A two-step formula constant optimization strategy for minimal standard deviation and zero mean prediction error in...

To investigate the precision and accuracy performance of a two-step approach for optimizing lens formula constants (FC) with a refractive offset correction (RO) as a second tuning parameter.

Using IOLMaster 700 biometric data from 4 datasets (886/613/821/467 eyes treated with the Hoya Vivinex/Johnson&Johnson ZCB00/Alcon SA60AT/Bausch&Lomb MX60 lens), and the power of the implanted lens and postoperative spherical equivalent refraction, FC and RO were optimized for SRKT, Hoffer Q, Holladay 1, and Haigis formulae using an iterative nonlinear optimization for RMSPE and sequentially according to Gatinel, optimizing first FC for standard deviation prediction error (SDPE) and then RO by the resulting mean prediction error.

The simple two-step approach yielded comparable results for the FC and RO for all four formulae and datasets under test. The differences in the formula prediction error were commonly in the third decimals comparing both optimization strategies without clinical relevance. Direct optimization of the FC for SDPE showed large offsets in the formula constant for all datasets and especially for the Hoffer Q and Haigis formulae, resulting in systematic refractive offset values in the formula prediction.

This simple two-step approach using FC with a second tuning parameter performs excellently for the four formulae and four datasets under test and allows for both reducing the scatter and zeroing the refractive offset. Multicentric studies with other populations and biometers are required to further investigate the clinical applicability.