A proposed method of logarithmic transformation of optical coherence tomography data for use in clinical research

Abstract

Purpose: To evaluate a logarithmic transformation of retinal thickness measurements from optical coherence tomography as a new approach to assess clinically meaningful changes in retinal thickness.

Design: Methodologic, evidence-based review.

Methods: Standard published approaches for assessing change in retinal thickness over time, as measured by optical coherence tomography (OCT), were compared with a new approach based on a logarithmic transformation of the retinal thickness data. Comparative examples were derived using published data from a clinical trial comparing intravitreal corticosteroid injections for diabetic macular edema with standard laser treatment.

Main outcome measures: Comparative examples using Diabetic Retinopathy Clinical Research Network data.

Results: Logarithmic transformation of retinal thickness data results in a more normalized distribution of OCT data and allows for data analyses assessing proportionate changes in retinal thickness during follow-up.

Conclusions: For analysis of grouped data, a logarithmic transformation of the OCT retinal thickness measurements (logOCT) provides several analytic advantages. Distributions of retinal thickness in groups of eyes with diabetic macular edema, and many other causes of macular thickening, tend to be skewed to the right; the logOCT transformation tends to normalize these distributions, which has value for statistical comparisons. For assessing whether the observed OCT change in a patient is real (and not due to testing variability), a 1-step log scale change exceeds the measurement error for all degrees of retinal thickness in current instruments. In addition, this log scale is similar to the logarithm of the minimum angle of resolution (logMAR) scale used for visual acuity. Steps on the log scale for change in thickness seem to be better related to clinical importance than the actual change in microns because each step on the log scale is the same proportionate change in thickness, with a 3-step change equaling a halving or doubling of thickness, regardless of the baseline value. Transformation of OCT retinal thickness data to logOCT may assist in the assessment of clinically meaningful changes in retinal thickness just as use of the logMAR scale has helped to assess clinically meaningful changes in visual acuity.

Figure 1

Distributions of Optical Coherence Tomography (OCT) Central Subfield Thickness Measurements and the Log Transformation of Central Subfield Thickness Measurements (LogOCT) from Baseline Measurements Made in the Diabetic Retinopathy Clinical Research Trial of Intravitreal Triamcinolone vs. Standard Laser Therapy for Diabetic Macular Edema.

Figure 2

Mean Change in (a) Optical Coherence Tomography (OCT) Central Subfield Thickness (CST) and (b) the Log Transformation of Central Subfield Thickness (LogOCT) from Baseline for the 4mg Intravitreal Triamcinolone Acetonide Group and the Focal/Grid Laser Treated Group during 2 year Follow-up in the Diabetic Retinopathy Clinical Research Trial of Intravitreal Triamcinolone vs. Standard Laser Therapy for Diabetic Macular Edema.

Figure 3

The Proportion of Subjects with a 2 or Greater Step Improvement in Log Transformation of Central Subfield Thickness (LogOCT) From Baseline in the 4mg Intravitreal Triamcinolone (IVT) Acetonide Group and the Focal/Grid Laser Treated Group during Two-year Follow-up in the Diabetic Retinopathy Clinical Research Trial of Intravitreal Triamcinolone vs. Standard Laser Therapy for Diabetic Macular Edema.

Figure 4

Mean Change from Baseline in Log Transformation of Central Subfield Thickness (LogOCT) and Mean Change in the Logarithm of the Minimum Angle of Resolution (LogMAR) in Patients Assigned to Focal/Grid Laser Treatment during 2-year Follow-up in the Diabetic Retinopathy Clinical Research Trial of Intravitreal Triamcinolone vs. Standard Laser Therapy for Diabetic Macular Edema.