Unraveling the Heritability of Ocular Rigidity and Myopia-Related Traits: A Siblings-Based Study

Abstract

Purpose

Ocular rigidity (OR) is a macroscopic biomechanical parameter that represents the distensibility of the ocular globe, particularly of the sclera. To better understand the role of OR in refractive development, this study aimed to quantify the heritability of OR and other myopia-related traits in healthy siblings.

Methods

A validated method based on video rate choroidal optical coherence tomography imaging and dynamic contour tonometry was used to measure OR in siblings. We estimated heritability of OR, as well as IOP, ocular pulse amplitude, axial length, spherical equivalent refraction, submacular choroidal thickness, pulsatile choroidal thickness change, and pulsatile choroidal volume change, using maximum likelihood variance components methods.

Results

Forty-five subjects (21 sibling groups, 58% female, 47% with myopia) aged 11.7 ± 4.9 years were included in this study. Crude heritability estimates for OR were 0.59 (95% confidence interval [CI], 0.32–0.81; P = 0.0003) without adjustments, and 0.59 (95% CI, 0.33–0.81; P = 0.0002) after adjusting for age and sex. Unadjusted heritability estimates were 0.49 (95% CI, 0.20–0.78) for IOP, 0.33 (95% CI, 0.09–0.71) for OPA, 0.57 (0.30–0.80) for axial length, 0.03 (0.00–0.99) for spherical equivalent refraction, 0.51 (95% CI, 0.24–0.77) for choroidal thickness, 0.45 (95% CI, 0.18–0.75) for pulsatile choroidal thickness change, and 0.40 (95% CI, 0.14–0.73) for pulsatile choroidal volume change.

Conclusions

This study presented the first quantification of heritability for OR, indicating substantial familial aggregation of OR among siblings. While these findings can have implications in myopia, further investigation is needed to determine the influence of familial factors, both genetic and environmental, on the sclera.

Myopia is highly prevalent and develops in childhood and early adolescence.¹ The mechanisms regulating eye growth are multifactorial,² yet much remains unknown about myopigenesis. Genetic contributions to myopia are currently a major research focus.^3–7 Myopia is highly heritable, and genetic factors are reported to influence its onset and progression.⁸ Twin and family studies support this hypothesis, with reported heritability estimates as high as 80% in some twin cohorts.^9–11 Genome-wide association studies have identified more than 200 genetic loci associated with myopia,^12,13 with key genes being involved in scleral remodeling, including those encoding collagen and other extracellular matrix proteins. Despite the identification of numerous genetic variants, each variant individually contributes only a small effect, underscoring the polygenic nature of myopia. When both parents are myopic, studies report that the likelihood of their offspring developing myopia, and the rate of progression once myopia occurs, is substantially higher compared with children of nonmyopic parents.^5,14,15 Similarly, twin and sibling studies have shown significant correlation in refractive error, ocular biometric parameters, and visual environment among siblings.¹⁶

Beyond genetic determinants, experimental and clinical data underscore the importance of scleral biomechanics in myopia development and progression.^17–22 Ocular rigidity (OR) represents the distensibility of the eye globe, particularly of the sclera which composes 80% of the ocular shell.^23,24 OR can be described using the Friedenwald function,²³ which relates IOP and volume (V) changes in the eye as follows:

$$\begin{array}{c}\hfill ln\frac{IOP}{IO{P}_0}=OR*\left(V-V_0\right).\end{array}$$ (1)

A higher OR value represents a rigid eye or stiffer sclera (akin to a soccer ball), whereas a lower OR value represents a more compliant eye (akin to a birthday balloon).

OR can be measured using a reliable, direct, and validated method in children and young adults. The noninvasive measurement method uses dynamic optical coherence tomography imaging to estimate choroidal filling and contour tonometry to measure the corresponding pulsatile IOP change.^25–27 This method was validated against an invasive procedure,²⁶ shown to have good repeatability,²⁷ and shown to have relevance to several ocular conditions including myopia and glaucoma.^{22,24,28–32} In myopia, longer eyes were shown to have a lower OR, reflecting a more compliant sclera.^21–23,33

Given the central role of the sclera in the development and progression of myopia, and the strong evidence of familial influence on myopia risk, we hypothesize that OR will show measurable heritability in first-degree relatives. Specifically, in our sibling cohort, we sought to quantify the familial heritability of OR and other myopia-related traits as the sibship-level proportion of phenotypic variance (h²), which we interpret as familial aggregation reflecting the combined influence of shared genetic and/or shared environment. This study, therefore, provides the first clinical assessment of the heritable interplay between familial influences and scleral biomechanics in living eyes.

Methods

This study followed the tenets of the Declaration of Helsinki and was approved by the University of Houston Institutional Review Board. After providing informed consent (and assent when applicable), subjects were enrolled and OR and other potential myopia endophenotypes were measured.

Children and young adults aged 6 years and older were recruited from the University Eye Institute at the University of Houston College of Optometry and the community as part of a larger prospective study on OR in healthy and diseased eyes. Participants were required to have clear ocular media and adequate fixation, with no history of eye injury, trauma, surgery, narrow angles, or nystagmus. Subjects with systemic collagen disease or diabetes mellitus (which can influence OR), keratoconus, or irregular cornea were excluded. Rigid contact lens wearers as well as past or currently treated for myopia control were also excluded. Siblings were defined as having the same biological father and mother.

All measurements were carried out on one eye, chosen randomly, independent of myopia status. We previously described the noninvasive method to measure OR.^25–27 Briefly, video rate optical coherence tomography imaging (Spectralis Spectral Domain OCT2, Heidelberg Engineering, Heidelberg, Germany) with enhanced depth imaging was carried out along with simultaneous finger oximetry. A custom neural network approach was adapted for automated segmentation of the choroid and used to measure subfoveal choroidal thickness (CT) and the pulsatile CT change (ΔCT) through the time series²⁷ (Fig. 1A). Heart rate was used to confirm correspondence with the frequency of the ΔCT detected in the optical coherence tomography videos (Fig. 1B). The pulsatile choroidal volume change (ΔV), or V–V₀, was then derived using a two-sphere mathematical model of the choroid (Fig. 1C) according to the following equation:

$$\begin{array}{c}\hfill \Delta V=\frac{\pi }{2}{\left(AL-ACD+CT\right)}^2·\Delta CT,\end{array}$$ (2)

where AL is the axial length, and ACD is the anterior chamber depth measured using the Lenstar LS900 (Haagstreit, Germany) optical biometer. The two-sphere model has been described in detail elsewhere²⁶ and is based on anatomical data from adult eyes with refractive errors and sizes consistent with ranges included in this study. In the two-sphere model, the inner sphere's diameter is equal to the AL minus the anterior chamber depth, and the outer sphere's diameter is larger by the equivalent of mean the CT. The average radius of the outer sphere represents one-half of the adjusted AL plus the mean submacular CT. The net movement of the larger sphere's diameter at each heartbeat is equal to the ΔCT. Pulsatile ocular volume changes were estimated through ΔV because approximately 90% of the blood flow into the eye is through the choroid.

Figure 1.

(A) Automated segmentation of the choroid in a single B-scan from an optical coherence tomography video. CT corresponds to the distance between BM and CSI. The pulsatile ΔCT is computed as the CT change between each frame of the video. (B) (Top) Frequency spectrum analysis of ΔCT showing raw CT fluctuations versus time (black) and band-pass filtered CT signal (red). (Bottom) The dashed blue lines indicate the first two harmonics of the measured heart rate. The frequency spectrum analysis shows correspondence with the heart rate frequency, confirming that fluctuations in CT with time are due to the pulsatile blood flow. (C) Two-sphere mathematical model of choroidal thickness. The diameter of the inner sphere is equal to the measured AL minus the anterior chamber depth (AL_adj). The outer sphere with diameter of (AL_adj + CT) increases by ½ ΔCT at systole and decreases by the same amount at diastole, equivalent to a net expansion of ΔCT at each heartbeat. (A and B reprinted from Reyes M, Smith S, Lam K, Adel Y, Patel NB, Sayah DN. The noninvasive measurement of ocular rigidity and the pulsatile choroidal volume change in children and young adults. Ophthalmol Sci. 2025;5(5):100814. © 2025 by the American Academy of Ophthalmology, published open access under the CC BY-NC-ND license. Part C adapted from.²⁶).

Immediately after imaging, one drop of anesthetic (proparacaine HCl 0.5%) was instilled in the study eye and the diastolic IOP and ocular pulse amplitude was measured using the Pascal tonometer (Ziemer Ophthalmic Systems, Port, Switzerland), which is independent of corneal biomechanical properties,^34–36 according to the following equation:

$$\begin{array}{c}\hfill \frac{IOP}{IO{P}_0}=\frac{IOP+OPA}{IOP}.\end{array}$$ (3)

Finally, OR was computed from the volume and pressure changes ensued in the eye between the systole and diastole using Friedenwald's equation.

Open-field autorefraction was carried out using the Grand Seiko WAM-5500. Spherical equivalent refraction (SER) was calculated as the sum of the sphere and half of the negative cylindrical power, and myopia was defined as a SER of −0.50 diopters or less.

Statistical Analysis

To estimate heritability of OR and other myopia-related traits, we quantified the proportion of phenotype attributable to familial (sibship) clustering using linear mixed-effects models with a sibling-group random intercept. Models were fit by maximum likelihood variance components methods^37,38 and heritability was computed as the ratio of the sibling-group variance to total variance. Evidence for a nonzero sibling-group variance component was evaluated via a likelihood ratio test, comparing the random intercept model with a model with the sibling-group variance constrained to zero (i.e., comparing −2 log-likelihoods). We report likelihood ratio test results, heritability estimates with associated standard errors (SE), and 95% confidence intervals (CIs). Because the sibling-group random intercept captures within-sibship resemblance, reflecting both shared genetic and/or shared environmental influences, we report the estimated sibship-level proportion of variance as heritability (h²) and interpret it is as familial aggregation for the purpose of this study.

We performed both unadjusted and adjusted sensitivity analyses to examine how covariates age, sex, body mass index, ethnicity, and AL impact our findings. Covariates were modeled individually and in multivariable models to assess the stability of the sibling-group variance component and heritability estimates across these models. We additionally performed age-focused sensitivity subgroup analyses to assess the robustness of age-related variation to be included as Supplementary Materials.

Power was estimated using a design-matched, simulation-based approach for the likelihood ratio test of a nonzero sibship random-intercept variance component in the mixed model of OR. Simulations used the observed sibship configuration (21 sibships, predominantly pairs) and variance components consistent with the fitted model. Because the sibship variance component is constrained to be non-negative and is tested under a boundary null (variance = 0), we empirically calibrated the α = 0.05 decision threshold using null simulations and then estimated power under the alternative. Under this framework, we estimated approximately 92% power to detect a sibship effect of the magnitude observed for OR in the study sample. Given that power was evaluated for the base model without covariates, we assessed sensitivity to covariate adjustment by examining the stability of the sibship variance component and derived heritability estimates across adjusted model specifications, rather than conducting separate power computations for each model. Prior simulation studies suggest that heritability estimation is typically more stable when true heritability is moderate and that larger samples may be required when true heritability is low (<0.2).³⁹

Results

We first describe the study sample (Table 1). We then report heritability estimates from variance components models for OR (primary outcome) and other myopia-related traits (Table 2), followed by OR-specific robustness and age-sensitivity analyses (Table 3; Supplementary Table S1).

Table 1.

Demographic and Clinical Characteristics of the Study Sample (n = 45, Families = 21)

Demographics	Value
Age (years)	11.7 ± 4.9
Sex
Male	19 (42.2)
Female	26 (57.8)
Ethnicity
Asian	3 (13.3)
Black	4 (8.9)
Hispanic	25 (55.6)
White	10 (22.2)
Clinical
IOP (mm Hg)	15.6 ± 2.73
OPA (mm Hg)	1.85 ± 0.71
OR (1/µL)	0.019 ± 0.011
SER (diopters)	−0.54 ± 1.73, −0.45 (−1.24, 0.39)*
AL (mm)	23.3 ± 1.10
CT (µm)	299 ± 49.6
ΔCT (µm)	10.72 ± 5.72
ΔV (µL)	7.05 ± 3.68

OPA, ocular pulse amplitude.

^*Values are mean ± standard deviation, median (25th, 75th percentiles) or number (%).

Table 2.

Heritability Estimates Across OR and Other Myopia-Related Traits (n = 45, Families = 21)

Trait	Unadjusted h2 (SE)	P Value	95% CI	Adjusted h2 (SE)	P Value	95% CI
OR	0.59 (0.14)	0.0003	0.32–0.81	0.59 (0.13)	0.0002	0.33–0.81
IOP	0.49 (0.17)	0.0085	0.20–0.78	0.54 (0.16)	0.0060	0.24–0.81
OPA	0.33 (0.18)	0.0383	0.09–0.71	0.27 (0.19)	0.0860	0.05–0.18
AL	0.57 (0.14)	0.0008	0.30–0.80	0.58 (0.15)	0.0012	0.30–0.82
SER	0.03 (0.20)	0.445	0.00–0.99*	0.06 (0.23)	0.3937	0.00–0.99
Cycloplegic SER*	0.10 (0.20)	0.313	0.001–0.907	0.03 (0.22)	0.4471	0.00–0.99
CT	0.51 (0.15)	0.002	0.24–0.77	0.40 (0.17)	0.012	0.14–0.73
ΔCT	0.45 (0.16)	0.007	0.18–0.75	0.36 (0.19)	0.027	0.10–0.74
ΔV	0.40 (0.17)	0.016	0.14–0.73	0.28 (0.19)	0.056	0.06–0.70

Adjusted models include age and sex as fixed effects for all traits. Expanded OR results are presented separately in Table 3.

^*Cycloplegic SER is reported for n = 38.

Table 3.

OR Heritability Under Expanded Covariate and Sensitivity Model Specifications

Model	h2	SE	P Value	95% CI
Unadjusted	0.586	0.135	0.0003	0.322–0.809
Adjusted age	0.590	0.133	0.0002	0.328–0.809
Adjusted sex	0.593	0.135	0.0003	0.327–0.814
Adjusted BMI	0.589	0.139	0.0003	0.318–0.816
Adjusted ethnicity	0.595	0.141	0.0006	0.318–0.823
Adjusted AL	0.586	0.135	0.0003	0.322–0.809
Adjusted sex age	0.592	0.134	0.0002	0.329–0.811
Adjusted sex age AL	0.594	0.134	0.0003	0.330–0.813
Adjusted sex age AL BMI	0.620	0.133	0.0002	0.350–0.831
Adjusted sex age AL BMI ethnicity	0.621	0.142	0.0007	0.335–0.843

BMI, body mass index.

Results pertain to the estimated heritability. P values correspond with the likelihood ratio test comparing the random-intercept model with a model in which the sibling-group variance component is constrained to zero.

Sample Characteristics

Our initial sample of subjects included 47 (22 sibling groups); however, one pair was excluded due to anisometropia. Forty-five subjects (21 sibling groups) were eligible for this study. Sibling group size ranged from 2 to 4, among which 18 (86%) were sibling pairs. The mean age was 11.7 ± 4.9 years (range, 6–27 years). The sample was 58% female, 56% Hispanic, 22% White, 9% Black, and 13% Asian. Although not a part of the enrollment protocol, most participants (87%) were younger than 18 years, and 47% had myopia. Across sibling groups, 5 (24%) were all myopic, 10 (48%) included a mix of myopic and nonmyopic, and 6 (28%) were all nonmyopic. The median within-sibship age difference was 2 years (25th, 75th percentile, 2, 4 years) (range, 1–10 years). Participant characteristics are summarized in Table 1.

Heritability Estimates Across OR and Other Myopia-related Traits

OR showed strong evidence of heritability in both unadjusted and age- and sex-adjusted models (Table 2; unadjusted h² = 0.59 [SE, 0.14]; P = 0.0003; 95% CI, 0.32–0.81; adjusted h² = 0.59 [SE, 0.13]; P = 0.0002; 95% CI, 0.33–0.81). Figure 2 provides a descriptive visualization of within-sibship concordance in OR.

Figure 2.

Scatterplot of OR (1/µL) in the youngest versus oldest sibling within each sibship (n = 21 sibships). Each point represents one sibship. The dashed line indicates equal OR between siblings; distance from the line reflects within-sibship differences. Shown for descriptive visualization; inference is based on the variance components model reported in Tables 2 and 3.

Across other myopia-related traits summarized in Table 2, IOP heritability was moderate and similar with covariate adjustment (unadjusted h² = 0.49; 95% CI, 0.20–0.78; adjusted h² = 0.54; 95% CI, 0.24–0.81). For ocular pulse amplitude, the unadjusted model suggested modest heritability (h² = 0.33; 95% CI, 0.09–0.71), whereas evidence was weaker after adjustment (h² = 0.27; 95% CI, 0.05–0.18) and the sibling-level variance component was not statistically distinguishable from zero in additional adjusted specifications including AL (results not presented). For AL, the sibling-level variance component was statistically greater than zero and heritability was estimated as h² = 0.589 (95% CI, 0.32–0.81), with similar estimates after adjustment. In contrast, SER heritability estimates were low and imprecise (noncycloplegic, h² = 0.03; 95% CI, 0.00–0.99), and among those with cycloplegic measurements (n = 38), h² = 0.10 (95% CI, 0.001–0.907). For choroidal measures, heritability estimates for CT, ΔCT, and ΔV were h² = 0.51 (95% CI, 0.24–0.77), h² = 0.45 (95% CI, 0.18–0.75), and h² = 0.40 (95% CI, 0.14–0.73), respectively. Age- and sex-adjusted models yielded heritability estimates that were approximately 20% lower than unadjusted estimates for these markers (Table 2); for ΔV, the sibling-level variance component was not statistically distinguishable from zero in the adjusted model.

OR: Expanded Covariate and Sensitivity Analyses

In OR-specific models (Table 3; Supplementary Table S1), the sibling-group random effect was statistically greater than zero and OR heritability was robust to covariate adjustment. Across model specifications that included fixed effects for age and sex (primary adjusted models) and sensitivity models that included body mass index, ethnicity, and AL (modeled individually and in multivariable models), fixed-effect estimates were generally imprecise (95% CIs included 0), whereas the sibling-level variance component remained consistently nonzero and heritability estimates were similar across specifications (h² = 0.586–0.620) (Table 3).

To assess whether age heterogeneity influenced familial variance estimates for OR, we conducted age-focused sensitivity analyses by refitting variance component models within age-defined subsets, among sibling pairs spanning age thresholds, and under within-sibship age-span restrictions. Across age-threshold subsets, point estimates varied (h² = 0.36–0.42 in younger groups and h² = 0.875–0.885 in older subsets) with substantially wider uncertainty in stratified analyses, limiting inference from between-subset contrasts. Estimates for sibling pairs spanning the age thresholds were more moderate (h² = 0.568–0.593 across thresholds). Full age-threshold, mixed-pair, and within-sibship age-span results and sample sizes are provided in Supplementary Table S1.

Discussion

To our knowledge, this study is the first to estimate the heritability of OR in a clinical sibling cohort. We observed substantial familial aggregation in OR among siblings, with a heritability estimate of 0.59 (95% CI, 0.32–0.81). Consistent with the magnitude of this estimate, the variance components model indicated that the sibship random intercept component accounted for a significant amount of variability in OR (likelihood ratio test P < 0.001). The estimate was similar after adjustment for age and sex (h² = 0.59; 95% CI, 0.33–0.81). Thus, our findings indicate that more than one-half of the variance in OR (59%) may be attributable to family-level factors, including shared genetic influences and/or environmental influences (e.g., family lifestyle, near-work habits, light exposure, and educational/household environments).

Interestingly, the inclusion of demographic covariates had minimal impact on the OR h² estimate, suggesting that the familial contribution to OR is largely independent of these measured demographic factors in our sample. For IOP, AL, and SER, estimated heritability increased after covariate adjustment. This finding is consistent with the scenario where fixed effects account for some individual-level variability, thereby reducing the residual variance and increasing the relative proportion of the remaining variance attributed to the sibship-level component. In modest clustered samples, however, such shifts may also reflect limited precision in variance component estimates. In contrast, for CT, ΔCT, and ΔV, the inclusion of fixed effects was accompanied by lower h², consistent with variance components models in which covariates account for shared variation, thereby reducing the total variance available for partitioning, which may shift variance away from the familial component.⁴⁰ Given our modest sample size, design differences across studies, and the novelty of OR as a phenotypic biomarker, these trait-specific estimates are best interpreted as complementary context and as a broad consistency check against existing heritability literature, rather than as directly comparable.

We compared our results with previously reported heritability estimates for myopia-related ocular traits. Our heritability estimate for IOP is consistent with findings from studies in first-degree relatives (h² = 0.53)⁴¹ and twin cohorts, where familial factors accounted for approximately 63% of the variation in Pascal IOP.⁴² Similarly, our estimate for ocular pulse amplitude (h² = 0.33) is lower than that observed in twins (h² = 0.62), which may reflect the reduced genetic similarity between nontwin siblings.⁴³ In contrast with the low heritability observed for SER (discussed elsewhere in this article), we observed a high heritability for AL (unadjusted h² = 0.57), consistent with previous estimates (unadjusted h² = 0.65), and also underscoring the strong familial (genetic and/or shared environment) basis of ocular structural determinants of myopia.⁴⁴ CT was also found to be heritable, in agreement with previous studies reporting moderate heritability in both Amish (h² = 0.40)⁴⁵ and twin cohorts (h² = 0.76).⁴⁶ Although pulsatile choroidal blood flow and ΔV represent different choroid-related pulsatility measures, prior work in adult first-degree relatives reported modest heritability estimates for pulsatile choroidal blood flow (unadjusted h² = 0.20; adjusted h² = 0.16).⁴¹ In our cohort, the pulsatile choroidal ΔV was attenuated after adjustment for age and sex (h² = 0.28; P = 0.056) relative to the unadjusted estimate (h² = 0.40). Despite broad alignment with previous reports, inference based on statistical significance for individual trait-specific heritability estimates, particularly for traits beyond OR and for covariate-adjusted models, should be interpreted cautiously given the modest sample size and limited power.

As noted, we observed a low heritability estimate of SER (unadjusted h² = 0.03; adjusted; h² = 0.06; h² = 0.10 for cycloplegic SER) in this cohort, suggesting a greater influence of environmental or nonshared factors in the refractive development in this sample. Published SER heritability estimates span a wide range of SER heritability (8%–90%) across studies,^44,47,48 likely reflecting differences in cohort-specific factors such as age and refractive error distribution. In our study, low SER heritability may reflect limited power or from sources that could increase within-family variability, including age-related refractive developmental changes, measurement variability in autorefraction, heterogeneity of refractive states within sibships (mix of myopes and nonmyopes), and our use of a single randomly selected eye, which may weaken between-sibling correlations. In general, heritability estimates are method dependent and reflect both the study population and analytic choices, including how SER (or myopia status) is operationalized in the statistical model. Studies focused specifically on the heritability of myopia among siblings also reported a wide range of heritability, with higher heritability estimates for high myopia and lower estimates for mild myopia, suggesting potential regional and cohort differences.^49–54 In age-focused sensitivity analyses, familial clustering was essentially undetectable in children younger than 11 years (h² = 0) and only modest in those 11 years and older (h² = 0.16), with wide uncertainty; in concordant-family myopia strata, concordant nonmyopic families showed a small h² (∼0.08) and concordant myopic families showed little to no clustering (h² = 0). We therefore interpret these subgroup analyses as exploratory robustness checks, rather than evidence that SER heritability truly differs by age or myopia context in this sample.

Because siblings can differ meaningfully in age (and therefore in developmental stage and time at risk), we conducted sensitivity analyses to evaluate whether the OR variance component findings were robust to age heterogeneity. These included analyses within age-threshold subsets, among sibling pairs spanning age thresholds, and with restrictions on within-sibship age span (Supplementary Table S1). These analyses were intended to assess the stability of the primary inference under alternative ways of handling age variation, not to test for age-specific differences in heritability; accordingly, any between-strata differences in point estimates should be treated as exploratory. As additional context (and not as a direct test of environmental effects), we examined within- and between-sibship age differences as a coarse proxy for differences in time at risk (i.e., duration of potential exposure) over time.⁵⁵ Across sensitivity specifications, estimates were less precise in restricted and stratified subsets, and the results did not show a consistent pattern, indicating that the primary conclusion was driven by a single age cut or by a small number of sibships with extreme age separation.

The current research leverages a cohort originally collected to characterize OR and provides preliminary familial aggregation and heritability estimates for OR for the first time. Given the exploratory nature of this work, we note key limitations and study design considerations for future heritability research. First, this study provides an initial sibling-based estimate in a modestly sized clinical cohort (45 participants across 21 sibships); accordingly, subgroup and stratified analyses should be interpreted as sensitivity checks rather than definitive tests of heterogeneity and we emphasize effect sizes and 95% CIs throughout (Supplementary Table S1). In small, clustered family samples, additional covariates and stratification can decrease precision and model stability by increasing parameterization relative to the available within- and between-family information; therefore, we limited adjustment to a small set of a priori covariates and interpret more parameterized models cautiously. Although smaller familial effects may be difficult to resolve in modest sibship designs, the OR effect observed here was estimated with reasonably narrow uncertainty. More broadly, prior family studies of modest scope have shown that such designs can provide useful initial estimates of familial aggregation and help to inform sample-size needs for larger studies.⁴¹ Prior methodological work indicates that substantially larger family samples are typically required to reliably detect low heritability signals, whereas moderate-to-large familial effects are more readily detectable in modest designs.³⁹ Considering that siblings share both genes and early life environment, sibling-based estimates may differ from parent–offspring or extended family estimates, particularly when shared environment effects are more separable in other designs.⁵⁶

Our sample was heterogeneous, with 56% Hispanic, 22% White, 9% Black, and 13% Asian. Refractive error and ocular biometry are known to vary across ethnic groups,^57,58 raising the possibility that the between-family demographic makeup could contribute to apparent familial clustering. Yet ethnicity is considered an indicator of environmental factors rather than of inherent genetic differences between groups.⁵⁹ As an additional sensitivity analysis, we statistically adjusted our models for ethnicity (by including ethnicity as a fixed effect), and the OR heritability estimate was essentially unchanged (Table 3), suggesting that sibship-level variance is not driven solely by the measured demographic/ethnic composition.

Conclusions

This study provides the first quantitative evidence of familial contribution (genetic and/or shared environmental factors) to OR, suggesting that familial factors may play a meaningful role in scleral biomechanics and, by extension, in myopia susceptibility. Despite high heritability, OR and other myopia-related traits may still be affected by individual environmental factors. Future studies should incorporate environmental covariates and longitudinal designs to more comprehensively characterize the heritability and modifiability of OR as a phenotypic trait relevant to myopia development.