1. Goals: Minimize cost Maximize suitable IOL powers
A statistical model for planning the distribution of IOL powers to order for Humanitarian Missions
Goals: Minimize cost Maximize suitable IOL powers
Peter Lombard MD, LCDR MC USN
Scott McClatchey MD, CAPT MC USN
Presenter has no financial interest in the products discussed. The opinions expressed in this paper are solely those of the authors, and do not reflect the official policy or position of the Department of the Navy, the Department of the Defense, or the US Government.
Naval Medical Center, San Diego
Uniformed University of the Health Sciences, Bethesda MD
Loma Linda University, Loma Linda CA

2. Methods Subjects Measurements 108 adults from Navy missions in 2007
AL, K
Ideal (IOL) powers were calculated based on these measurements for each eye

3. Results
For the first part of this study, we calculated the mean and standard deviations for the IOL powers. For 108 cataract surgeries, the average intraocular lens power was diopters. Our data are consistent with previously published studies for mean IOL powers.
IOL requirements for a population, for the most part, conform to a standard distribution about the mean, as can be seen here.
Now, lets say you are planning for a humanitarian mission in which you are capable of performing cataract surgery on 100 patients… what range of lens powers do you order? How many lenses at each half-diopter increment in power do you order?

4. Similar results found in Vietnam study
La Nauze J, et al, Ophthalmic Epidemiology 1999

5. Variance in a Gaussian curve

6. IOL Power Prediction Model
First animation: We created a spreadsheet model that calculates just that. It allows us to input the estimated number of cataract surgeries to be performed along with the mean IOL and standard deviation found in our study. The spreadsheet then calculates the number of lenses that should be ordered at each power.
Second and Third animation: For each IOL power in this column, the total IOLs to order are depicted in this column. The goals of our model were twofold: we wanted to make sure enough IOLs were available at each power so that we didn’t run out, and we did not want to waste money on unused IOLs. In order to accomplish this we introduced parameters that reduced the number of “extra” lenses required at each lens power above the standard distribution curve.
Fourth animation: To illustrate, this graph demonstrates the lens requirements for the standard distribution of a sample of 100 patients, based on the Mean IOL and SE from our study. Now, for a random selection of 100 patients, there will be variation in the number of patients requiring lens powers at each of these values. For example, you might have 15 patients requiring a 20 diopter lens, instead of the 13 predicted by the standard distribution. Clearly, if you don’t want to run out of lenses at any given power, you will want extra lenses at each power corresponding the variation above the standard curve. By using multiple computer generated randomized patient population samples, we found that this variation is approximately equal to the square root of the height of the standard curve at that IOL power.
It turns out that for a patient with an ideal lens requirement of, say 20 Diopters, you can use a lens power a little above or a little below 20 diopters, and still obtain acceptable vision. In fact, in large volume cataract surgery missions to rural areas of Nepal and India, their strategy is to use only a single lens power at the mean. In our example here, they would simply order 100 lenses at the mean power. Clearly that leaves a number of patients with potentially large refractive errors, but for the purposes of restoring useful vision to patients who would otherwise be blind, this is an acceptable trade off. We found that if we introduce a tolerance strategy of just accepting lenses a half diopter below, or a full diopter above, a patient’s ideal lens power, we are able to reduce the number of “extra” lenses to order at each power, while not sacrificing patient visual outcomes.

7. IOL Power Prediction Model
A total of 39 extra IOLs are predicted, using the square root of the number of patients at each power.
Without a tolerance strategy, there is a 3-4% chance of not having a suitable lens for each patient.
In the absence of using a tolerance strategy, for our random sample of 100 patients, including the full amount of variation above each value (using the square root of the height at each lens power) would require an additional 39 lenses. Even with all these extra lenses at each power, for a random sample of patients, there would be a 3% chance that their ideal lens power would be unavailable.
However, if we introduce the lens tolerance strategy of accepting a lens half a diopter below or a full diopter above the best-fit lens power, we can reduce to < 0.5% the chance of running out of lenses within the tolerance range for any patient. So the next question we asked: How far can we trim down the extra IOLs at each power and still maintain a <1% chance of rejection?
Animation: Using Excel macros and running multiple, multiple iterations of our spreadsheet model using a large number of computer generated randomized sample populations of various sizes, we found that we could decrease the number of extra lenses to a proportion of the fourth root of the height at each lens power (as opposed to the square root used previously), and still maintain the chance of suitable lens unavailability to less than one percent. Here we see a total of 19 extra lenses are predicted, compared to 39 lenses.
A total of 19 extra IOLs are predicted, using a proportion of the fourth root of the patients at each power.
Using tolerance, there is less than a 1% chance of not having a suitable lens for each patient.

8. Abel 2218 – Gravity Lens
Link to Spreadsheet