Reduction of trend errors in power calculation by linear transformation of measured axial lengths

To find a method to improve the refractive outcome in short eyes and long eyes without sacrificing the outcome in normal eyes.

St. Erik's Eye Hospital, Stockholm, Sweden.

In a prospective study, 148 patients eligible for cataract surgery were measured with 2 different A-scans (BVI Axis, B.V. International; Sonomed 1500, Sonomed Inc.). Refraction was determined 6 weeks postoperatively. The postoperative refraction was compared with the refraction predicted by the Holladay 1, Hoffer Q, and SRK/T formulas; formula constants were optimized to give a zero mean error. The mean absolute error (MAE) was used as an outcome measure.

The BVI Axis measured consistently shorter than Sonomed 1500. The mean axial lengths (ALs) were 23.033 mm and 23.435 mm, respectively. With the BVI Axis, an MAE of 0.44 diopter (D), 0.44 D, and 0.47 D was obtained, with the Holladay 1, Hoffer Q, and SRK/T formulas, respectively, with a trend toward undercorrecting short eyes and overcorrecting long eyes. The MAE with the Sonomed 1500 was 0.38 D, 0.39 D, and 0.40 D, respectively. By adding 0.402 mm to each measured value in the BVI Axis data set, the mean AL was transformed to 23.435 mm. With the transformed data, the MAE improved to 0.42 D, 0.43 D, and 0.44 D, respectively, with a reduced trend toward undercorrection and overcorrection. The 0.04 D difference between the instruments, although not statistically significant, may depend on measurement precision. Extending the concept of transformation, a minimum MAE of 0.41 D was obtained with the Holladay 1 at a mean AL of 24.0 mm, 0.43 D with Hoffer Q at 23.9 mm, and 0.40 D with SRK/T at 24.4 mm. The trend toward undercorrection and overcorrection was eliminated at the optimum for each formula.

There were systematic differences in measured AL depending on equipment. Thus, the calculated powers differed and caused error in the degree of compliance between the labeled formula constant of an intraocular lens and the equipment used. Although personalization of formula constants reduces the mean error, in general a trend toward undercorrection of short eyes and overcorrection of long eyes will persist. Transforming the AL scale can eliminate the trend error and improve the overall refractive outcome. Transformation to a population mean AL of about 24.0 mm was close to optimum for the 3 formulas.