Related Experiment Video
Updated: May 16, 2025

Simulating the Mechanics of Lens Accommodation via a Manual Lens Stretcher
Published on: February 23, 2018
Jackknife and bootstrapping resampling techniques to evaluate the precision of lens formula constants
Achim Langenbucher1, Jascha Wendelstein1,2, Alan Cayless3
1Department of Experimental Ophthalmology, Saarland University, Homburg, Saar, Germany.
Purpose:
The purpose of this study was to develop a method for evaluating intraocular lens (IOL) formula constant uncertainties using two modern statistical techniques-jackknife and bootstrap resampling.
Methods:
Using two datasets (dataset 1: 888 eyes treated with the aberration correcting Hoya Vivinex IOL, dataset 2: 821 eyes with the spherical Alcon SA60AT/SN60AT IOL), formula constant uncertainties for the SRK/T (Aconst), Hoffer-Q (pACD), Holladay 1 (SF), simplified Haigis (a0) with preset a1/a2, Haigis (triplet a0/a1/a2), Castrop (triplet C/H/R) and Olsen formula (ACD) were evaluated. All input parameters were jackknife and bootstrap (NB = 1000) resampled, and formula constants for each sample derived using nonlinear iterative optimisation techniques.
Results:
In single constant formulae where the constant acts directly on the effective lens position (Hoffer-Q, Holladay 1, simplified Haigis, Olsen), the formula constant in each case showed a standard deviation (SD) of about 0.01 with both jackknife and bootstrap sampling. The SRK/T Aconst showed a SD of about 0.018, and the Haigis and Castrop formulae with constant triplets showed large variations in the 3 constants (a0/a1/a2 about 0.036/0.005/0.002, C/H/R about 0.001/0.011/0.012). Direct formula reversion and solving for the formula constant yielded systematically larger SD values (Aconst/pACD,SF/a0/ACD = 0.586/0.395/0.403/0.324/0.304) with highly skewed distributions.
Conclusion:
The distributions of formula constants with relevant benchmarks such as SD or confidence intervals can be derived with jackknife and bootstrap resampling techniques, offering potential advantages over direct formula reversion which yields skewed distributions, making central metrics such as the formula constant distribution mean unsuitable for constant optimisation.
More Related Videos
06:55Scanning Light Scattering Profiler SLPS Based Methodology to Quantitatively Evaluate Forward and Backward Light Scattering from Intraocular Lenses
Published on: June 6, 2017
08:27Quantification of Oculomotor Responses and Accommodation Through Instrumentation and Analysis Toolboxes
Published on: March 3, 2023
Related Concept Videos
Bootstrapping
Uncertainty in Measurement: Accuracy and Precision
Sample Size Calculation
The sample size for the given experiment or sampling effort is fundamental to any study design. Sample size decides the number of...
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
On...
Random Sampling Method
Confidence Intervals
A...