**1. Introduction**

The accuracy of intraocular lens (IOL) power calculation is a matter of grea<sup>t</sup> importance in cataract surgery [1,2]. IOL power is determined by three factors: preoperative biometric data (axial length (AL), anterior chamber depth (ACD), and mean corneal power (K)), the IOL power calculation formula, and the IOL constant [3]. Cataract surgeons have aimed to create an IOL formula for the determination of the ideal refractive outcome. The prediction of postoperative ACD or effective lens position (ELP) is the most important process in IOL power calculation, and IOL power calculation error is, for the most part, due to errors in predicting ELP [4].

Although more than 10 years have passed since the concept of the Haigis formula was introduced, it still shows high predictive accuracy [5,6]. The T2 formula, using only AL and K for ELP, shows the highest predictive accuracy [5,7]. However, there is an important limitation that the two formulas above are designed based on multiple linear regression analysis [8,9]. A multiple linear regression analysis, in principle, requires the independence of explanatory variables. However, ACD and K have significant relationships with AL, which can cause errors. Statistically, the explanatory variables used in ELP prediction are considered to have a collinearity problem [10,11].

**Citation:** Yoo, Y.-S.; Whang, W.-J. Conditional Process Analysis for Effective Lens Position According to Preoperative Axial Length. *J. Clin. Med.* **2022**, *11*, 1469. https:// doi.org/10.3390/jcm11061469

Academic Editor: Nobuyuki Shoji

Received: 31 January 2022 Accepted: 27 February 2022 Published: 8 March 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Hayes presented dozens of models in PROCESS macros for conditional process analysis [12–14]. Conditional process analysis includes not only independent variables, but also the concept of a mediating variable and a moderating variable. Using this method, we can solve the problem of multicollinearity and identify relationships between explanatory variables and develop a more accurate structural equation model for a dependent variable.

In this study, considering that the formula yielding excellent accuracy differs according to AL, we divided a total of 621 eyes into four groups according to AL. We determined the ideal model for predicting ELP in each group on the basis of conditional process analysis and the results were compared with existing IOL formula derived from a multiple linear regression analysis.

#### **2. Materials and Methods**

This retrospective case series study included 621 eyes of 621 patients who underwent uneventful and micro-coaxial phacoemulsification cataract surgery without any intraoperative complications between March 2018 and September 2019. None of the patients had a history of ocular disease, previous ocular surgery, or general disorders affecting the cornea. Exclusion criteria were amblyopia, corneal opacity, glaucoma, retinal disease, history of ocular inflammation, history of ocular trauma, and history of exposure to other intraocular surgeries. The study methods adhered to the tenets of the Declaration of Helsinki for use of human participants in biomedical research. The Institutional Review Board (IRB #SC20RASI0071) for Human Studies at Yeouido St. Mary's Hospital approved this study, and informed consent was exempted by IRB of Yeouido St. Mary's Hospital.

Preoperative biometric measurements, such as K of anterior surface, ACD, and AL, were obtained with an IOLMaster optical biometer (version 5, Carl Zeiss, Oberkochen, Germany) to calculate IOL power. All procedures were performed by two surgeons (H.S. Kim and W.J. Whang). All patients underwent cataract surgery through a 2.2 mm micro coaxial incision under topical anesthesia (proparacaine hydrochloride 0.5%, Alcaine, Alcon). After performing continuous curvilinear capsulorhexis with an intended diameter of 5.0 mm and hydrodissection, phacoemulsification of the nucleus was performed using an OZil torsional handpiece with the Centurion vision system (Alcon, Fort Worth, TX, USA). Following phacoemulsification, the intraocular lens (ZCB00, Johnson & Johnson Vision, Santa Ana, CA, USA) was inserted into the capsular bag using an injector and disposable cartridge system before removing the ophthalmic viscosurgical device. Finally, a balanced salt solution was injected into the corneal incision site with stromal hydration. After the surgery, postoperative antibiotic and corticosteroid eye drops were used four times daily and tapered over a month.

Subjective refraction was measured 3 months postoperatively with manifest refraction by an experienced ophthalmologist (J. Y. Lee) and ELP was back-calculated using the following thin-lens formula [15]:

$$\text{IOL power} = \frac{1336}{\text{AL} - \text{ELP}} - \frac{1336}{\frac{1336}{\text{Z}} - \text{ELP}}$$

$$\text{Z} = \frac{(nc - 1) \times 1000}{r} + \frac{1000}{\frac{1000}{\text{PostR} \times \text{R}} - VD}$$

where *nc* is the fictious corneal refractive index (1.3315), *r* (millimeter) is the mean value of the preoperative corneal radius, *PostRx* is the postoperative spherical equivalent, and *VD* (millimeter) is the vertex distance.

The 621 eyes were stratified into 4 subgroups to investigate the appropriate structural equation model according to the preoperative AL:


The ELP prediction error was defined as the value calculated by subtracting the predicted ELP from the back calculated ELP based on the thin-lens formula described above. Conditional process analysis was defined as the method for calculating ELP prediction in the present study. The accuracy of refractive outcomes (prediction error (PE), median absolute error (MedAE), and mean absolute error (MAE)) using conditional process analysis was compared to those using the Haigis formula. Refractive outcomes using the Haigis formula were calculated using an optimized IOL constant for the IOLMaster (ZCB00; a0 = −1.302, a1 = 0.210 and a2 = 0.251 based on ULIB site) and the zeroing of ME was performed based on the analysis methods suggested by Hoffer et al. [16]. PE was defined as the actual postoperative spherical equivalent minus the predicted spherical equivalent using the IOL power actually implanted. MedAE and MAE were the median and the average from the absolute value of the PE, respectively. The percentages of eyes with PE within ±0.25 D, ±0.50 D and ±1.00 D were also obtained.
