Other comparators for outcomes in treatment of astigmatism with toric intraocular lenses

In the paper by Abulafia et al.,1 the authors use the vector difference between the achieved refractive astigmatism and the target refractive astigmatism as their comparator. This vector has been termed the “difference vector.”2,3 However, if a toric intraocular lens (IOL) cylinder power prediction is perfectly accurate but the IOL is misaligned, there is a resultant difference vector with a power and axis value. The difference vector will not effectively show that the power prediction is correct. The purpose of the study by Abulafia et al.1 was to compare accuracy of toric IOL power prediction between the methods of calculation used. In this they “excluded the influence of [incisional] SIA and minimized errors in toric IOL alignment by using the postoperative corneal measurements and by measuring the actual toric IOL axis alignment,” and they concentrated on the power prediction. Perhaps a further measure they might derive from their data is the magnitude of the error.2,3 This is the power difference between the vector representing the attempted change from preoperative astigmatism to the target postoperative astigmatism and the vector representing the actual change to the achieved postoperative astigmatism. In vector terminology, it is the surgically induced astigmatism (SIA) vector (SIA of the toric IOL) power minus the target induced astigmatism (TIA) vector power. This value will be zero if the IOL power prediction is accurate, a negative value if the prediction is an underestimate, and a positive value if it is an overestimate. Its mean absolute value is a useful comparator between groups of eyes or methods of calculation. In this, it closely resembles an assessment of the success of an IOL sphere prediction. It will not produce a power value in the presence of a perfect power prediction and a misalignment, unlike the difference vector. It can therefore be used to adjust the IOL power prediction for subsequent eyes in a way the difference vector cannot. Abulafia et al.1 gave 2 formulas to represent the adjustment provided by the published Baylor nomogram saying, “The predicted net corneal astigmatism assessment for the Baylor nomogram was calculated using the published regression equations by subtracting (0.1005 × measured corneal astigmatism + 0.221) or adding (−0.011 × measured corneal astigmatism + 0.225) to the corneal astigmatism as measured by keratometry for WTR and ATR stigmatism, respectively.” However, these formulas do not appear in either of their referenced publications. It would be very helpful for the authors to show how these formulas are derived from the published nomogram. Furthermore, the Baylor nomogram aims to “leave the eyes with a small WTR refractive astigmatism.”3 Is that aim included in the formulas above? In Table 2, a standard deviation (SD) for each centroid value is given.1 A centroid is a summated vector mean that includes axis and power in its calculations. The usual formula for an SD does not include an expression for vector direction. How was the SD of the centroid derived? On the data presented that compares the ability to predict astigmatism power after toric IOL insertion while minimizing the effect of axis misalignment, it appears as though the Barrett toric IOL calculator in combination with Lenstar LS 900 keratometry achieved the best prediction. Specifically excluded is the variable effect of the corneal SIA resulting from the incision. Obviously, this is a significant exclusion when compared with the surgeon’s choice of IOL power before an operation. The flattening effect of the corneal SIA of past performance of incisions at any corneal meridian is a key value that should be entered into all calculators for the precise determination of the toric power of an IOL to be used. These predictions of post-incision corneal power are not perfect4 and should the comparisons in Abulafia et al. be made of eyes having surgery for which these calculations would be necessary rather than of postoperative eyes for which they are not, the conclusions might differ from those presented. In addition, the statement that the values derived from the (Atlas) corneal topographer “are less reliable for toric IOL calculations” might have overlooked the recent innovation in 2012 of CorT (anterior) value,5 which showed greater accuracy and reliability over simulated keratometry from the Atlas device and over other automated techniques. It would be a valuable addition to the paper to see analyses that include the flattening effect of the incision and the magnitude of error for the power chosen. This might enable the authors to confirm or modify their assertion that the Barrett calculator is the best of the 3 examined.