purpose. A time-varying statistical model was proposed to predict the risk of regression toward myopia after laser in situ keratomileusis (LASIK) and to identify significant predictors within a time frame.

methods. A total of 615 eyes of 311 patients derived from a retrospective cohort who underwent LASIK in 2003 were analyzed. Refraction outcomes were recorded at 1 day, 1 week, and 1, 3, 6, 9, and 12 months or longer after LASIK. A cross-validated design was used, to split data into trained (*n* = 308) and validated (*n* = 307) data sets. These data sets were used in an interval-censored model to predict the probability of regression toward myopia and to assess the predictors including demographic features and preoperative and postoperative variables.

results. Myopia regression was observed in 164 (26.7%) of 615 eyes during the follow-up period of 12 months or longer after LASIK. Significant predictors for myopia regression after LASIK included preoperative manifest spherical equivalent (*P* = <0.0001), mean preoperative central corneal curvature (*P* = 0.001), size of optic zone (*P* = 0.0043), undercorrection (*P* = 0.04), and age (*P* = 0.0734). The risk of regression toward myopia after LASIK increased rapidly within 1 month, slowed down between 1 and 6 months, and became steady after 6 months, regardless of risk group. The risk of myopia regression up to 6 months after LASIK was 21% in average-risk eyes (based on all eyes).

conclusions. The proposed interval-censored model was useful not only for predicting the probability of myopia regression after LASIK but also for identifying the evolution of patients within low, moderate, and high-risk groups.

^{ 1 }treatment with LASIK (laser in situ keratomileusis) has increasingly gained attention. However, the incidence of regression toward myopia (hereafter, myopia regression) after LASIK varies across studies, ranging from 5.5% to 27.7%.

^{ 2 }

^{ 3 }

^{ 4 }

^{ 5 }

^{ 6 }

^{ 7 }Most of the previous studies in which investigators identified clinical correlates responsible for refractive outcome after LASIK were focused only on cases involving retreatment,

^{ 2 }

^{ 4 }

^{ 8 }

^{ 9 }

^{ 10 }rather than on all patients with different degrees of regression toward myopia, from mild to severe. However, patients’ tolerance of residual myopia and their ophthalmologists’ threshold for determining the need for retreatment play vital roles in their decisions for retreatments.

^{ 4 }As retreatment cases may represent only a small proportion of patients who had severe myopia regression after LASIK, this selection bias may lead to the failure of completely identifying clinical correlates related to myopia regression and may underestimate the risk of regression.

^{ 11 }considering the degree of myopia regression occurring during a specific time interval after LASIK, was proposed to tackle this problem. The purposes of this study, conducted in all identifiable cases of myopia regression after LASIK, were therefore (1) to report the risk of myopia regression within a time frame; (2) to identify significant predictors; and (3) to develop a time-varying predictive model for estimating the probability of myopia regression by different time intervals of follow-up based on (1) and (2).

*n*= 4), those undergoing surgery with complications (

*n*= 7), those lacking complete preoperative measurement records (

*n*= 23), those having postoperative visits for <1 month (

*n*= 78), and those having postoperative complications such as SOS (sands of the Sahara) syndrome (

*n*= 8), 615 eyes (311 subjects) met the inclusion criteria and were used in the analysis.

^{ 6 }: group 1 (low myopia), baseline refraction below −6.0 D; group 2 (moderate myopia), baseline refraction from −6.0 D to less than −10 D; and group 3 (high myopia), baseline refraction greater than or equal to −10 D.

^{ 12 }

^{ 13 }and therefore the eyes were stratified into another two groups for assessment of the refraction change after LASIK: group 1, eyes with optic zone greater than or equal to 6.0 mm; group 2, eyes with optic zone <6.0 mm.

*t*-test and ANOVA were used to assess the differences of relevant clinical correlates across two or three groups. Differences were considered statistically significant at

*P*< 0.05. To detect multicollinearity, we applied the Pearson product moment correlation analysis to examine the correlation between independent variables and to classify three groups in the light of correlation coefficients.

^{ 11 }

_{ ij }is the probability that the

*i*th subject will have myopia regression in the

*j*th period and γ

_{ j }is the regression coefficient of the

*j*th follow-up period denoted by γ

_{1,}γ

_{2}, … , γ

_{5}, corresponding to five intervals between follow-up visits: 1 week to 1 month, 1 month to 3 months, 3 months to 6 months, 6 months to 9 months, 9 months to 12 months or longer after surgery. Note that since the interval between examinations was not equivalent, the variable “period” was treated as a categorical variable. The risks for the development of myopia regression in each period (γ

_{ j }) were also estimated.

_{ i }represents the magnitude of the risk of having myopia regression based on clinical correlates, for the

*i*th subject. It can be written as follows

*X*is a set of predictors, and β is the corresponding regression coefficients that can be trained by the application of the interval-censored model using equations 1 and 2with the trained data set.

*y*-axis) against 1 − specificity (

*x*-axis), both of which were calculated by cross-tabulating the predicted with the observed, using the trained and validated data sets, respectively, given a series of cutoff points based on scores in equation 2 . The larger the area under the ROC, the better the internal validity of the model. Whether the lower limit of the 95% confidence interval (CI) for the area under the ROC curve was larger than 50% was used to assess statistical significance for the adequacy of the predictive model. Note that the calculations were performed for both the trained and validated data sets, but the result from the validated model is more important than that from the trained model, because the former was not involved in training regression coefficients. All statistical analyses were performed using the SAS 9.1 program for Windows.

*n*= 242; 77.8%), and the mean age was 31.1 ± 6.2 (SD) years (interquartile range: 27, 35 years). The mean manifest spherical equivalent refraction was −7.08 ± 2.49 (SD) D (interquartile range: −8.88, −5.13 D). The mean ablation depth of the optic zone was 99.27 ± 26.95 μm (interquartile range: 82.2, 120.6 μm) with a mean optic zone diameter of 5.81 ± 0.34 mm (interquartile range: 5.6, 6.0 mm).

*P*= <0.0001), mean preoperative corneal curvature (β = −0.1807,

*P*= 0.0009), diameter of optic zone (β = −0.6593,

*P*= 0.0043), undercorrection (β = 0.5530,

*P*= 0.0396), and age (β = 0.0297,

*P*= 0.0734). The risks of myopia regression in the five periods (γ

_{1,}γ

_{2}, … , γ

_{5}) are also shown in Table 2 .

_{1},β

_{2}, … , β

_{5}are the coefficients for each period in Table 2 . Calculation of equation 1shows that the predicted probability (π

_{1}) of myopia regression in the first period (from 1 week to 1 month after LASIK) is

_{1}is the regression coefficient of the first follow-up period (Table 3) . The predicted probability of other periods (π

_{2,}π

_{3,}π

_{4,}and

_{π5}) for the same patient can be calculated in a similar manner. Therefore, the cumulative probability of myopia regression until period 5 is equivalent to

^{ 2 }

^{ 3 }

^{ 4 }

^{ 5 }

^{ 6 }Lyle et al.

^{ 2 }reported 114 eyes re-treated for regression with an overall regression rate of 5.5% in a large case study (114/2065 eyes with preoperative myopia of −6.11 ± 2.35 D). The lower rate may be attributable to the exclusion of the cases of regression that did not undergo retreatment. The definition of regression in Lyle et al.

^{ 2 }was a residual myopia of greater than −0.5 and a 0.25-D or greater shift toward myopia between follow-ups except in the cases of undercorrection. Chayet et al.

^{ 3 }found a regression rate of 28% (13/47 eyes were retreated for regression) in patients with mean preoperative myopia of −14.02 ± 5.3 D based on the definition of regression as a 0.25-D or greater myopic shift occurred between follow-up visits. If we take different operative definitions of myopia regression in previous studies

^{ 2 }

^{ 3 }

^{ 5 }

^{ 6 }

^{ 14 }

^{ 15 }as a reference, our regression rate defined by a residual myopia of −1.0 D or greater and myopic shift by 0.5 D or greater during follow-up visits is 26.7%, close to the 28.01% predicted value reported in Table 3 . The incidence of myopia regression found in our study is probably more comprehensive than that reported in the previous studies, because we analyzed the evolution of all cases undergoing LASIK by one surgeon instead of retreatment cases only.

^{ 3 }

^{ 8 }

^{ 16 }

^{ 17 }

^{ 18 }but only one study included follow-up to 1 to 2 years after surgery.

^{ 2 }In cases of high preoperative myopia, regression has been observed to peak within 6 months after the initial LASIK surgery and then to stabilize afterward.

^{ 3 }

^{ 16 }This finding was consistent with our estimated results based on the average-risk group. Cumulative risk for myopia regression increased from 10% within a month to 21% within 6 months after LASIK but then became stable (Table 3) . In eyes with preoperative myopia of −14 D, Chayet et al.

^{ 3 }reported a regression rate of 27.7% within 3 months after surgery that then stabilized between 3 and 6 months. Their result was higher than the 14% reported in our study (Table 3) , because patients treated with LASIK in their study had a higher grade of myopia than did those in our study (−14 D vs. −7.08 D). Perez-Santonja et al.

^{ 16 }reported a regression of 0.53 D between 1 and 3 months after surgery in eyes with preoperative mean myopia of −13 D, but no significant regression after 3 months after surgery. Based on Figure 2in Perez-Santonja et al.,

^{ 16 }the regression rate when −1 D was used as a criterion 6 months after surgery was ∼19.56%, which was close to the 21% in our study (Table 3) .

^{ 2 }

^{ 3 }

^{ 4 }

^{ 6 }

^{ 7 }

^{ 16 }

^{ 19 }

^{ 20 }

^{ 21 }

^{ 22 }corneal curvature,

^{ 2 }

^{ 3 }

^{ 14 }

^{ 16 }corneal thickness,

^{ 3 }

^{ 6 }

^{ 15 }

^{ 20 }flap thickness,

^{ 23 }

^{ 24 }

^{ 25 }ablation depth,

^{ 2 }optic zone size,

^{ 6 }

^{ 12 }chronic dry eye,

^{ 5 }age,

^{ 4 }surgeon,

^{ 4 }IOP,

^{ 2 }

^{ 16 }and humidity.

^{ 2 }Using an interval-censored model, we not only identified clinical correlates related to myopia regression but also predicted time-varying risk for myopia regression. We considered multicollinearity between variables and chose the appropriate ones, given the orthogonal properties between two of each. Significant predictors identified in multivariate analysis of the interval-censored model included manifest refraction, preoperative keratometry reading, size of optic zone, and undercorrection. Our significant predictors were consistent with those identified in the previous findings. Greater preoperative refraction

^{ 2 }

^{ 3 }

^{ 4 }

^{ 6 }

^{ 7 }

^{ 16 }

^{ 19 }

^{ 20 }

^{ 21 }

^{ 22 }increased the probability of myopia regression or retreatment; size of optic zone

^{ 6 }

^{ 12 }

^{ 16 }was associated with refractive outcome after LASIK; flatter preoperative keratometry was associated with a more myopic outcome after LASIK

^{ 16 }; and preoperative keratometry <43.5 D predicted greater undercorrection (greater residual myopia shift at 3 months after surgery, according to the definition in Rao et al., which may contain some regressed eyes, according to our definition).

^{ 14 }

^{ 2 }

^{ 3 }

^{ 26 }our study treated undercorrection as one of our independent variables in multivariate analysis instead and found that undercorrection led to a higher probability of myopia regression. However, a high association between undercorrection and preoperative MSE is probable. This probability raises a concern as to whether both, if included in the same model, may cause colinearity. However, as tested by the VIF, a method for detecting colinearity, no apparent colinearity problem was revealed and thus undercorrection and preoperative MSE should be thought of as two independent predictors of myopia regression.

^{ 4 }developed a mathematical predictive formula for retreatment, with multiple variables including age, preoperative cycloplegic sphere, and surgeon. Our study had two characteristics that were different from those in Hu et al.

^{ 4 }: In their study, the risk of myopia regression was not reported in a longitudinal time frame, and only retreatment cases were included. A logistic regression model that treats retreatment or not as a binary variable (yes/no) predicted an 18% rate of retreatment, which is slightly lower than the predicted 28% rate a year after LASIK— the time when myopia regression reached a plateau. The higher rate in our study compared with that in Hu et al. was partly due to the inclusion of myopia regression in our study rather than only retreatment as in Hu et al. and also was partly due to different types of predictive models in our study (interval-censored model) and their study (logistic regression model). Another disparity is that the “surgeon factor” was taken into account in their study in which patients were treated by two surgeons who had variations in threshold for retreatment, whereas only one ophthalmologist was involved in our study. Our model focused on each eye rather than a subject (person) with cross-validated design by randomly selecting one eye from each subject to build up the predictive model. This method may eliminate the problem of correlation between both eyes of a patient.

^{ 3 }

^{ 15 }

^{ 16 }the definition of myopia regression would have been more valid if the measurement of the postoperative Mean K and CCT had been collected together. Second, one of our variables in the model is undercorrection, which is identified after surgery, and thus may limit the model’s application in patient counseling before LASIK but is still useful for predicting the evolution of refraction during follow-up after LASIK.

Variable | Mean | SD | Lower Quartile | Upper Quartile |
---|---|---|---|---|

Age (y) | 31.1 | 6.2 | 27 | 35 |

Manifest refraction | ||||

Msph (D) | −6.61 | 2.40 | −8.50 | −4.75 |

Mcyl (D) | −0.95 | 0.76 | −1.25 | −0.50 |

Maxis (deg) | 104.88 | 79.99 | 15.00 | 170.00 |

MSE (D) | −7.08 | 2.49 | −8.88 | −5.13 |

Cycloplegic refraction | ||||

Csph (D) | −6.39 | 2.84 | −8.00 | −4.50 |

Ccyl (D) | −1.13 | 3.11 | −1.25 | −0.50 |

Caxis (deg) | 96.95 | 74.02 | 11.00 | 170.00 |

CSE (D) | −6.95 | 3.24 | −8.75 | −4.88 |

Nomogram-adjusted refraction | ||||

Nomo_sph (D) | −6.73 | 2.39 | −8.50 | −5.00 |

Nomo_cyl (D) | −0.93 | 0.83 | −1.25 | −0.50 |

Nomo_axis (deg) | 102.61 | 182.04 | 5.00 | 170.00 |

NomoSE (D) | −7.19 | 2.50 | −9.00 | −5.25 |

MeanK (D) | 43.67 | 1.95 | 42.83 | 44.63 |

Flap_thick (μm) | 131.71 | 6.96 | 130.00 | 130.00 |

Flap_diameter (mm) | 8.97 | 0.17 | 9.00 | 9.00 |

Size_OZ (mm) | 5.81 | 0.34 | 5.60 | 6.00 |

Size_TZ (mm) | 6.83 | 0.37 | 6.70 | 7.00 |

Depth_OZ (μm) | 99.27 | 26.95 | 82.20 | 120.60 |

Depth_TZ (μm) | 17.15 | 6.69 | 13.50 | 20.40 |

Central corneal thickness (CCT) (μm) | 546.75 | 55.81 | 529.00 | 571.00 |

RBT (μm) | 315.76 | 60.93 | 287.00 | 344.20 |

IOP (mm Hg) | 15.53 | 6 | 13.00 | 17.00 |

Schirmer test (mm) | 20.35 | 10.31 | 14.00 | 26.00 |

**Figure 1.**

**Figure 1.**

**Figure 2.**

**Figure 2.**

Variable | Regression Coefficient | SE | P (Wald Test) |
---|---|---|---|

Intercept | 5.9856 | 2.8238 | 0.0340 |

Period (γ) | 0.0219 | ||

Period 1 | 0 | ||

Period 2 | −0.9541 | 0.3496 | |

Period 3 | −0.2530 | 0.3280 | |

Period 4 | −0.8615 | 0.5998 | |

Period 5 | −0.8945 | 0.6016 | |

MSE (β_{1}) | −0.3570 | 0.0505 | <0.0001 |

Mean K (β_{2}) | −0.1807 | 0.0544 | 0.0009 |

Size_OZ (β_{3}) | −0.6593 | 0.2311 | 0.0043 |

Undercorrection (β_{4}) | 0.5530 | 0.2688 | 0.0396 |

Age (β_{5}) | 0.0297 | 0.0166 | 0.0734 |

Eye | MSE | MEANK | Size_OZ | Under correction^{*} | Age | Score | Period^{, †} | Probability^{, ‡} | Cumulative Probability^{, §} |
---|---|---|---|---|---|---|---|---|---|

1 | −13.625 | 44.24 | 5.5 | 0 | 23 | −0.0875 | 1 | 0.6002 | 0.6002 |

2 | 0.2975 | 0.7191 | |||||||

3 | 0.5092 | 0.8621 | |||||||

4 | 0.3211 | 0.9064 | |||||||

5 | 0.3126 | 0.9357 | |||||||

2 | −8.25 | 42.75 | 5.5 | 0 | 35 | −1.3807 | 1 | 0.2223 | 0.2223 |

2 | 0.0923 | 0.2941 | |||||||

3 | 0.1773 | 0.4193 | |||||||

4 | 0.1008 | 0.4778 | |||||||

5 | 0.0977 | 0.5288 | |||||||

3 | −2.75 | 44.69 | 6.5 | 0 | 23 | −4.7105 | 1 | 0.0091 | 0.0091 |

2 | 0.0035 | 0.0124 | |||||||

3 | 0.0071 | 0.0194 | |||||||

4 | 0.0039 | 0.0232 | |||||||

5 | 0.0017 | 0.0248 | |||||||

All eyes (mean) | −7.08 | 43.67 | 5.81 | 0.13171 | 31 | −2.2094 | 1 | 0.1040 | 0.1040 |

2 | 0.0414 | 0.1411 | |||||||

3 | 0.0817 | 0.2113 | |||||||

4 | 0.0453 | 0.2470 | |||||||

5 | 0.0439 | 0.2801 |

**Figure 3.**

**Figure 3.**

**Figure 4.**

**Figure 4.**