COMBINING META- AND MEGA- ANALYTIC APPROACHES FOR MULTI-SITE DIFFUSION IMAGING BASED GENETIC STUDIES: FROM THE ENIGMA-DTI WORKING GROUP

Abstract

Meta-analyses estimate a statistical effect size for a test or an analysis by combining results from multiple studies without necessarily having access to each individual study’s raw data. Multi-site meta-analysis is crucial for imaging genetics, as single sites rarely have a sample size large enough to pick up effects of single genetic variants associated with brain measures. However, if raw data can be shared, combining data in a “mega-analysis” is thought to improve power and precision in estimating global effects. As part of an ENIGMA-DTI investigation, we use fractional anisotropy (FA) maps from 5 studies (total N=2,203 subjects, aged 9–85) to estimate heritability. We combine the studies through meta- and mega-analyses as well as a mixture of the two – combining some cohorts with mega-analysis and meta-analyzing the results with those of the remaining sites. A combination of mega- and meta-approaches may boost power compared to meta-analysis alone.

1. INTRODUCTION

The structure of the human brain is highly heritable, and in recent years, genetic variants associated with heightened risk for Alzheimer’s disease and several neuropsychiatric disorders have been reported to associate with variations in brain structure across populations. Brain measures may be used as “endophenotypes” – heritable intermediate quantitative traits linking genes to disease. Genome-wide association studies (GWAS) of brain images have also successfully discovered novel genetic variants that shape the brain and disease risk. This offers a deeper understanding of their role in neurological development and disease, and enables possible pharmaceutical advances targeting neurological disease. GWAS studies detect genetic associations by screening around a million common genetic variants across the genome. They test for statistical associations between all genotyped variants and a measure extracted from brain scans - such as the volume of a brain structure, the fractional anisotropy (FA) of a tract, or the thickness of a particular cortical region. Often over a million genetic variants are tested, so the significance threshold for discovery is extremely stringent (p < 10⁻⁸). To obtain sufficient power, large sample sizes are needed, and typically a replication sample is critical to verify effects.

Successful imaging genetics studies, such as those of the Enhancing Neuroimaging Genetics through Meta-Analysis (ENIGMA) Consortium (http://enigma.ini.usc.edu) can involve up to 26,000 subjects with genome-wide genotype data and MRI or DTI scans. In one such study [1], meta-analysis was used to jointly analyze data from over 20 imaging sites around the world to discover genetic variants associated with hippocampal and intracranial volumes.

Before embarking on GWAS using measures derived from diffusion tensor imaging (DTI), it is important to establish the reliability, reproducibility, and heritability of measures that can be extracted. A trait that is not heritable is not an ideal target for genetic analysis as most of its variance will be attributable to non-genetic factors or measurement error, rather than genomic variation. Previously, we determined the heritability for regional and voxel-wise measures derived from FA maps, in two large cohorts by using meta- and mega- analysis [2]. In a meta-analysis, each site independently processes their own data, and sends summary results to a central site for joint meta-analysis of all individual results. Mega-analysis, on the other hand, involves analyzing all groups’ individual-level data together, while taking into account site-related differences by regressing covariates out of each site’s data individually and normalizing residual values before combining the data. We previously found that mega-analysis can be more stable and robust than meta-analysis [3]; unlike meta-analysis, mega-analysis requires sharing of raw data, including measures derived from brain scans and each subject’s genotypes and related covariates.

Given the sensitivity of private health information such as genetic data and brain images, even sharing anonymized data across institutions for mega-analysis is not always feasible. Consent forms and local ethics boards may require data not to leave the site where it was acquired. The standard procedure is to use various fixed and random effects meta-analyses for jointly analyzing data. However, some imaging studies with genetic information on patients may be planned by the same set of investigators (for example, two separate studies may be planned by an investigator, one exploring the genetics of normal adolescent development, and another the genetics of bipolar disorder in adulthood). In such cases, there may be no legal complications in sharing the genetic and imaging data between these studies. Rather than treating each cohort as separate, we set out to determine if mega-analysis of at least some of the cohorts (among which some data is shared) would improve power for an overall, larger imaging genetics meta-analysis.

Here, we mega-analyzed the heritability of average FA in several tracts of interest across the white matter skeleton. We assume that the mega-analysis gives the most precise heritability estimate and compare results from meta-analyzing all 5 cohorts, as well as combining both meta- and mega- analysis – mega-analyzing 3 or 4 cohorts together and meta-analyzing the results with the remaining site.

2. METHODS

2.1. Subject Demographics and Image Acquisitions

Five family-based cohorts¹ were jointly analyzed. Further details and information on the cohorts can be found in [3]. Table 1 summarizes basic demographic and image acquisition differences across the cohorts. The GOBS cohort consists of extended pedigrees, while the others include twins and siblings. Overall, DTI images from 2,203 healthy subjects aged 9 to 85 were analyzed. Magnetic field strengths ranged from 1.5T to 4T and the number of gradient directions ranged from 32 to 94.

Table 1 –

Subject demographics and image acquisition information.

	GOBS	QTIM	TAOS	BrainSCALE	NTR
N Subjects	814	625	319	199	246
Sex	350M/464F	231M/394F	158M/161F	100M/99F	93M/153F
Age range (yrs.)	19–85	21–29	12–15	9–10	18–45
Scanner	Siemens	Bruker	Siemens	Achieva	Intera
N-acquisitions	1	1	1	2	1
Field Strength	3T	4T	3T	1.5T	3T
Voxel size (mm)	1.7×1.7×3.0	1.8×1.8×2.0	1.7×1.7×3.0	2.5×2.5×2.5	2.5×2.5×2.5
N-gradients	55	94	55	32	32
N-b0	3	11	3	8	1
b-value (s/mm2)	700	1159	700	1000	1000

2.2. Data Preprocessing

All FA images were processed according to protocols previously explored and described [2], which are available online at http://enigma.ini.usc.edu/ongoing/dti-working-group/. In short, distortion corrected FA maps were created for each individual and registered to the ENIGMA-DTI template in MNI space. The registered FA images were then projected onto the ENIGMA-DTI skeleton (derived using TBSS [4]). Regions of interest (ROIs) corresponding to the Johns Hopkins University white matter atlas [5] were then extracted from along the skeleton. Average FA was calculated for the entire skeleton and bilaterally in the regions listed in Table 2.

Table 2 –

Average FA was calculated for the full skeleton and bilaterally for the ROIs listed here.

GCC	Genu of the corpus callosum
BCC	Body of corpus callosum
SCC	Splenium of corpus callosum
FX	Fornix
CGC	Cingulum (cingulate gyrus) - L and R combined
CR	Corona radiata - L and R anterior and posterior sections combined
EC	External capsule - L and R combined
IC	Internal capsule - L and R anterior limb, posterior limb, and retrolenticular parts combined
IFO	Inferior fronto-occipital fasciculus - L and R combined
PTR	Posterior thalamic radiation - L and R combined
SFO	Superior fronto-occipital fasciculus
SLF	Superior longitudinal fasciculus
SS	Sagittal stratum (include inferior longitudinal fasciculus and inferior fronto-occipital fasciculus) - L and R combined
CST	Corticospinal tract

2.3. Heritability estimates

For each ROI measure, the heritability for each individual cohort was calculated and implemented in the Sequential Oligogenic Linkage Analysis Routines (SOLAR) software package (http://www.nitrc.org/projects/se_linux) [6]; the algorithms in SOLAR use maximum likelihood variance decomposition methods. The covariance matrix Ω for a pedigree of individuals is:

$$\text{Ω}=2\cdot \text{Φ}\cdot {\sigma }_g^2+I\cdot {\sigma }_e^2$$ (1)

Here ${\sigma }_{\text{g}}^2$ is the variance due to additive genetic factors, $\text{Φ}$ is the kinship matrix representing the pair-wise kinship coefficients among all individuals (1 for monozygotic twins, 0.5 for non-identical siblings, etc.), ${\sigma }_{\text{e}}^2$ is the variance due to unique environmental effects and/or measurement error, and $I$ is an identity matrix. Narrow sense heritability, which is our focus for this paper, is the fraction of phenotypic variance, ${\sigma }_{\text{P}}^2$, attributable to additive genetic factors:

$$h^2=\frac{{\sigma }_g^2}{{\sigma }_P^2}$$ (2)

Variance parameters are estimated by comparing the observed phenotypic covariance matrix to the covariance matrix predicted by kinship [6]. Prior to testing for the significance of heritability, phenotype values for each individual within each cohort were adjusted for covariates including sex, age, age², age x sex interaction, and age² x sex interaction. Inverse Gaussian transformation was also applied to ensure Normality of the measurements.

2.4. Joint heritability estimates

Mega-analysis:

We also performed a mega-analysis, again using SOLAR. First, two data normalization steps were performed. First, the regression of covariates (as specified above) was performed, per site, followed by the per-site inverse Gaussian normalization of data. Individual cohort heritability estimates were obtained by fitting a polygenic model for each population. Secondly, a joint pedigree structure was created by merging the kinship matrices from all cohorts, and finally, a polygenic model was then fit for the combined dataset. The $h^2$ value, its significance, and standard error (SE) are tabulated for this genetic mega-analysis.

Meta-analysis:

We meta-analyzed the heritability estimates by weighting estimates from each cohort by its sample size [7]. The overall $h^2$, and its SE, weighted by sample size is:

$$h_{\text{MA-N}}^2(v)=\frac{{\sum }_j{n}_j{h}_j^2(v)}{{\sum }_j{n}_j}$$ (3)

$$Var\left(h_{\text{MA-N}}^2(v)\right)=\frac{{\sum }_j{n}_j^{2}s{e}_j^2(v)}{{\left({\sum }_j{n}_j\right)}^2}$$ (4)

where $v=1$ to $N_v$ indexes the ROIs, and $j=1,\dots ,5$ indexes the cohort.

The meta-analysis p-values were then calculated from the heritability estimates and standard errors, without consulting individual cohort p-values. Specifically, these were found by computing z-scores, ratios of $h_{\text{MA-N}}^2(v)$ values (Eq. 3) with their standard errors (square root of the terms in Eq. 4); from these z-scores, p-values were found based on the asymptotic Normality of maximum likelihood estimates [8].

2.5. Comparing joint heritability estimates

Given our prior work determining the enhanced stability of the mega-analytic approach, we assumed here that this approach provides the most reliable estimates of heritability. We first compared this to the approach where all 5 cohorts were meta-analyzed. We then used the mega-analytic approach to jointly estimate the heritability of 3 of the 5 cohorts in all 10 possible combinations. For each of the 10 possibilities, we used sample-size weighted meta-analysis to combine the mega-analytic approach with the other 2 cohorts, under the assumption that the data from these two cohorts could not be shared. Following this line of thought, we also examined the effects of using mega-analysis for combining 4 out of the 5 sites, and combining that with the remaining site using meta-analysis.

Heritability values, their standard errors, and significance (p-values) were compared. Correlations were assessed between the results of the full 5-group mega-analysis approach and all other heritability estimates.

3. RESULTS AND DISCUSSION

Individual cohorts:

Despite demographic and imaging acquisition differences across cohorts, heritability was detectable for most ROIs and showed similar trends.

Meta-analysis and Mega-analysis:

When directly comparing the mega-analytic approach to the meta-analytic approach, the mega- approach constantly led to higher estimates of heritability (Figure 2).

Figure 2 –

The heritability of FA in ROIs is jointly analyzed with meta- and mega-analysis procedures.

Mixed Mega- and Meta-analysis:

We computed 15 combinations of mega- and meta- analysis. 10 combinations were computed by mega-analyzing three sites, and combining those results with those from the other two individual sites through meta-analysis. The other 5 combinations were formed by mega-analyzing four of the 5 sites and meta-analyzing the result with the remaining site. Figure 3 shows correlations between heritability values from each analysis with that of the mega-analysis.

Figure 3 –

Joint heritability ($h^2$) values are shown for combinations of mega- and meta-analysis across the 5 sites, as compared to the full mega- and full meta- analyses (first 2 rows of matrix). Correlations between the combinations and the full group mega- analysis are displayed on the left. All combinatoric procedures result in lowest heritability measures for the CST and the FX. In general, when more groups are included in the mega-analysis, the greater the $h^2$.

Average Z-scores from the joint mega- and meta- analytic approaches were compared to both the full meta- and mega- approaches using a paired Student’s t-test. The average of the 10 ways of combining 3 data sets with mega analysis before meta-analysis of the full group was significantly different from both full meta (p=3.3×10⁻⁸) and mega analyses (p=3.5×10⁻⁴); the average of the 5 ways to combine 4 sites with mega analysis results was also significantly different from both full meta (p=1.6×10⁻⁷) and mega analyses (p=1.1×10⁻³). Both analyses were more similar to the full mega-approach.

4. CONCLUSION

In this collaborative work from the ENIGMA-DTI working group, data from 5 cohorts from around the world was shared to perform a statistical mega-analysis. While this type of data sharing is not feasible in most large imaging genetics consortia due to privacy and other legal or ethical restrictions, a subset of the participating groups may be permitted to share data with each other. Here, we show if mega-analysis is used to jointly analyze a small set of cohorts, the full meta-analysis of all results will be more powerful than if all sites were meta-analyzed 100% independently. Our imaging genetics study here focuses on variance-component based heritability estimates, but our conclusions may also apply to analyses of point estimates such as those from GWAS.

Figure 1 –

Across all cohorts, relatively low heritability values were observed for the CST. The TAOS cohort showed no detectable heritability for the EC or SS.

Table 3 –

We compare the significance (p-values) of $h^2$ estimates from the average of all 10 possible instances of meta-analysis after using 3 cohorts in a mega- analysis, and all of 5 possible instances of using 4 cohorts in a mega- analysis, with the approaches using either mega or meta. Combining some cohorts with mega-analysis provides lower p-values than meta-analysis alone.

	5-Mega	5-Meta	3Mega+2Meta	4Mega+1Meta
AverageFA	7.65E-49	5.38E-25	6.62E-31	1.42E-43
BCC	1.40E-55	3.61E-42	1.72E-45	9.31E-67
CGC	9.71E-41	2.06E-35	2.51E-35	4.94E-47
CR	3.39E-58	1.25E-52	5.51E-56	5.55E-84
CST	6.44E-19	2.54E-06	1.08E-07	7.52E-09
EC	1.91E-59	1.29E-17	1.56E-18	4.35E-27
FX	1.21E-31	4.71E-15	9.21E-17	1.41E-21
GCC	1.28E-46	8.30E-45	4.10E-51	3.58E-60
IC	3.53E-51	5.64E-35	4.01E-39	2.57E-57
IFO	1.68E-51	1.80E-12	2.07E-13	7.83E-20
PTR	2.90E-54	1.15E-36	1.99E-39	2.45E-59
SCC	4.24E-41	6.70E-36	2.21E-39	1.34E-49
SFO	8.78E-44	1.14E-23	2.27E-26	1.00E-36
SLF	8.09E-62	2.06E-31	1.31E-32	1.93E-47
SS	1.85E-43	5.86E-17	5.84E-18	7.50E-23