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PhilScore improvement ideas ​

A literature review on matching donated glasses to a prescription, and proposals for changing the matching algorithm based on it. It builds on the PhilScore deep dive, which explains the current rules. Nothing here is implemented. Every proposal breaks REIMS1 parity on purpose, so each would join the deliberate differences that Matching Algorithm lists, ideally with sign-off from PVH optometrists.

Summary ​

  • The only published formula for grading donated glasses is Arnold 2021, fitted on 8 to 10 people and never tested on dispensing outcomes. REIMS1 (in use since 1996), ReSpectacle and WinGlasses don't publish theirs. What counts as "close enough" has to come from studies of ready-made glasses and of blur.
  • That evidence backs the general shape of PhilScore but disagrees in three places:
    • Axis is free in the score. A lens 10 degrees off at -1.50 cylinder scores 0.003, but leaves as much blur as a sphere 0.25 to 0.5 D off.
    • Cylinder may be too cheap. Per diopter of blur, one acuity study finds astigmatism costs twice as much as defocus, while blur-limit studies and optics say the two are equal. PhilScore weighs it equally at best, and patients often dislike dropped cylinder (Reddy 2017).
    • Asymmetry follows age, not sphere sign. Too much minus hurts every presbyope, not only hyperopes.
  • The biggest proposal deletes code: one weighted power-vector distance instead of the bonus rules.

Literature ​

Recycled glasses programs ​

SourceFinding
Ramke 2006, Tuvalu13 % of 102 donated pairs were usable. Pairs with more than 1.00 D cylinder or 0.50 D anisometropia were excluded.
Wilson 20127 % of 275 donated pairs were usable, at US$20.49 per delivered pair, twice the cost of ready-made glasses.
Wan 2015, Timor-Leste29 of 200 prescriptions (14.5 %) matched at least one of 1,854 donated pairs, but a match had to be near exact: 0.125 D in sphere and cylinder, axis within 5 degrees, PD within 3 mm.
Pearce 2014, systematic reviewNo outcome study of recycled glasses met the inclusion criteria.
IAPB 2014 position paperAdvises against recycled glasses, partly because sphere, cylinder, axis and lens centration make matching hard.
REIMS1, VOSH and CVDW 2004Matches on spherical equivalents and axis tolerances. Built once the hand-sorted stock reached about 10,000 pairs (1995), in use from 1996, later also at other VOSH chapters.
ReSpectacle, 2011Shows a percentage: green from 90 %, yellow 80 to 90 %, red 70 to 80 %. Formula unpublished.
WinGlasses, Huang 2021Matches on spherical equivalent and axis. Proprietary, behind a network of 10 clinics in Mexico, the US and Haiti. Optimizes one value for both eyes, which offered pairs that worsened the weaker eye.
Arnold 2021, two papersA, B and C grades for 1, 3 and 6 lines of acuity lost. The astigmatism allowance grows with the Rx cylinder, the over-minus allowance shrinks with age, PD and anisometropia graded too. Free Excel tool.
VOSH Southeast field guideAxis within 5 to 10 degrees, lens cylinder not above the Rx cylinder, aim for 20/40.

Ready-made glasses: what can be left out ​

Ready-made glasses have no cylinder and the same sphere in both eyes, so trials of them show what patients tolerate.

SourceFinding
Brady 2012, 363 adultsGlasses at the SE of the eye with less error satisfied about as well as custom ones. Patients with more than 2.00 D cylinder gained less.
Zeng 2009, childrenExcluded 2.00 D cylinder or more, myopic anisometropia of 2 D or more and hyperopic anisometropia of 1 D or more.
Morjaria 2017, childrenEligible with anisometropia below 1.0 D and SE acuity within one line of full correction. Wear rates matched custom glasses.
Reddy 2017, age 41 meanSide by side with full correction, 100 % were comfortable with SE for 0.25 D cylinder, 43 % for 0.50, 26 % for 0.75 and 19 % for 1.00. None of those given SE glasses returned them.
du Toit 2007Wearers tolerate up to 0.5 prism diopters vertical and 1.0 horizontal induced prism. Optical centre mismatch rarely matters up to +-1.50 D.

What each error costs ​

SourceFinding
Thibos 1997, Thibos 2001Power vectors (M, J0, J45). Their length B measures overall blur.
Raasch 1995, Blendowske 2015One combined dioptric distance predicts acuity for mixed sphere and cylinder errors. Blendowske: relative acuity 1 / (1 + B^2), fitted to pooled sphere and cylinder data with no extra weight on J.
Atchison 2005Blur becomes noticeable at about 0.3 D, troublesome at 1.6 to 1.8 times that, objectionable at 2.1 to 2.5 times. Larger letters raise all three.
Atchison 2009, Guo 2010Blur limits for crossed cylinders are about 90 % of those for defocus, for plain cylinders 30 to 50 % higher, as blur strength predicts. Per unit of B, astigmatism and defocus are about equal.
Atchison 2011, Mathur 2015Acuity drops 0.33 logMAR per diopter of astigmatic blur strength, against 0.18 for defocus. Only 8 and 22 subjects, blur up to 0.375 D, and eye drops (cycloplegia) only for the defocus runs, a confound the authors name. No measurable age effect.
Kobashi 2012, Wolffsohn 2011Some axes hurt more: oblique in Kobashi, 45 and 180 more than 90 in Wolffsohn. Guo 2010 puts the axis effect at about 20 %, Remón 2017 found none.
Rosenfield 1995, Bullimore 1998A repeated refraction varies by +-0.27 D with the same examiner and by about +-0.8 D in SE between two clinicians, 95 % limits.
Joseph 2021, 400 adultsGlasses from a handheld autorefractor were liked as much as glasses from subjective refraction, with SE limits of -0.68 to +0.83 D.
Skov 2026, reviewInduced anisometropia just under 1 D is well tolerated.
Burge 2019, Rodriguez-Lopez 2026Different blur in the two eyes causes motion illusions, visible for some people.
Guyton 1977Cylinder corrections distort space, mostly binocularly. Less cylinder means less distortion.
Pointer 1995The add people need rises steeply from the early 40s, and slower after the mid 50s.

Where PhilScore disagrees ​

Rx -1.50 -1.50 x 90, scored with a Python port of calcSingleEyePhilscore that reproduces the deep dive's table. B is the Thibos blur strength of the difference. Weighted B counts J twice (sqrt(dM^2 + 4 * (dJ0^2 + dJ45^2))), the upper end of the evidence (Atchison 2011, Mathur 2015).

LensPhilScoreBWeighted B
-1.75 -1.50 x 90, sphere off 0.250.250.250.25
-1.50 -1.25 x 90, cylinder off 0.250.130.180.28
-1.75 -1.00 x 90, SE with 0.50 D cyl dropped0.250.250.50
-2.00 -0.50 x 90, SE with 1.00 D cyl dropped1.000.501.00
-1.50 -1.50 x 80, axis 10 degrees off0.0030.260.52
  • Axis. The last lens passes the filter and ranks first, though it leaves 0.52 D of astigmatism. The score caps axis at 0.025 and the filter only looks at the lens cylinder.
  • Two budgets for one error. Dropping cylinder and rotating the axis both leave astigmatism (dJ). The axis table caps rotation at 0.3 to 1.0 D of residual, about 0.5 in the common range. The SE candidates let a lens drop up to 2.00 D of cylinder: Rx -2.00 -2.00 matches a -2.75 sphere.
  • SE swaps. Dropping 0.50 D of cylinder costs as much as a 0.25 sphere error. That's what blur strength says too, but one acuity study puts it at 0.50, and only 43 % in Reddy 2017 were comfortable with it.
  • Asymmetry. The hyperope penalty keys on sphere and sphere sign. For Rx +2.00 -1.00, the exact-SE lens +1.75 -0.50 scores 0.45, worse than the over-plus +2.25 -1.00 at 0.25.
  • False precision. Tie-break terms of 0.01 to 0.05 decide the order, while refractions repeat only to +-0.25 D or worse.
  • Eyes alone. Errors of -0.25 in one eye and +0.25 in the other tie with -0.25 in both, though the first adds 0.50 D of anisometropia.
  • Add. For Rx +1.00 add +2.50, lens +1.00 add +2.00 scores 0.05 although near power is 0.50 off. Lens +1.25 add +2.25 has exact near power and scores 0.275.

Proposals ​

Roughly from smallest to biggest change.

#ProposalEvidenceEffortNew data
1Axis error in the scorestrongsmallno
2One residual-astigmatism limitstrongsmallno
3Quality tiersmoderatesmall, UIno
4Too much minus, by agemoderatesmalloptional age
5Binocular balancemoderatesmallno
6Near power for multifocalsclinical callsmallno
7Weighted power-vector scorestrong, weight openmedium, deletes codeno
8Never return nothingprecedentmedium, UIno
9Store the Rx on dispenseenables evaluationsmallyes
10PD against optical centresmoderatemediumyes
11Spare scarce pairsweaklargeno

1. Axis error in the score ​

Replace axisDiff / 3600 with the residual astigmatism |dJ| from power vectors, a few lines of trig. Zero cylinder then needs no special case, since its J is 0 whatever the stored axis, so the axis term on spherical lenses and zero-cylinder Rx goes away. Works alone, with the rest of PhilScore unchanged.

2. One residual-astigmatism limit ​

Filter on SE (|dM| within the tolerance) and on residual astigmatism (2 * |dJ| below a budget), instead of the axis table and the SE candidate windows. Rotation and dropped cylinder then share one budget. Ready-made trials accept 1 to 2 D, Ramke 2006 used 1 D. Pick the value by replaying past searches so the match rate stays about where it is.

3. Quality tiers ​

Show three or four bands instead of a decimal, cut at the blur limits of Atchison 2005: below 0.3 D equivalent blur hardly noticeable, then noticeable, troublesome and poor. ReSpectacle does the same with colours, Arnold 2021 with A, B and C. Blendowske 2015 turns each cut into acuity: 0.25 D keeps 94 % of best acuity, 0.5 D 80 %, 1 D 50 %. Within a band, staff can pick by frame size and looks, which matters: IAPB 2014 names poor fit and dated looks as reasons people reject donated glasses. This replaces the percentage idea in Matching Algorithm.

4. Too much minus, by age ​

Standard refraction gives the most plus that still gives best acuity. A young patient focuses through extra minus, a presbyope can't, so extra minus blurs every distance. Penalize a lens whose SE is more minus than the Rx SE, for multifocal searches and for single vision patients over about 45. Using SE instead of sphere stops the penalty from hitting exact-SE swaps. An optional age field would replace the cutoff with a scale, for example from Hofstetter's minimum accommodation of 15 - 0.25 * age D.

5. Binocular balance ​

Score the difference between the eyes' SE errors (|dM_od - dM_os|): free up to 0.25, penalized from 0.50, filtered from 1.00 D, the cutoff most ready-made trials use. For multifocals, extra vertical power difference between the lenses causes vertical prism at reading height (Prentice: about 1 prism diopter per diopter at 1 cm below centre), and du Toit 2007 puts the limit at 0.5.

6. Near power for multifocals ​

Score distance (S) and near (S + add) errors instead of add / 10. Too little add pushes reading farther out (+2.00 reads at 50 cm, +2.50 at 40 cm), too much narrows the range, so under-add should cost more. The weight is a clinical decision for PVH optometrists.

7. Weighted power-vector score ​

Per eye, sqrt(dM^2 + w^2 * |dJ|^2) plus the asymmetry of 4, then 5 and 6 on top. w sits between 1 (optics, blur limits, Blendowske 2015) and 2 (acuity at small blur, Atchison 2011, Arnold 2021), an open question for optometrists. Arnold 2021 lets the allowance grow with the Rx cylinder. This replaces calcInitialDiffScore's weights, the three exclusive rules, the SE candidates and the axis table. PhilScore already ranks like plain B (Kendall tau 0.89 in the deep dive), so most rankings stay. The changes land where the literature disagrees: axis, SE swaps and plus prescriptions. Extra weight on oblique J45 is possible, but the evidence is mixed, so leave it out at first. Worked out together with 3 to 6, and replayed against real data, in Predicted-blur matching.

8. Never return nothing ​

Rank beyond the tolerance window and show the best few below a "poor" divider, instead of an empty list. Still log an unsuccessful search when nothing reaches the good tiers. Bring back REIMS1's "two single vision pairs" for failed multifocal searches: a distance pair, plus a reading pair at S + add.

9. Store the Rx on dispense ​

There's no ground truth today. The deep dive's replay had to use dispensed pairs as stand-in prescriptions. Storing the searched Rx, and which rank was picked, with each dispense would show what staff actually choose. It does break the rule that prescriptions only reach the server on unsuccessful searches, though no names are involved.

10. PD against optical centres ​

Record the optical centre distance when adding glasses and the patient's PD when searching, then penalize the prism this induces (Prentice's rule). du Toit 2007 tabulates the tolerable mismatch: 7 mm at +-1.00 D, 5 mm at 2.00, 3 mm at 3.00, 1 mm at 5.00 to 6.00. Arnold 2021 grades it the same way. That's two new fields and a measuring step per pair, so only worth it if strong lenses are common.

11. Spare scarce pairs ​

Within a tier, prefer the pair fewer other likely prescriptions could use, judged from dispense and unsuccessful-search history. Most code, least evidence, likely not worth it at REIMS's scale.

Evaluating a change ​

  • Replay. As in the deep dive, run dispensed pairs from 2023 to 2026 as prescriptions against the stock at that time. Count how often the first and top three suggestions change and how the match rate moves, then read the changed cases.
  • Blind review. Show PVH optometrists the cases where old and new top suggestion differ, unlabelled, and ask which pair they'd dispense. Until proposal 9 exists, this is the only ground truth.
  • Ship between campaigns, not during one.

References ​

All PubMed links unless noted.

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