 version, our Rasch scorings of the VF-14 gained only 6% (separate version) and 7% (stacked version). In the group of cataract surgery patients who had ocular comorbidities, Gothwal et al. 39 found a precision gain of 77%, whereas we found only a 1% to 2% gain in precision. Last, they reported a gain in precision of 144% when detecting change in cataract patients with no ocular comorbidity, and we found a relatively minor difference between the Rasch and the Likert forms (8% gain in precision). These differences may be explained by the composition of the versions of the Visual Function Index involved: Gothwal et al. 39 used a short form version, the VF-11R (resulting from the deletion of three items that showed misfit), and we used the original, comprehensive, nonaltered 14-item version. It seems likely that deleting items that according to the Rasch method worsen targeting the construct would lead to better discrimination indices. Nevertheless, our intention was not to develop the most discriminative Visual Function Index, rather we set out to ascertain which scoring system (Rasch versus Likert) produced better indices of discrimination when applied to the same sample. This is the reason that we did not continue to further analyze the VF-14 questionnaire and delete items. We were interested in the comprehensive version of the VF-14, as is, and as it is used in most clinical settings. 
The discriminative ability of the VF-14 had already been explored in a study of its development. 4 Our results also indicated that the VF-14 adequately discriminates between different known patient groups, using either the Rasch or traditional scoring system. The reported ES values obtained using the standard method of scoring are similar to those reported in a study of responsiveness and reproducibility of the VF-14. 43 Our results found higher ES values for the VF-14 in detecting change across time than for its ability to discriminate between groups. In particular, the Rasch stacked scoring of the VF-14 obtained better precision indices than the raw summative method in detecting postoperative change and obtained similar or lower precision in discriminating among patient groups at baseline. Our results show that the Rasch scoring is more precise than the summative scoring in detecting change over time, and similarly or a bit less precise in discriminating between groups at baseline. A possible explanation of these results relates to the potential benefits of Rasch-based scoring over summative-based scoring for measuring health outcomes. 42 As noted in other studies, 39,44,45 Rasch-based scoring reduces standard errors and increases measurement precision, by expanding scales at the upper and lower extremes of the range of the scale compared with summative-based scoring, whereas there is greater linearity between the two methods in the middle, 46 which implies a lower percentage of patients with extreme scores when using the Rasch-based scoring. The difference in this percentage between Rasch and summative-based approaches is particularly evident after surgery. Many patients improve their visual function as a consequence of surgery; therefore, they score closer to the upper extremes. To illustrate this, according to the summative-based scoring, 53.83% of our study sample scored ≥90 in the VF-14 after surgery, in contrast to Rasch-based scoring (stacked data) which found only 33.3% in that extreme range. Consequently, the Rasch-based scoring performs better than the summative-based scoring in detecting changes, since both preoperative and postoperative scores are involved. 
The prospective design of the present study and the large sample of patients with cataracts are among the study strengths. A limitation was that we applied only one possible method of Rasch analysis; other Rasch methods might have produced a different pattern of results. 
Our findings suggest that, if feasible, gains in precision over a summative-based scoring approach are achieved by using the Rasch scoring model for longitudinal design studies that are designed to detect change. Either scoring system is valid for cross-sectional design studies, in which the primary goal is to detect differences between groups of patients. 
Footnotes
 Supported in part by Grants PI03/0550, PI03/0724, PI03/0471, PI03/0828, and PI04/1577 from the Spanish Fondo de Investigación Sanitaria; Grant (2003/11045) from the Department of Health of the Basque Country; and Grant G03/220 from the thematic network IRYSS of the Carlos III Health Institute.
Footnotes
 Disclosure: C. Las Hayas, None; A. Bilbao, None; J.M. Quintana, None; S. Garcia, None; I. Lafuente, None
The authors thank the staff members of the different services, research quality units, and medical records sections of the participating hospitals for their support and the patients for participating in the study. 
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Appendix A
Table A1.
 
Comparison of VF-14 Summative Scores, Rasch Separate Scores, and Rasch Stacked Scores, All Raw and Standardized to a 0 to 100 Scale
Table A1.
 
Comparison of VF-14 Summative Scores, Rasch Separate Scores, and Rasch Stacked Scores, All Raw and Standardized to a 0 to 100 Scale
Summative Score Rasch Separate Score Rasch Stacked Score Summative Score Rasch Separate Score Rasch Stacked Score
Raw 0–100 Raw 0–100 Raw 0–100 Raw 0–100 Raw 0–100 Raw 0–100
0 0.00 −6.98 0.00 −6.84 0.00 29 51.79 0.26 53.71 0.22 53.04
1 1.79 −5.71 9.42 −5.57 9.54 30 53.57 0.37 54.53 0.33 53.87
2 3.57 −4.91 15.36 −4.78 15.48 31 55.36 0.48 55.34 0.44 54.70
3 5.36 −4.41 19.07 −4.28 19.23 32 57.14 0.60 56.23 0.55 55.52
4 7.14 −4.02 21.96 −3.90 22.09 33 58.93 0.71 57.05 0.67 56.42
5 8.93 −3.69 24.41 −3.58 24.49 34 60.71 0.83 57.94 0.78 57.25
6 10.71 −3.40 26.56 −3.30 26.60 35 62.50 0.94 58.75 0.89 58.08
7 12.50 −3.14 28.49 −3.05 28.47 36 64.29 1.06 59.64 1.01 58.98
8 14.29 −2.90 30.27 −2.82 30.20 37 66.07 1.17 60.46 1.12 59.80
9 16.07 −2.68 31.90 −2.60 31.86 38 67.86 1.29 61.35 1.24 60.71
10 17.86 −2.47 33.46 −2.40 33.36 39 69.64 1.41 62.24 1.37 61.68
11 19.64 −2.27 34.94 −2.21 34.79 40 71.43 1.54 63.20 1.49 62.58
12 21.43 −2.08 36.35 −2.03 36.14 41 73.21 1.67 64.17 1.62 63.56
13 23.21 −1.91 37.61 −1.86 37.42 42 75.00 1.80 65.13 1.75 64.54
14 25.00 −1.73 38.95 −1.70 38.62 43 76.79 1.94 66.17 1.89 65.59
15 26.79 −1.57 40.13 −1.54 39.82 44 78.57 2.08 67.21 2.03 66.64
16 28.57 −1.41 41.32 −1.39 40.95 45 80.36 2.23 68.32 2.18 67.77
17 30.36 −1.26 42.43 −1.25 42.00 46 82.14 2.39 69.51 2.34 68.97
18 32.14 −1.12 43.47 −1.11 43.05 47 83.93 2.55 70.70 2.51 70.25
19 33.93 −0.98 44.51 −0.97 44.10 48 85.71 2.73 72.03 2.69 71.60
20 35.71 −0.84 45.55 −0.84 45.08 49 87.50 2.93 73.52 2.89 73.10
21 37.50 −0.71 46.51 −0.72 45.98 50 89.29 3.15 75.15 3.11 74.76
22 39.29 −0.58 47.48 −0.59 46.96 51 91.07 3.39 76.93 3.35 76.56
23 41.07 −0.45 48.44 −0.47 47.86 52 92.86 3.68 79.08 3.64 78.74
24 42.86 −0.33 49.33 −0.35 48.76 53 94.64 4.03 81.68 3.99 81.37
25 44.64 −0.21 50.22 −0.24 49.59 54 96.43 4.50 85.16 4.46 84.90
26 46.43 −0.09 51.11 −0.12 50.49 55 98.21 5.25 90.73 5.22 90.61
27 48.21 0.03 52.00 −0.01 51.31 56 100.00 6.50 100.00 6.47 100.00
28 50.00 0.14 52.82 0.11 52.22
Appendix B
The IRYSS Cataract Group
Antonio Escobar (Unidad de Investigación, Hospital Basurto, Bizkaia/CIBER (Centro Investigación en Red de Epidemiología y Salud Pública [CIBERESP], Spain); Txomin Alberdi (Servicio de Oftalmología, Hospital Galdakao-Usansolo, Bizkaia, Spain); Jesús Martínez-Tapias and Eduardo Briones (Hospital Universitario Virgen de Valme, Sevilla, Spain); Marisa Baré and Gemma Navarro (Unidad de Epidemiología y Evaluación, Corporació Sanitaria Parc Taulí, Sabadell, Spain); Elena Andradas, Juan Antonio Blasco, and Nerea Fernández de Larrea (Unidad de Evaluación de Tecnologías Sanitarias, Agencia Laín Entralgo, Madrid, Spain); José M. Beguiristain and Belén Elizalde (Dirección Territorial de Gipuzkoa, Spain); Idoia Garai (Dirección Territorial de Bizkaia, Spain); Felipe Aizpuru (Unidad de Investigación, Hospital Txagorritxu, Araba/CIBER de Epidemiología y Salud Pública-CIBERESP, Spain); Inmaculada Arostegui (Departamento de Matemática Aplicada, UPV-CIBER Epidemiología y Salud Pública (CIBERESP, Spain); and Nerea González and Urko Aguirre, (Unidad de Investigación, Hospital Galdakao-Usansolo, Bizkaia/CIBER de Epidemiología y Salud Pública-CIBERESP, Spain). 
Figure 1.
 
Item-person map of the VF-14 for preoperative data (n = 4335). Both individuals and items are presented on the same logit scale.
Figure 1.
 
Item-person map of the VF-14 for preoperative data (n = 4335). Both individuals and items are presented on the same logit scale.
Figure 2.
 
Comparison of item difficulties (n = 4335).
Figure 2.
 
Comparison of item difficulties (n = 4335).
Figure 3.
 
Item difficulty scores based on separate and stacked Rasch analysis.
Figure 3.
 
Item difficulty scores based on separate and stacked Rasch analysis.
Table 1.
 
Indices Resulting from Rasch Analysis for Preoperative and Postoperative Samples
Table 1.
 
Indices Resulting from Rasch Analysis for Preoperative and Postoperative Samples
Item Preoperative* Postoperative†
n (%) Item Difficulty SE Infit MNSQ Outfit MNSQ n (%) Item Difficulty SE Infit MNSQ Outfit MNSQ
14 961 (22.17) 1.80 0.05 1.33 1.32 839 (19.35) 1.79 0.02 1.36 1.43
1 4050 (93.43) 1.70 0.02 1.23 1.24 3982 (91.86) 1.94 0.02 1.15 1.21
2 3956 (91.26) 1.14 0.02 0.93 0.91 3918 (90.38) 1.31 0.03 0.94 0.86
7 3821 (88.14) 0.90 0.02 1.01 0.99 3674 (84.75) 1.19 0.03 0.95 0.93
8 4012 (92.55) 0.10 0.02 0.91 0.87 3952 (91.16) 0.49 0.03 0.96 0.89
13 1014 (23.39) −0.02 0.04 1.16 1.10 943 (21.75) −0.45 0.07 1.19 1.03
12 4198 (96.84) −0.03 0.02 0.95 1.03 4176 (96.33) −0.54 0.03 1.01 1.16
6 3976 (91.72) −0.16 0.02 1.02 1.05 4044 (93.29) −0.51 0.03 0.99 0.97
3 4030 (92.96) −0.55 0.02 1.07 1.04 4012 (92.55) −0.49 0.03 1.20 0.95
5 4200 (96.89) −0.57 0.02 1.02 1.07 4178 (96.38) −0.60 0.03 1.05 1.16
10 3452 (79.63) −0.77 0.02 0.82 0.81 3507 (80.90) −0.71 0.04 0.87 0.71
9 2735 (63.09) −0.83 0.03 0.77 0.70 2817 (64.98) −0.71 0.04 0.89 0.72
4 4197 (96.82) −1.29 0.02 1.11 1.12 4184 (96.52) −1.58 0.04 1.11 0.99
11 3351 (77.30) −1.43 0.03 0.88 0.85 3342 (77.09) −1.11 0.04 1.06 1.01
Table 2.
 
Comparisons of the RP and ES Values of the Three Scoring Methods for Discriminating between Clinical Groups differing in Ocular Morbidity and Preoperative VA
Table 2.
 
Comparisons of the RP and ES Values of the Three Scoring Methods for Discriminating between Clinical Groups differing in Ocular Morbidity and Preoperative VA
Scoring System Simple Cataract Cataract with Comorbidities Difference between Groups F RP ES
Ocular Pathology
n 3197 969
Summative 62.34 (0.39) 57.09 (0.75) 5.25 (0.82) 41.01 1.00 0.23
Rasch separate 59.79 (0.26) 56.66 (0.48) 3.13 (0.54) 34.03 0.83 0.21
Rasch stacked 59.28 (0.26) 56.17 (0.48) 3.11 (0.54) 33.63 0.82 0.21
Preoperative VA
VA ≤6/12 >6/12
n 3933 201
Summative 60.75 (0.36) 68.83 (1.39) 8.09 (1.62) 24.97 1.00 0.36
Rasch separate 58.82 (0.23) 64.16 (0.96) 5.33 (1.06) 25.45 1.02 0.36
Rasch stacked 58.31 (0.23) 63.64 (0.97) 5.33 (1.06) 25.38 1.02 0.36
Extreme Preoperative VA
VA <6/60 >6/12
n 484 201
Summative 49.99 (1.22) 68.83 (1.39) 18.85 (2.09) 81.04 1.00 0.76
Rasch separate 51.81 (0.86) 64.16 (0.96) 12.35 (1.47) 70.32 0.87 0.70
Rasch stacked 51.38 (0.86) 63.64 (0.97) 12.26 (1.47) 69.84 0.86 0.70
Table 3.
 
Mean Score Change Based on Ocular Pathology, Change in VA, and Satisfaction
Table 3.
 
Mean Score Change Based on Ocular Pathology, Change in VA, and Satisfaction
Scoring System Simple Cataract Cataract with Comorbidities Mean Difference between Groups F RP ES
Ocular Pathology
n 3070 936
Summative 24.62 (0.43) 21.51 (0.83) 3.11 (0.90) 11.92 1.00 0.13
Rasch separate 20.31 (0.34) 16.36 (0.63) 3.95 (0.71) 31.09 2.52 0.21
Rasch stacked 20.52 (0.34) 16.49 (0.63) 4.03 (0.71) 31.90 2.68 0.21
VA Change (Snellen Lines Gained)
VA ≤5 >5
n 2182 1572
Summative 22.47 (0.51) 26.56 (0.60) 4.10 (0.79) 26.88 1.00 0.17
Rasch separate 17.82 (0.40) 22.12 (0.48) 4.30 (0.62) 47.64 1.77 0.23
Rasch stacked 18.00 (0.40) 22.34 (0.48) 4.35 (0.63) 47.96 1.78 0.23
Extreme VA Change (Snellen Lines Gained)
VA ≤1 Line ≥9 Lines
n 365 193
Summative 14.08 (1.37) 31.99 (1.71) 17.92 (2.26) 62.84 1.00 0.71
Rasch separate 10.61 (1.03) 27.20 (1.32) 16.59 (1.71) 93.72 1.49 0.86
Rasch stacked 10.71 (1.04) 27.48 (1.33) 16.77 (1.72) 94.88 1.51 0.87
Postoperative Satisfaction
Satisfied Dissatisfied
n 3126 345
Summative 27.96 (0.41) 1.55 (1.34) 26.40 (1.31) 409.31 1.00 1.09
Rasch separate 22.99 (0.32) 1.19 (0.94) 21.81 (1.02) 456.19 1.11 1.15
Rasch stacked 23.23 (0.33) 1.22 (0.94) 22.01 (1.03) 458.00 1.12 1.15
Table 4.
 
Mean Score Based on Ocular Pathology, Change in VA, and Satisfaction
Table 4.
 
Mean Score Based on Ocular Pathology, Change in VA, and Satisfaction
Scoring System Preoperative Mean (SD) Postoperative Mean (SD) Change Mean (SE) F RP ES
Overall
    Summative 61.53 (22.21) 85.42 (17.82) 23.90 (0.38) 3913.75 1.00 1.08
    Rasch separate 59.32 (14.46) 78.71 (16.84) 19.39 (0.30) 4158.96 1.06 1.34
    Rasch stacked 58.81 (14.47) 78.39 (17.04) 19.58 (0.30) 4177.04 1.07 1.35
Ocular pathology
    Simple cataract
        Summative 62.81 (21.76) 87.44 (15.59) 24.62 (0.43) 3310.85 1.00 1.13
        Rasch separate 60.10 (14.28) 80.41 (15.82) 20.31 (0.34) 3560.51 1.08 1.42
        Rasch stacked 59.58 (14.31) 80.11 (16.03) 20.52 (0.34) 3576.04 1.08 1.43
    Cataract with comorbidities
        Summative 57.31 (23.16) 78.82 (22.49) 21.51 (0.83) 665.64 1.00 0.93
        Rasch separate 56.77 (14.76) 73.13 (18.77) 16.36 (0.63) 674.44 1.01 1.11
        Rasch stacked 56.27 (14.73) 72.76 (18.92) 16.49 (0.63) 677.04 1.02 1.12
Change in VA (Snellen lines gained)
    ≤0.5
        Summative 61.01 (22.30) 83.48 (19.45) 22.47 (0.51) 1936.88 1.00 1.01
        Rasch separate 59.07 (14.53) 76.89 (17.45) 17.82 (0.40) 1991.84 1.03 1.23
        Rasch stacked 58.56 (14.54) 76.56 (17.63) 18.00 (0.40) 2000.77 1.03 1.24
    >0.5
        Summative 62.11 (22.01) 88.68 (14.11) 26.56 (0.60) 1933.36 1.00 1.21
        Rasch separate 59.63 (14.11) 81.75 (15.40) 22.12 (0.48) 2119.68 1.10 1.57
        Rasch stacked 59.12 (14.13) 81.46 (15.63) 22.34 (0.48) 2127.05 1.10 1.58
Table A1.
 
Comparison of VF-14 Summative Scores, Rasch Separate Scores, and Rasch Stacked Scores, All Raw and Standardized to a 0 to 100 Scale
Table A1.
 
Comparison of VF-14 Summative Scores, Rasch Separate Scores, and Rasch Stacked Scores, All Raw and Standardized to a 0 to 100 Scale
Summative Score Rasch Separate Score Rasch Stacked Score Summative Score Rasch Separate Score Rasch Stacked Score
Raw 0–100 Raw 0–100 Raw 0–100 Raw 0–100 Raw 0–100 Raw 0–100
0 0.00 −6.98 0.00 −6.84 0.00 29 51.79 0.26 53.71 0.22 53.04
1 1.79 −5.71 9.42 −5.57 9.54 30 53.57 0.37 54.53 0.33 53.87
2 3.57 −4.91 15.36 −4.78 15.48 31 55.36 0.48 55.34 0.44 54.70
3 5.36 −4.41 19.07 −4.28 19.23 32 57.14 0.60 56.23 0.55 55.52
4 7.14 −4.02 21.96 −3.90 22.09 33 58.93 0.71 57.05 0.67 56.42
5 8.93 −3.69 24.41 −3.58 24.49 34 60.71 0.83 57.94 0.78 57.25
6 10.71 −3.40 26.56 −3.30 26.60 35 62.50 0.94 58.75 0.89 58.08
7 12.50 −3.14 28.49 −3.05 28.47 36 64.29 1.06 59.64 1.01 58.98
8 14.29 −2.90 30.27 −2.82 30.20 37 66.07 1.17 60.46 1.12 59.80
9 16.07 −2.68 31.90 −2.60 31.86 38 67.86 1.29 61.35 1.24 60.71
10 17.86 −2.47 33.46 −2.40 33.36 39 69.64 1.41 62.24 1.37 61.68
11 19.64 −2.27 34.94 −2.21 34.79 40 71.43 1.54 63.20 1.49 62.58
12 21.43 −2.08 36.35 −2.03 36.14 41 73.21 1.67 64.17 1.62 63.56
13 23.21 −1.91 37.61 −1.86 37.42 42 75.00 1.80 65.13 1.75 64.54
14 25.00 −1.73 38.95 −1.70 38.62 43 76.79 1.94 66.17 1.89 65.59
15 26.79 −1.57 40.13 −1.54 39.82 44 78.57 2.08 67.21 2.03 66.64
16 28.57 −1.41 41.32 −1.39 40.95 45 80.36 2.23 68.32 2.18 67.77
17 30.36 −1.26 42.43 −1.25 42.00 46 82.14 2.39 69.51 2.34 68.97
18 32.14 −1.12 43.47 −1.11 43.05 47 83.93 2.55 70.70 2.51 70.25
19 33.93 −0.98 44.51 −0.97 44.10 48 85.71 2.73 72.03 2.69 71.60
20 35.71 −0.84 45.55 −0.84 45.08 49 87.50 2.93 73.52 2.89 73.10
21 37.50 −0.71 46.51 −0.72 45.98 50 89.29 3.15 75.15 3.11 74.76
22 39.29 −0.58 47.48 −0.59 46.96 51 91.07 3.39 76.93 3.35 76.56
23 41.07 −0.45 48.44 −0.47 47.86 52 92.86 3.68 79.08 3.64 78.74
24 42.86 −0.33 49.33 −0.35 48.76 53 94.64 4.03 81.68 3.99 81.37
25 44.64 −0.21 50.22 −0.24 49.59 54 96.43 4.50 85.16 4.46 84.90
26 46.43 −0.09 51.11 −0.12 50.49 55 98.21 5.25 90.73 5.22 90.61
27 48.21 0.03 52.00 −0.01 51.31 56 100.00 6.50 100.00 6.47 100.00
28 50.00 0.14 52.82 0.11 52.22
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