This study was a randomized clinical trial registered at ClinicalTrial.gov (NCT03191942) and approved by the Ethics Committee of the Hong Kong Polytechnic University (HSEARS20170118004). It was conducted following the tenets of the Declaration of Helsinki, according to the procedures described previously [19]. At least 24 subjects were required for each group to achieve 80% power to detect an 0.18-mm between group difference in AL (over two years) [19]. All subjects gave informed assent and parents and/or guardians provided informed consent prior to participation.

After fulfilling the inclusion criteria and passing lens handling training, subjects were randomly fitted with 6-mm (6-MM) or 5-mm (5-MM) BOZD ortho-k lenses in both eyes. All subjects were of Chinese ethnicity, aged 6 to < 11 years old, with myopia between − 4.00 to − 0.75 D, and anisometropia less than 1.00 D. Total astigmatism was required to be ≤ 2.50 D for with-the-rule axes (180º ± 30º) and ≤ 0.50 D for other axes. Subjects with other conditions were excluded from participating, including a history of myopia control treatment, strabismus or amblyopia, contraindications to contact lens/ortho-k wear, systemic/ocular conditions affecting refractive status, poor compliance with follow-ups and lens wear/handling, and poor visual/ocular response after lens modification.

Subjects were fitted with either spherical or toric BE Free Lenses (Precision Technology Services, Vancouver, B.C., Canada) with a series of lens diameters (10.2–11.2 mm) and a compression factor of 0.75 D for all lenses. Complimentary care solutions (Ophtecs Corporation, Tokyo, Japan) were provided for cleaning (rub and rinse), rinsing, disinfecting, and releasing bound lenses, respectively: O2 Daily Care Solution Pure, Cleadew saline, Cleadew GP, and Tiare W artificial tears. Subjects were instructed to wear ortho-k lenses for eight hours each night and attend regular aftercare visits.

Measurements were conducted prior to commencing ortho-k treatment (baseline visit) and every six months thereafter, within ± 2 h of the time of baseline visit, to reduce potential confounding effects of diurnal variations.

Corneal topography was measured using an E300 Topographer (Version 6.1.2, Medmont International Pty. Ltd., Nunawading, VIC, Australia). Pupil diameter was estimated using the E300 under dark room lighting, but was considered a photopic pupil diameter measurement because of the internal equipment lighting (18.8 Lux) [20]. The TZ, enclosed by points with zero local paraxial power change, was determined by exporting raw tangential curvature data from the Medmont software which were fitted with a best-fit ellipse using a Python-based software developed previously [8]. The horizontal TZ diameter was selected to represent the TZ changes in the current study.

Monochromatic (wavelength of 555 nm) ocular aberrations of the right eye were measured using a Shack-Hartmann aberrometer (COAS version 1.44.12, Wavefront Sciences Ltd., Albuquerque, NM, USA) in a dark room (five lux) with the left eye occluded. Participants viewed an external target through a Badal system, to correct their non-cycloplegic spherical equivalent refraction (SER) and ensure relaxed accommodation [21]. Measurements were repeated five times (each containing 25 frames) and averaged for analysis. The 125 measurements obtained at each visit were screened using customised software, excluding measurements with pupil size or RMS of total HOAs beyond the median of the sample, by 0.50 mm and 0.10 µm, respectively. The screened measurements were then fitted with a Zernike polynomial up to and including the 6th radial order and averaged.

Previous studies investigating HOAs have used a range of pupil diameters for analyses (4 mm [22], 5 mm [17], or 6 mm[16]). A 4-mm pupil diameter was used in the current study, as this is more likely to be the typical pupil diameter of children during daily activities (e.g., near work under photopic conditions) rather than a larger cycloplegic pupil diameter. The data was rescaled to a 4-mm pupil diameter using Schwiegerling’s technique [23], to avoid potential errors when extrapolating the Zernike polynomials to a larger pupil size. The RMS of total HOAs, individual Zernike coefficients of LOAs (2nd order) and HOAs (3th to 6th order), and RMS of SA (combination of \(_^\) and \(_^\)) and coma (combination of \(_^\), \(_^\), \(_^\), and \(_^\)) were calculated.

Two drops of 1% cyclopentolate were instilled with a 5-min interval in between, and full cycloplegia was achieved when there was no pupil reaction to light and less than 2.00 D accommodation (using an RAF ruler). Post-cycloplegic subjective refraction was assessed by the same practitioner using trial (ophthalmic) lenses. Axial length (AL) measurements (IOLMaster 500; Carl Zeiss Meditec AG, Jena, Germany) were performed after cycloplegia by a masked examiner (masked for AL measurements). Five measurements with a signal-to-noise ratio ≥ 5 and between-differences ≤ 0.02 mm were averaged for analysis.

All statistical analyses were conducted using SPSS (ver. 26.0, IBM Corporation, Amonk, NY, USA). Only data from the right eyes were included in the analysis. Subjects with missing baseline HOAs were excluded. The normality of the data was investigated with the Shapiro-Wilk test. Unpaired t-test and Mann-Whitney test were performed to compare baseline measurements between subjects who completed and who dropped out from the study, and between the two groups, for normally or non-normally distributed data, respectively. Sex was compared using the Chi-squared test. Repeated measures ANOVA was used to examine changes in TZ diameter, AL, and various HOA and LOA metrics within subjects (time effect), between subjects (group effect), and their interaction (group by time interaction). Due to limited aberration data at the 18-month visit (6-MM group: n = 12; 5-MM group: n = 14) (interrupted data collection schedule due to social unrest and COVID-19), this visit was excluded from the repeated measures analysis. Post-hoc analysis was conducted using paired or unpaired t-tests with Bonferroni correction. Simple linear regression was used to evaluate the association between the horizontal TZ diameter and AE.

Horizontal TZ diameter at the 6-month visit was included as a fixed factor in all linear mixed models (LMMs). An initial LMM, using the pooled data (5-MM and 6-MM groups combined), was constructed to investigate the parameters (lens design, baseline age, sex, SER, AL, pupil diameter, and change in SER) associated with the horizontal TZ diameter. A series of LMMs (Models 1–5) were then used to investigate the association between baseline data (age, sex, SER, pupil diameter, AL, and corresponding HOAs or LOAs terms) and the horizontal TZ diameter with the changes in various ocular aberration terms. An LMM was applied to explore the effect of sex, TZ diameter at 6 months, and baseline data (pupil diameter, SER, best-corrected visual acuity, AL, RMS HOAs, and RMS LOAs) on AL over two years (Model 6), using pooled data and each group independently. Model 6 determined which baseline factors should be included in subsequent modelling (Models 7–11), which included aberration metrics. To explore the aberration terms associated with AL over two years, a series of LMMs, controlling for the significant baseline parameters found in Model 6, were used (Models 7–11), both with the pooled data and each group independently: Model 7 included the RMS HOAs; Model 8 analysed the RMS LOAs; Model 9 included RMS SA and RMS coma for analysis; Model 10 analysed primary (\(}_^\)) and secondary (\(}_^)\) SA; and Model 11 included each second order aberration term. All LMMs were constructed using a first-order autoregressive covariance and restricted maximum likelihood estimation, including individual subject’s slope and intercept as random effects and unstructured covariance matrix to control inter-subject variations. A backward stepwise approach was used, excluding the least significant factors to improve the fit of each model, based on the Akaike information criterion [24]. A P value of less than 0.05 was considered statistically significant.