**Purpose**:
To demonstrate methods that enable visual field sensitivities to be compared with normative data without restriction to a fixed test pattern.

**Methods**:
Healthy participants (*n* = 60, age 19–50) undertook microperimetry (MAIA-2) using 237 spatially dense locations up to 13° eccentricity. Surfaces were fit to the mean, variance, and 5th percentile sensitivities. Goodness-of-fit was assessed by refitting the surfaces 1000 times to the dataset and comparing estimated and measured sensitivities at 50 randomly excluded locations. A leave-one-out method was used to compare individual data with the 5th percentile surface. We also considered cases with unknown fovea location by adding error sampled from the distribution of relative fovea–optic disc positions to the test locations and comparing shifted data to the fixed surface.

**Results**:
Root mean square (RMS) difference between estimated and measured sensitivities were less than 0.5 dB and less than 1.0 dB for the mean and 5th percentile surfaces, respectively. Root mean square differences were greater for the variance surface, median 1.4 dB, range 0.8 to 2.7 dB. Across all participants 3.9% (interquartile range, 1.8–8.9%) of sensitivities fell beneath the 5th percentile surface, close to the expected 5%. Positional error added to the test grid altered the number of locations falling beneath the 5th percentile surface by less than 1.3% in 95% of participants.

**Conclusions**:
Spatial interpolation of normative data enables comparison of sensitivity measurements from varied visual field locations. Conventional indices and probability maps familiar from standard automated perimetry can be produced. These methods may enhance the clinical use of microperimetry, especially in cases of nonfoveal fixation.

^{1}Calculation of global indices like mean deviation (MD) and pattern standard deviation (PSD) also relies on knowledge of the mean and variance of normative data.

^{1}Such comparisons enable the clinician to efficiently estimate the likelihood that a patient's test results could be produced by a normal visual system.

^{3,4}and in the detection of early functional impairments due to retinal lesions.

^{5}Such visual defects may indicate the necessity for treatment to prevent further vision loss.

*n*= 60, median age 26; range, 19–50 years) were recruited from the staff and student population of the University of Nottingham (Nottingham, UK). Inclusion criteria were visual acuity 0.2 logMAR or better in the tested eye, spherical refractive error within the range that can be compensated for by the MAIA-2 (−15.00 diopters [D] to +10.00 D; CenterVue, Padova, Italy), cylindrical refractive error less than 4.00 D as per the manufacturer's guidelines and no known current or previous ocular disease. One eye was tested per participant, chosen randomly if both eyes met the inclusion criteria.

^{6}This left 228 locations for fitting. The present data were not adjusted for sensitivity decline with ageing as data on this for the MAIA-2 are not available in the public domain. Based on a previous study using the Humphrey Field Analyzer (Carl Zeiss Meditec, Jena, Germany),

^{7}the age-related sensitivity difference between the median and youngest or oldest participants in our dataset is expected to be less than 1 dB, excluding one outlier (age 50) whose difference is expected to be 1.3 dB. These differences were deemed small enough to be within measurement variability in this study.

^{8,9}In preliminary testing (data not shown), Universal Kriging was found to most frequently provide the best fits to subsets of the data, and so was used for the main study, however all of the above methods provided clinically acceptable fits to our data once suitable fitting parameters had been found. Universal Kriging is a spatial interpolation technique originally developed for geostatistical applications that estimates interpolated points without penalization for lack of smoothness, thereby predicting the most likely intermediate values given the available measurements.

*R*(ver 3.2.0)

^{10}using the MASS and spatial packages. Universal Kriging was done with a quadratic trend surface, chosen to reflect the expected shape of the hill of vision, and an exponential covariance matrix, chosen over the alternatives (Gaussian and spherical) as giving the best fits to our data in initial testing. Fitting a surface by Universal Kriging additionally requires the selection of two parameters, a range parameter (

*d*), that determines the range within which surrounding points are considered in choosing intermediate values, and a “nugget parameter” (

*α*) that controls the extent to which local maxima and minima in the data are smoothed. We selected these parameters separately for each of the three surfaces because previous studies of normative perimetric data have shown unequal variance in sensitivity across the visual field,

^{7}therefore it was expected that the parameters would optimally differ for the different surfaces.

*d*) and nugget (

*α*) parameters for each surface we used a grid search to trial all combinations of

*d*in the range [1, 1.5…10] and α in the range [0, 0.05…1] (total 399 parameter combinations). The goodness-of-fit was assessed as follows:

- Fit the surface with the chosen parameters to the data excluding a randomly selected subset of 50 locations,
- Calculate root mean square (RMS) difference between the predicted and actual values at the excluded subset of locations,
- Repeat steps 1 and 2, 200 times and take the mean of the RMS differences as an overall measure of goodness-of-fit.

^{1}: where

*x*is the measured sensitivity at location

_{i}*i*,

*N*is the normal reference sensitivity at location

_{i}*i*,

*s*is the variance at location

^{2}_{i}*i,*and

*n*is the total number of test locations. Similarly PSD is calculated as

^{1}: Total and pattern deviation probability plots can also be easily produced by comparing patient data to surfaces fit with the appropriate percentiles of normative data.

^{7}

^{11}

*ρ*= 0.3) and 95% of all position shifts resulted in an absolute change in number of locations falling beneath the 5th percentile surface of 3 (1.3%) or fewer.

^{3,4}(Krishnan A et al. IOVS 2016:57:ARVO E-Abstract 6100) may provide a useful early biomarker of disease progression that may allow treatment to be initiated to prevent further spread of pathology and associated vision loss. Microperimeters also typically allow custom placement of test locations that may be useful in assessment of macular visual function in glaucoma where spatially accurate stimulus placement relative to retinal structures is indicated by recent work.

^{12}However, the lack of tools for comparison to normative data hampers the clinical use of microperimetry, as it is difficult to separate measurements of healthy visual function from those likely to be affected by disease. Previous normative studies for microperimetry have concentrated on common test patterns centered on the fovea,

^{13–18}which is therefore limited to use in patients with central fixation, and where the clinician elects to test the central region using the same pattern of test locations.

^{19–22}The surface fit to the variance had larger error, with an estimated upper bound of median 1.4 dB (range, 0.8–2.7 dB), though this is still within typical measurement variability. This was due to a larger variation in the variance across the tested visual field region meaning that the inclusion/exclusion of some points whose variance in sensitivity was markedly different from nearby points had a large effect on the surface fit. This larger error affects only the accuracy of global summary indices that require data on variance such as MD and PSD; point estimates of TD and PD and their associated probability maps do not use this surface. It is further worth noting that the metrics reported herein can be considered lower bounds on the accuracy of the surface fitting approach (upper bounds on fitting error), because for a clinical application no test locations would be excluded from the fit.

^{23–25}and additional variation from the selection of the optic disc center by the clinician. Both types of variation are taken into account in our data, which suggests that using this specific measurement method the distribution of optic disc position is (15.54 ± 1.05°, 2.12 ± 0.85° [mean ± SD in right eye format]) relative to the fovea. By repeatedly adding error sampled from this distribution to the position of the test grid we found that the change in number of locations falling beneath the 5th percentile surface was less than 3 of 228 (1.3%) in 95% of patients. This small proportion suggests that assuming the location of the fovea in this way is likely to be suitable for most clinical purposes.

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