purpose. To investigate the underestimation of field loss in functional field score (FFS) between the Goldmann isopters III-4e and V-4e in visually impaired patients, in order to develop a predictive model for the FFS_{III-4e} based on FFS_{v-4e} that adjusts for possible confounders. Although the visual field is generally evaluated using Goldmann isopter III-4e, it has the disadvantage that not all low-vision patients are able to see the stimulus corresponding to this isopter.

methods. Goldmann visual fields were obtained from 58 patients with a variety of eye diseases. Eligibility criteria were age of 18 years or older and valid results of a Goldmann III-4e and V-4e visual field test in at least one eye. Linear regression was used to develop the model, setting FFS_{III-4e} as the dependent variable and FFS_{V-4e} as the independent one.

results. The FFS_{V-4e} was higher than the FFS_{III-4e}, the mean difference being 14.56 points (95% CI, 12.48 –16.64). Multiple linear regression analysis showed that age, functional acuity score, primary eye disease, and central–peripheral loss were not confounders for the prediction of FFS_{III-4e}. FFS_{III-4e} was estimated with the following equation: FFS_{III-4e} = −19.25 + 1.063 · FFS_{V-4e}.

conclusions. The relationship between FFS_{III-4e} and FFS_{V-4e} is linear, and the FFS_{V-4e} can be used to estimate the FFS_{III-4e}. In practice, just subtracting 19.25 points of the value of FFS_{V-4e} will be sufficient to estimate the value of FFS_{III-4e}. This model should give confidence about using the bigger isopter for determining the visual impairment of a person by the FFS.

^{ 1 }The isopter that is generally used to evaluate the visual field of the patient is the Goldmann isopter III-4e, and legal blindness currently requires a visual field defined in terms of the size of the isopter generated by a Goldmann III-4e stimulus. The Goldmann III-4e stimulus consists of a target of 4 mm

^{2}with a luminance of 318 cd/m

^{2}(1000 apostilbs) projected onto a background luminance of 10 cd/m

^{2}(31.5 apostilbs).

^{ 2 }

^{ 3 }In such cases, the size V stimulus seems to be preferable.

^{ 4 }The Goldmann V-4e stimulus consists of a target of 64 mm

^{2}with a luminance of 318 cd/m

^{2}. Compared to stimulus III-4e, this means a 16-fold increase in area of the stimulus, although the intensity of the stimulus is the same.

^{ 5 }determined the normal position of isopters III-4e and V-4e in the peripheral visual field in healthy patients aged between 19 and 42 years. However, they plotted the average position, which resulted in an underestimation of the field loss when the larger isopter was used and therefore a possible overestimation of the patient’s functional vision.

^{ 6 }

^{ 7 }visual acuity,

^{ 8 }pupil size,

^{ 9 }the interference of eyelid and nose, cooperation,

^{ 10 }and interaction with the examiner and level of education of the patient.

^{ 11 }However, there seems to be no evidence of factors that could cause the difference between the visual field areas resulting from a change in the size of the stimulus. We hypothesize that age, primary eye disease, central or peripheral field loss and visual acuity may affect the difference between the visual field areas of the two isopters.

*Guides to the Evaluation of Permanent Impairment*.

^{ 12 }

^{ 13 }One part consists of guidelines for evaluating visual impairment based on the functional vision score (FVS). The FVS is built on the functional acuity score (FAS) and functional field score (FFS). To determine the FFS, the visual field score (VFS) for the right monocular field (VFS

_{OD}), left monocular field (VFS

_{OS}), and binocular field (VFS

_{OU}) are first scored separately.

^{ 5 }in their study of normal sight can be used to calculate the VFS and FFS. This results in a normal FFS

_{III-4e}of 106 (95% CI, 99–118) points, whereas the normal FFS

_{V-4e}is 113 (95% CI, 103–124) points. However, they did not plot the position of the isopters in low-vision patients.

^{ 14 }As a consequence, benefits may be wrongly calculated. It is therefore important to be able to estimate the FFS

_{III-4e}when only isopter V-4e is available.

_{III-4e}based on FFS

_{v-4e,}while adjusting for possible confounders.

^{ 14 }(Fig. 1B) . The grid is constructed so that the lower field receives 60% of the weight and the upper field, 40%. The central 10° field and the peripheral field both receive 50 points. With the grid overlay on the Goldmann visual field, we counted only the points that fell within the isopter, ignoring those on or outside it, or within scotomas. Binocular isopters were constructed by superimposing the isopters for the left and the right eye, if available. For persons blind in one eye, the VFS of that eye was recorded as 0, and the binocular VFS was taken as equal to the monocular VFS. To obtain the patient’s FFS, we inserted the VFS for each monocular field and the binocular field into equation 1 . We then plotted the overlay grid (AutoCAD 2002; Autodesk Inc., San Rafael, CA).

^{ 15 }and concluded that both FFSs have a near-perfect reliability. Patients were scored three times: once by rater 1 and twice by rater 2. The mean of these three scores was taken as the best estimate of the FFS. Patients who joined the study at a later stage were scored once.

*t*-test to assess the difference between the FFSs of isopters III-4e and V-4e.

_{III-4e}as the dependent variable and FFS

_{V-4e}as the independent one. We took the variation between subjects into account by calculating a 95% prediction interval (i.e., a range of possible values for FFS

_{III-4e}given a certain value of FFS

_{V-4e}). This interval is not constant, being at its narrowest near the middle of the range and becoming wider toward the extremes.

^{ 16 }

_{V-4e}was changed by more than 10% after adding one of the possible confounders.

^{ 17 }

^{ 18 }

^{ 19 }

^{ 20 }Bootstrapping replicates the process of sample generation from an underlying population of the same size as the original data set, by drawing samples with replacement from the original data set.

_{III-4e}. In this way, we tested the hypothesis that the corresponding slope and intercept are equal to 1 and 0, respectively.

^{ 15 }whereas 27 patients joined at a later stage. For 15 patients, the binocular VFSs for isopters III-4e and V-4e were taken to be equal to the monocular VFSs each patient was blind in one eye.

_{III-4e}(Table 4) , the variance being almost completely explained by FFS

_{V-4e}as the independent variable (

*R*

^{2}= 0.91). Therefore, the bootstrap analysis was repeated with only the FFS

_{V-4e}as the independent variable. The estimates of the regression coefficients and their standard errors are given in Table 5 .

_{III-4e}from FFS

_{V-4e}:

_{V-4e}and FFS

_{III-4e}, and Figure 3shows how this relationship varied according the category of disease.

_{V-4e}suggest constancy and linearity of the error terms (results not given). As the neutral value of 0 was absent from the 95% CI, for the regression coefficient of FFS

_{III-4e}, we can assume that the relationship between FFS

_{V-4e}and FFS

_{III-4e}is linear. We could assume that the variables were independent, because each case represented one patient. An approximately normal distribution for the dependent variable FFS

_{III-4e}is suggested by the appearance of the raw score histograms fitted with normal distribution curves, as well as that of the Q-Q plots of variable distribution quantiles against quantiles for the normal distribution.

_{III-4e}. The regression equation is

_{III-4e}is equal to 0.95 (

*P*< 0.001). Table 6gives the percentage error encountered when comparing the FFS

_{V-4e}and the predicted FFS

_{III-4e}with the observed FFS

_{III-4e}. Of the predicted values for FFS

_{III-4e}, 81.0% are within the range of ±10 points of the observed values, 94.8% are within 15 points, and 98.3% are within 20 points. For the values of FFS

_{V-4e}this was 37.9%, 58.6%, and 77.6%, respectively.

^{ 14 }In the comparison of the predicted and the observed functional field scores, the CI of the slope of the regression line contains the value of 1. Therefore, the slope does not differ significantly from 1, indicating a linear relationship between the FFS of the two isopters. In practice, simply subtracting 19.25 points of the value of FFS

_{V-4e}is sufficient for an estimate of the value of FFS

_{III-4e}.

_{V-4e}.

_{III-4e}and FFS

_{V-4e}. There seems to be no evidence (for example, difference in concentration or understanding of procedure) to explain the difference in FFS between young and elderly adults.

_{V-4e}and FFS

_{III-4e}. We noted that the intercepts of the disease categories macular degeneration and diabetic retinopathy were smaller than those of the other disease categories (Fig. 3) , but the sample sizes for each category were too small for meaningful conclusions about the relationship of diagnosis with FFS. There was no difference in the perception of the two stimuli between people with high or low visual acuity, showing that the FAS was also not a confounder for the relationship between FFS

_{III-4e}and FFS

_{V-4e}.

_{III-4e}are compared with the observed values, 81.0% of the points are within a range of 10 points of the observed values, which shows a considerably higher agreement than those of a comparison between the observed values of FFS

_{III-4e}and FFS

_{V-4e}. Within a range of 20 points, the agreement between observed and predicted comes close to 100%.

^{ 14 }vision is classified also according to FVS (Table 1) . From our results and equation 3 , it can be seen that an overestimation of the FFS by 19.30 points by using a larger isopter and also presuming FAS to be a constant variable, leads to a higher FVS score. The CI for the intercept ranges from −26 to −12 points. This may lead to someone’s being classified incorrectly with a difference of up to two classes. Estimation of the FFS

_{III-4e}leads to a more accurate FVS and the to patient’s receiving a fairer and appropriate benefit from, for example, his medical insurance.

_{V-4e}is 24. There were no patients with a lower score on isopter V-4e and for whom isopter III-4e could be produced. The use of regression as a prediction can only work over the limits of data collected. Therefore, the equation for calculating the FFS

_{III-4e}cannot be applied in the case of patients with a very low FFS

_{V-4e}. Second, the age range of the subjects was 20 to 66 years, and thus the model is valid only for this age category. Whether the model can be extended to children or elderly people remains to be investigated. Third, the number of participants in the analyses was relatively small, the CI for the estimation of the intercept ranging between −26 and −12 points. Although it is clear from our study that there is a marked difference between FFS

_{V-4e}and FFS

_{III-4e}of at least 12 and maximally 26 points, studies with large sample sizes are needed for more precise estimates. We used bootstrap analysis to evaluate the model’s performance for the same patients returning for further treatment. However, this was an internal procedure. As the goal of this study was to develop a general model, the model should be evaluated on new data from a population of patients who in age, number, and visual impairment differ from the original.

^{ 21 }

Class | Description | Estimated Ability to Perform Activities of Daily Living | FVS (Points) |
---|---|---|---|

1 | Range of normal vision | Has reserve capacity | >90 |

2 | Near-normal vision | Lost reserve capacity | 71–90 |

3 | Moderate low vision | Need for vision enhancement aids | 51–70 |

4 | Severe low vision | Slower than normal, even with enhancement aids | 31–50 |

5 | Profound low vision | Marginal visual performance, even with aids | 11–30 |

6 | (Near-) total blindness | Cannot perform visually; needs substitution aids | <10 |

**Figure 1.**

**Figure 1.**

Characteristics | |
---|---|

Mean age, y (95% CI) | 40.1 (36.8–43.5) |

Gender (% male) | 60.3 |

Mean functional acuity score (95% CI) | 42.44 (36.08–48.82) |

Primary ocular diagnosis (%) | |

TRD | 29.3 |

Optic neuropathy | 20.7 |

Macular degeneration | 13.8 |

Glaucoma | 10.3 |

Diabetic retinopathy | 6.9 |

Other | 19.0 |

Uveitis | 5.2 |

Cataract | 1.7 |

High myopia | 1.7 |

Achromatopsia | 1.7 |

Gyrate atrophy | 1.7 |

Choroideremia | 1.7 |

Corneal dystrophy | 1.7 |

Juvenile retinoschisis | 1.7 |

Homonymous cystinemia | 1.7 |

Type of field loss (%) | |

None | 3.4 |

Central loss only | 15.5 |

Peripheral loss only | 34.5 |

Central and peripheral loss | 46.6 |

β | 95% CI | β change^{*} (%) | R ^{2} ^{, †} | |
---|---|---|---|---|

FFS_{V-4e} | 1.063 | 0.973–1.152 | 0.910 | |

FFS_{V-4e} adjusted for age | 1.062 | 0.973–1.151 | −0.09 | 0.913 |

FFS_{V-4e} adjusted for location of field loss | 1.062 | 0.949–1.175 | −0.09 | 0.922 |

FFS_{V-4e} adjusted for FAS | 1.060 | 0.971–1.149 | −0.28 | 0.913 |

FFS_{V-4e} adjusted for diagnosis | 1.059 | 0.967–1.151 | −0.38 | 0.911 |

FFS_{V-4e} adjusted for all confounders | 0.978 | 0.849–1.108 | −8.00 | 0.937 |

Parameter | Original (Main) Regression | Bootstrap Model | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

β (95% CI) | SE | Significance | β (95% CI) | SE | Significance | |||||

Intercept | −19.30 (−26.36 to −12.24) | 3.51 | P < 0.001 | −19.25 (−25.58 to −12.37) | 3.52 | P < 0.001 | ||||

Slope | 1.063 (0.97 to 1.15) | 0.04 | P < 0.001 | 1.063 (0.98 to 1.14) | 0.04 | P < 0.001 |

**Figure 2.**

**Figure 2.**

**Figure 3.**

**Figure 3.**

**Figure 4.**

**Figure 4.**

Range Compared with Observed FFS_{III-4e} | Error FFS_{V-4e} (%) | Error Predicted FFS_{III-4e} (%) |
---|---|---|

±10 Points | 62.07 | 18.97 |

±15 Points | 41.38 | 5.17 |

±20 Points | 22.41 | 1.72 |