ArticleActa ophthalmologica2025
Jackknife and bootstrapping resampling techniques to evaluate the precision of lens formula constants.
Article in Acta ophthalmologica, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- Negative affect and psychotic-like experiences in social workers: mechanisms and the buffering role of mindfulness.Frontiers in psychiatry · 2026Article
- Jackknife and bootstrapping resampling techniques to evaluate the precision of lens formula constants.Acta ophthalmologica · 2025Article
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6 authors.
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Abstract
purposeThe 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.
methodsUsing 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 (N
resultsIn 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.
conclusionThe 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.
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