Reply : Errata in printed Hoffer Q formula (2006)

I am pleased to hear the good results obtained by Zuberbuhler and Morrell using the Hoffer Q formula as programmed on the Zeiss IOLMaster and Quantel Axis II (both Hoffer Q licensed). Their letter points out a problem that occurred with the Hoffer Q formula's original publication in 1993. The article contained both typographical errors and formula changes that were corrected by an erratum that appeared several months later in 1994 in another volume of JCRS.1 Those such as Zuberbuhler and Morrell who used the original article to program the formula had no way of knowing that the corrections were published in a later issue. The 3 mistakes in the original publication were as follows: An important and crucial minus sign was left out of the power formula (P), as Zuberbuhler and Morrell have noted. In the example calculations for the hyperopic eye (example 2), the results for emmetropia and ametropia were switched. I made a change in the parameters to calculate the Q formula for the anterior chamber depth (ACD). In the original article, limits were placed on the ACD. This was replaced with limits on the axial length (A) (see below). Unfortunately, the erratum did not stress that this was a replacement rather than an addition so many used the limitation on the AL as well as the limitation on the ACD, leading to errors in calculation. In addition to these, a fourth error has occurred. There are 2 limitations placed on the A. The first is as follows: If A ≤23, M = +1.0 and G = 28.0; if A >23, M = –1.0 and G = 23.5. The second was added in the errata: If A >31, A = 31.0; if A <18.5, A = 18.5. These A limitations apply only to the Q part of the formula to calculate the effective lens position and not to the power formula where A = axial length, C = anterior chamber depth or ELP (estimated lens position), K = mean central corneal power, P = IOL power, R = spherical equivalent desired target PO refractive error vertexed to the corneal plane using R = Rx/(1 – 0.012 × Rx); M and G are changing constants. Because of these problems, almost everyone attempting to program the Hoffer Q has gotten it wrong. The worst example was the major error by the Tomey ultrasound unit, which led to an article2 showing that in a series of microphthalmic pediatric eyes, the Hoffer Q had a mean error of 11.44 diopters (D) compared with 2.74 D for the Holladay 1 and 4.40 D for the SRK/T (Table 1). The actual result, when programmed correctly, showed that the Hoffer Q was more accurate than the other 2 formulas in this series (Table 2), with a mean error of 2.78 D; a four-fold error of almost 9.0 D. The authors published an erratum,3 which states that “[t]he error was caused by the incorrect power calculation program incorporated into the A-scan instrument (UD-7000, Tomey Corp.), which the authors failed to notice. Recalculation using the corrected program indicated that the Hoffer Q formula offered the most accurate predictions for the 5 microphthalmic eyes.” It is noteworthy that their results for the Holladay 1 formula were also incorrect. Tomey corrected the error in all their instruments and also issued an apology letter to ophthalmologists around the world.Table 1: Table 2 from the original article showing the Tomey incorrectly programmed Hoffer Q formula, yielding a mean prediction error greater than 11.0 D, with an error range of 17.6 D.Table 2: Table 2 from the erratum showing the Tomey correctly programmed Hoffer Q formula, yielding the lowest mean prediction error of 2.80 D, with an error range of 9.0 D.Because of these problems, I have required manufacturers to obtain a license before selling biometry units with the Hoffer Q formula installed. This license requires that I test the instrument with a series of 500 eyes to ensure the accuracy of the formula in all possible conditions. Every surgeon using the Hoffer Q should ask for assurance from the manufacturer of the device that the program being used is correct and duly licensed. Regarding Zuberbuhler and Morrell's note about “1,000” meaning “one thousand,” I am perplexed. In America, a comma is used to separate the 3 zeroes from the numeral before them; in Europe, a period is used. In America, a “million dollars and 56 cents” is written “$1,000,000.56”; in Europe, it is written “$1.000.000,56.” Thus, Zuberbuhler and Morrell may have thought that “1,000” was really 1.000 or the number one. Most have learned this difference. Perhaps using “1000” in the formula publication would have been preferable. I thank Zuberbuhler and Morrell for pointing out the value of the Hoffer Q formula over the past 13 years and the problems inherent in individuals programming this formula based on the publications without checking it with the author. I apologize for any confusion this has caused.