**Purpose.**:
To test the hypothesis that there is a major genetic determinant for central corneal thickness (CCT) in a large, population-based sample and to test whether such a determinant accounts for results previously ascribed to intraocular pressure (IOP).

**Methods.**:
Measurements of IOP and CCT were collected for 1356 individuals, 49 years of age or older, participating in the Blue Mountains Eye Study (third ascertainment call). Linear regression methods were used to adjust CCT for age. IOP was adjusted for CCT. A commingling analysis was performed with a C++ program, SKUDRIVER, to investigate whether the observed CCT and IOP data, adjusted for covariates, were best described by a one-, two-, or three-distribution model. The fitted models were compared by Akaike information criterion (AIC) values.

**Results.**:
Significant skewness was present in CCT and IOP distributions. The most parsimonious model for age-adjusted CCT was a single-distribution model. For IOP adjusted for CCT the most parsimonious model was a mixture of three distributions with means corresponding to 16.02, 23.36, and 35.59 mm Hg. The proportion of total IOP variance attributable to these distributions was 18.3%. Model parameters were almost identical with those in which IOP was not adjusted for CCT. None of the analyses suggested deviation from Hardy-Weinberg equilibrium.

**Conclusions.**:
The findings revealed no evidence of a single major genetic determinant for CCT. Previous results suggesting the presence of a major locus for IOP do not appear to be confounded by the influence of CCT on IOP.

^{ 1–3 }In most cases, POAG is inherited as a complex disease. It is assumed to result from many interactive genetic and environmental factors, none of which individually is necessary or sufficient to cause the disease. Although more than 25 chromosomal regions have been linked to the disease, only three genes (

*MYOC*,

^{ 4 }

*OPTN*,

^{ 5 }and

*WDR36*

^{ 6 }) have been identified. It is likely that these genes contribute to the pathogenesis of POAG in less than 5% of cases in the general population.

^{ 7–10 }Genes accounting for a greater proportion of the known heritable component of POAG thus remain to be identified.

^{ 11,12 }They may also have simpler genetic backgrounds, can be studied population-wide, and are less prone to misclassification.

^{ 13,14 }In brief, the analysis investigates whether the observed distribution of a quantitative trait is best modeled by a single distribution or by an admixture of multiple distributions. A single distribution suggests the lack of a single major genetic determinant for the trait, whereas multiple distributions suggest the presence of a major genetic determinant, especially if the distributions are in Hardy-Weinberg equilibrium (HWE) for population-ascertained data.

^{ 15 }for POAG. It is associated with illness in the population, it is heritable, it is present in an individual whether or not disease is present, and it cosegregates, to an extent, with the disease.

^{ 16 }and that the higher the IOP at screening, the greater the risk of POAG.

^{ 17 }

^{ 18 }

^{ 19–22 }and a commingling analysis

^{ 14 }has suggested the presence of a major gene accounting for 18% of the variance of IOP in a population. Commingling analysis investigates the strength of evidence that a single gene has a major effect and provides an estimate of the locus-specific heritability.

^{ 23–35 }and has also been proposed as an independent risk factor for POAG.

^{ 36–38 }Furthermore, several studies in different ethnic groups have demonstrated the high heritability of CCT.

^{ 39–41 }

^{ 14 }is robust to adjustment of IOP for CCT, rather than erroneously ascribing results to IOP that are actually due to the effects of CCT, through the surrogate measure of IOP.

^{ 42 }In brief, all permanent, noninstitutionalized residents 49 years of age or older were invited to participate. Of the 4433 eligible individuals, 3654 (82.4%) attended baseline eye examinations between 1992 and 1994. Among the 779 nonparticipants, 501 (11.3%) persons refused, 68 (1.5%) had died, and 210 (4.8%) had moved away from the area. The response rate compares well with the best population-based research in glaucoma.

^{ 43–45 }The BMES examined these 3654 patients aged 49+ years during 1992 to 1994 (baseline-known as BMES-1), 2335 (75% of 3111 survivors) at a 5-year examination (during 1997 to 1999 known as BMES-2), and 1935 (75% of 2581 survivors) at a 10-year examination (during 2002 to 2004, known as BMES-3).

*IOVS*2005;46:ARVO E-Abstract 3520). The disparity between the total number of participants in BMES-3 and those with recorded values of CCT arose due to instrumental difficulties at the time of CCT measurement. The cases in which CCT measurements were not performed did not show systematic bias compared with those in which CCT was measured. Three measurements were recorded for corneal thickness of each eye. The left eyes of 6 individuals and right eyes of 10 individuals were excluded from the study, as data for CCT were missing from their phenotypic data. This data deficit reduced the sample sizes to 1350 and 1346 for the left and right eye CCT, respectively. CCT commingling analyses were performed for both eyes separately, both with and without adjustments for covariates.

^{ 14 }In their study, Viswanathan et al.

^{ 46 }took a conservative approach: Only one eye of each subject was considered for analysis because of the problems relating to intereye correlation. To enable a comparison of findings between this work and the present study, we selected cases with CCT measurements from BMES-3 from the dataset used for the previous IOP commingling study. Hence, the sample size was reduced to 1305 for IOP commingling analyses with or without adjustment for CCT.

*V*), homozygote mean (

*U*), dominance (

*D*), displacement (

*T*), allele frequency (

*Q*), power transform variables (

*P*and

*R*), and inbreeding coefficient (

*F*). Displacement (

*T*) is defined as the difference between the mean values of the two homozygous distributions. Dominance (

*D*) represents the mean value of the heterozygous distribution relative to the two homozygotes. Thus, the three genotypic means are at

*U*,

*U*+

*DT*, and

*U*+

*T*. Since the input parameters in SKUDRIVER can be specified as either fixed or estimated, the user may constrain the model to a single distribution by fixing the value of

*T*as 0, or may specify a two-distribution model by fixing the value of

*D*as 0 or 1.

*Q*is assigned to be the frequency of the allele associated with the displaced distribution so that in the three-distribution model, under HWE, the proportions of the population within each of the distributions are (1 –

*Q*)

^{2}, 2

*Q*(1 –

*Q*), and

*Q*

^{2}. However, the program also allows deviation from HWE by introducing an inbreeding coefficient

*F*, so that the proportions within the distributions become (1 –

*Q*)

^{2}+

*FQ*(1 –

*Q*), 2

*Q*(1 –

*Q*)(1 –

*F*), and

*Q*

^{2}+

*FQ*(1 –

*Q*).

*P*and

*R*of a power transformation to reduce skewness of the form

*y*=

*R/P*[(

*x*/

*R*+ 1)

*− 1], where*

^{P}*R*is chosen such that every

*x*/

*R*+ 1 is positive in the sample and

*P*is optimized as part of the maximum-likelihood estimation. This method allows the fit of multiple distributions to be assessed after skewness has been removed, which is important since skewness in itself may lead to the mistaken conclusion that more than one distribution is present.

^{ 47 }Significant skewness may be tested with a likelihood ratio test comparing a model in which

*P*is fixed to a value of 1 (untransformed model) with a corresponding model in which

*P*is not constrained (transformed model).

*L*). The best-fitting model was chosen according to the Akaike information criterion (AIC), defined as −2 log

*L*+ twice the number of free parameters.

^{ 48 }The AIC penalizes for adding free parameters and thus selects the most parsimonious model that fits the data well.

*R*

^{2}. Both unadjusted and age-adjusted CCT were standardized before analysis with SKUDRIVER/SKUMIX. The results of the commingling analysis on the unadjusted left eye CCT are shown in Table 1.

Model | V | U | D | T | Q | P | −2 LL + Constant | AIC |
---|---|---|---|---|---|---|---|---|

1 Distribution, untransformed | 0.999 | 0.000 | — | — | — | 1 | 1915.07 | 1919.07 |

1 Distribution, transformed | 0.999 | −0.032 | — | — | — | 0.297 | 1911.05 | 1917.05 |

2 Distribution, untransformed | 0.969 | 0.000 | 0 | 3.341 | 0.052 | 1 | 1911.93 | 1919.93 |

2 Distribution, transformed | 0.696 | −0.050 | 0 | 1.162 | 0.805 | −0.102 | 1909.96 | 1919.96 |

3 Distribution, untransformed | 0.894 | 0.000 | 0.272 | 3.551 | 0.049 | 1 | 1911.39 | 1921.39 |

3 Distribution, transformed | 0.696 | 0.050 | 1.000 | 1.159 | 0.405 | −0.103 | 1909.96 | 1921.96 |

^{2}= 4.02,

*P*< 0.05). This process is reflected by the findings that the skewness of the untransformed left eye CCT data were 0.186, whereas after the power transformation (with a value of

*R*in the power transformation chosen as 11.0 and a value of

*P*optimized by SKUDRIVER/SKUMIX as 0.297), it was 0.057. The power transform had no significant effects in the two- and three-distribution models.

*F*) to vary (i.e., allowing departure from Hardy-Weinberg proportions) did not significantly improve the fit of any of the non-null models. For left eye CCT, the one-distribution model fit better than any two- or three-distribution model.

Model | V | U | D | T | Q | P | −2 LL + Constant | AIC |
---|---|---|---|---|---|---|---|---|

1 Distribution, untransformed | 0.999 | 0.000 | — | — | — | 1 | 1915.06 | 1919.06 |

1 Distribution, transformed | 0.999 | −0.032 | — | — | — | 0.302 | 1911.00 | 1917.00 |

2 Distribution, untransformed | 0.969 | 0.000 | 0 | 3.582 | 0.046 | 1 | 1911.16 | 1919.16 |

2 Distribution, transformed | 0.977 | −0.021 | 0 | 3.440 | 0.042 | 0.544 | 1909.83 | 1919.83 |

3 Distribution, untransformed | 0.896 | 0.003 | 0.255 | 3.805 | 0.046 | 1 | 1910.63 | 1920.63 |

3 Distribution, transformed | 0.974 | −0.021 | 0.057 | 3.459 | 0.042 | 0.546 | 1909.83 | 1921.83 |

^{2}= 27.86,

*P*< 0.000). However, a power transformation had a negligible effect in the two- and three-distribution models. In the latter model, the value of the

*P*parameter in the power transformation was optimized to 1.139. Allowing the inbreeding coefficient (

*F*) to vary did not significantly improve the fit of any of the non-null models, which suggests that HWE was maintained.

Model | V | U | D | T | Q | P | −2 LL + Constant | AIC |
---|---|---|---|---|---|---|---|---|

1 Distribution, untransformed | 0.999 | 0.00025 | — | — | — | 1 | 1851.03 | 1855.03 |

1 Distribution, transformed | 0.969 | −0.06750 | — | — | — | −0.529 | 1823.17 | 1829.17 |

2 Distribution, untransformed | 0.832 | 0.00026 | 0 | 3.415 | 0.121 | 1 | 1809.93 | 1817.93 |

2 Distribution, transformed | 0.847 | −0.0207 | 0 | 3.275 | 0.112 | 0.529 | 1808.21 | 1818.21 |

3 Distribution, untransformed | 0.788 | −0.00087 | 0.377 | 7.237 | 0.013 | 1 | 1804.56 | 1814.56 |

3 Distribution, transformed | 0.781 | 0.00533 | 0.369 | 7.514 | 0.013 | 1.139 | 1804.45 | 1816.45 |

Model | V | U | D | T | Q | P | −2 LL + Constant | AIC |
---|---|---|---|---|---|---|---|---|

1 Distribution, untransformed | 0.999 | 0.00000 | — | — | — | 1 | 1851.21 | 1855.21 |

1 Distribution, transformed | 0.966 | −0.06970 | — | — | — | −0.576 | 1820.95 | 1826.95 |

2 Distribution, untransformed | 0.841 | −0.00000 | 0 | 3.711 | 0.108 | 1 | 1807.25 | 1815.25 |

2 Distribution, transformed | 0.851 | −0.02327 | 0 | 3.455 | 0.104 | 0.477 | 1804.98 | 1814.98 |

3 Distribution, untransformed | 0.791 | −0.00116 | 0.376 | 7.406 | 0.012 | 1 | 1802.26 | 1812.26 |

3 Distribution, transformed | 0.614 | −0.12159 | −0.691 | 2.662 | 0.060 | −1.536 | 1800.99 | 1812.99 |

*P*= 1). The parameters of this model were: residual variance, 0.788; homozygote mean, –0.00087; dominance, 0.377; displacement, 7.237; allele frequency, 0.013; power transform variable

*P*(fixed), 1.0; and power transform variable

*R*(fixed), 11.0. As the total variance was 0.976 and residual variance 0.788, the variance due to genotypic means was 0.188. Thus, the percentage of variation explained by the major effect was 18.8%. The estimate of

*Q*as 0.013 corresponds to probabilities of 97.52%, 2.47%, and 0.01% of an individual in the population having genotype AA, Aa, or aa, respectively. On the original, unstandardized IOP scale the three component means correspond to 16.01, 23.20, and 35.12 mm Hg, respectively.

*P*(fixed), 1.0; and power transform variable

*R*(fixed), 11.0. As the total variance was 0.974 and residual variance 0.791, the variance due to genotypic means (i.e., mixing component) was 0.183, which implies that the 18.3% variation of IOP adjusted for CCT can be explained by the major effect. The estimate of

*Q*as 0.012 corresponds to 97.67%, 2.31%, and 0.02% probabilities that an individual in the population had genotype AA, Aa, and aa, respectively. On the original IOP scale, for a person with a CCT of 540 μm, three component means correspond to 16.02, 23.36, and 35.59 mm Hg, respectively.

*F*) to vary did not significantly improve the fit any of the non-null models, which suggests that HWE was maintained. So, for both the IOP data sets (either unadjusted or adjusted for CCT) the three-distribution model in HWE without transformation was the best model to describe the IOP data. The values of the best parameters were almost identical between adjusted and unadjusted datasets.

^{ 49 }and negative results have been postulated with smaller samples.

^{ 50 }

^{ 51 }Findings such as these are useful to elucidate the biology underlying the trait, but are of less use in risk stratification or the search for therapeutic targets. Our results suggest that the heritable component of CCT is determined by multiple genes of relatively small effect and various effect sizes. One of the limitations of commingling analysis is that, although genetic effect size may be estimated (via the model parameter for genetic displacement,

*T*), if a single major gene is implicated, effect sizes cannot be estimated if the results do not suggest a single major gene.

^{ 14 }Although IOP was associated with CCT, adjustment of IOP for CCT did not provide any notable changes in the model in comparison to the model for unadjusted IOP.

^{ 14 }and optic disc morphology

^{ 13 }do not suggest departure from HWE. Furthermore, a recent study

^{ 52 }of the complement factor H (CFH) single-nucleotide polymorphism rs1061170 (Y402H) in this cohort identified CC, CT, and TT genotypes in 13.6%, 46.7%, and 39.7% of the population, respectively. These proportions are in close HWE (χ

^{2}

*P*= 0.94 for T allele frequency 0.63).

^{ 53 }which found that 94.2% of samples could be assigned to one of the major European haplogroups.

^{ 14 }A quantitative trait locus (QTL), which accounts for 18.8% of the IOP trait variance, would be amenable to detection by QTL linkage methods.

^{ 54 }Evidence of commingling does suggest the possibility that a single locus has a major effect on the trait, and commingling analysis can provide guidance in the choice of initial parameter estimates for segregation analysis. Furthermore, these findings justify the effort and expense of a high-density genome-wide association study to identify the putative QTL associated with IOP in this cohort. This study is currently under way as part of the Wellcome Trust Case Control Consortium. Details are available at https://www.wtccc.org.uk/ccc2/projects/ccc2_gc.shtml.