Nomograms of human hippocampal volume shifted by polygenic scores

Nomograms are important clinical tools applied widely in both developing and aging populations. They are generally constructed as normative models identifying cases as outliers to a distribution of healthy controls. Currently used normative models do not account for genetic heterogeneity. Hippocampal volume (HV) is a key endophenotype for many brain disorders. Here, we examine the impact of genetic adjustment on HV nomograms and the translational ability to detect dementia patients. Using imaging data from 35,686 healthy subjects aged 44–82 from the UK Biobank (UKB), we built HV nomograms using Gaussian process regression (GPR), which – compared to a previous method – extended the application age by 20 years, including dementia critical age ranges. Using HV polygenic scores (HV-PGS), we built genetically adjusted nomograms from participants stratified into the top and bottom 30% of HV-PGS. This shifted the nomograms in the expected directions by ~100 mm3 (2.3% of the average HV), which equates to 3 years of normal aging for a person aged ~65. Clinical impact of genetically adjusted nomograms was investigated by comparing 818 subjects from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database diagnosed as either cognitively normal (CN), having mild cognitive impairment (MCI) or Alzheimer’s disease (AD) patients. While no significant change in the survival analysis was found for MCI-to-AD conversion, an average of 68% relative decrease was found in intra-diagnostic-group variance, highlighting the importance of genetic adjustment in untangling phenotypic heterogeneity.


Introduction
Brain imaging genetics is a rapidly evolving area of neuroscience combining imaging, genetic, and clinical data to gain insight into normal and diseased brain morphology and function 1 . Normative modelling is an emerging method in neuroscience, aiming to identify cases as outliers to a distribution of healthy controls and was shown to have potential to improve early diagnosis, progression models, and risk assessment 2; 3; 4; 5 . Unlike conventional case-control studies, normative models do not require cases and controls to be clustered separately. Nomograms are a common implementation of normative models and have been used as growth charts of brain volumes as functions of age in both developing and aging populations 6; 7; 8 .

Normative modelling identifies cases by their deviation from normality, however, genetics
shapes what is 'normal'. Heritability studies have found that whole brain volume is 90% ± 4.8% heritable 9 , hippocampal volume is 75% ± 5% 10; 11; 12 , and other cortical brain areas between 34% and 80% 13; 14 . Genome-wide association studies (GWAS) have identified genome wide significant variants that explain 13% ± 1.5% of the variation in hippocampal volume (HV) 15 , 34% ± 3% in total cortical surface area, and 26% ±2% in average cortical thickness 16 . The gap between estimates from GWAS hits and formal heritability estimates (termed the 'missing heritability') 17 implies that less significant variants also have an influence and that it may be captured through polygenic scores (PGS) 18; 19; 20 . In this work we demonstrate the impact of accounting for polygenic effects in normative modelling of HV.
Damage to the hippocampus (which is integral to memory processes 21 ) has been associated with major depressive disorder 22 , schizophrenia 23 , Epilepsy 24 , and Alzheimer's disease (AD) 25 . AD is a global health burden: 7% percent of people over 60 are diagnosed with dementia 26 of which AD accounts for 70% 27 . The pathophysiological processes underlying AD, namely amyloid and tau pathology accumulation, are thought to precede brain atrophy, which typically starts in the hippocampus and medial temporal lobe and then spreads throughout the neocortex 27 .
The normal variation of HV is of great clinical interest as the early and often prominent hippocampal atrophy seen in AD creates a need for early diagnosis and disease tracking.
Many studies have examined HV across age 28 However, the genetic impact on variation in HV in healthy population remains underexamined in the context of nomograms. In this work, we close this gap. We built HV nomograms using a gaussian process regression (GPR) method ( Figure 1A). We then computed a PGS of HV for subjects in our cohort and built genetically adjusted nomograms ( Figure 1B). We found that our GPR nomograms provided an extended age range compared to previous methods, and that genetic adjustment did in fact shift the nomograms.

Datasets
Data from a total of 39,664 subjects (18,718 female) aged 44 to 82 were obtained from the UKB (application number 65299) with available genotyping and imaging data. Imaging and genetic protocols are described in Bycroft et al. (2018) 36   Subjects were excluded based on HV quality scores (noted in columns 'RHIPQC', 'LHIPQC') and based on genetic ancestry (i.e., restricted to self-reported white non-Hispanic ancestry).
As with UKB, estimated volumes were stratified by sex, and ICV and scan date were regressed out of HV estimates. Demographics were obtained from the ADNIMERGE table (date accessed: 19-06-2020). Furthermore, we used genome-wide genotyping data available for subjects in ADNI, the data were pre-processed as previously described by Scelsi et.

Sliding Window Approach
As a baseline, we generated nomograms using the sliding window approach (SWA) described by Nobis et al. (2019) 30 . Briefly, we sorted samples by age, and formed 100 quantile bins, each containing 10% percent of the samples. This means that neighbouring bins had a 90% overlap. For example, if we had 5,000 samples, each bin contained 500 samples and consecutive bins were shifted by 50 samples. Thus, bin number four would start at index 151. Then, within each bin, the 2.5%, 5%, 10%, 25%, 50%, 75%, 90%, 95%, and 97.5% quantiles were calculated. The quantiles were then smoothed with a gaussian kernel of width 20.

Gaussian Process Regression
Our proposed approach uses GPR to build nomograms. Briefly, a GP is a probability distribution over possible functions that fit a set of points 43; 44 . In our application it is a distribution of possible 'HV trajectories across age'. We used the R library laGP 45 to train GPR models. We applied the commonly used squared exponential covariance kernel function: where 1 and 2 are any two age values from the training set. The kernel function is parameterized by a vertical scale ( ) and a length scale ( ), which, following initialization, are fitted using maximum likelihood estimation. The vertical scale is initialized to the mean HV of all samples, and the length scale is initialized to mean age difference between all samples. We trained models of left, right, and mean HV for each sex. Thanks to their probabilistic formulation, GP models naturally provide a standard deviation from which quantiles can be easily computed. After training, we generated models for ages 45 to 82 by increments of 0.25 years, and quantile curves at 2.5%, 5%, 10%, 25%, 50%, 75%, 90%, 95%, and 97.5%.

Polygenic Score for Hippocampal Volume
A polygenic score (PGS) is a sum of the impact of a selection of genetic variants on a trait, weighted by the allele count. That is: where ( ) is the effect size (e.g., beta or log(odds) ratio from GWAS summary statistics), and ( ) is the allele count of SNP in the subject (either 0,1 or 2

Longitudinal Analysis
As nomograms are often used to track progression, we examined the impact of the genetically adjusted nomograms on prospective longitudinal data. To this end, we analysed patients from the ADNI cohort that were initially diagnosed as MCI and either converted to AD (progressor) or remained MCI (stable) within five years of follow-up. We tested whether the PGS-adjusted nomograms improved the separation between stable and progressor patients using Cox proportional hazards models while accounting for sex and age.

Results
In the UKB sample 453 subjects were excluded for various conditions, 3497 for genetic ancestry, and 28 subjects were outliers: leaving a total of 35,686 subjects. In the ADNI application dataset, 26 subjects were excluded for genetic ancestry, and 314 based on HV quality scores: leaving 818 subjects.

SWA vs GPR for nomogram estimation
Nomograms generated using the SWA and GPR method displayed similar trends ( Figure 2).
However, GPR nomograms spanned the entire training dataset age range (45-82 years) compared to the SWA (52-72 years). This extension allowed 86% of samples from the ADNI to be evaluated versus 56% in the SWA Nomograms ( Figure 2). Furthermore, our GPR nomograms confirmed previously reported trends: Overall, the average 50 th percentile in male nomograms (4162 ± 222) was higher than the female nomograms (3883 ± 170), and within each sex, right HV was larger than left HV (Figure 2). We also observed that along

Polygenic Score for Hippocampal Volume
The calculated PGS, based on an earlier GWAS for average bilateral hippocampal volume 15 , as expected, showed a strong correlation with HV in the UKB data. Overall, the PGSs showed a significant positive correlation with HV across all -value thresholds and training sample subsets ( <2.7E-24; Table 1). PGSs explained more variance in males versus females.
Furthermore, PGS scores did not show detectable differences in left versus right HV; and explained the most variance in mean bilateral HV (Table 1, Supplementary Table 1). In all tested settings, the distribution of PGS scores explained variance (R 2 ) across -value was bimodal: with one peak at the 1E-7 threshold (capturing few but very significant SNPs), a higher peak at the 0.75 threshold (capturing many SNPs with mostly small effect sizes), and a trough between them at the 0.01 threshold (Figure 3). For the ADNI dataset, this distribution was not bimodal but increased with the threshold. When investigating mean HV across percentile of PGS at the 0.75 threshold (highest R 2 ), the top and bottom 20% of scores accounted for 41% of the variance in HV ( Figure 3); with similar values observed across thresholds in both datasets (Supplementary Figures S1, S2).

Genetics stratified Nomograms
We will focus on the -value threshold of 0.75 as it achieved best or close to-best performance overall (Supplementary Table S1 Figure S4).

External Evaluation on ADNI data
In the ADNI dataset we investigated whether the shift in genetically adjusted nomograms could be leveraged for improved diagnosis. Using the non-adjusted nomogram, cognitively normal (CN) participants ( = 225) had a mean bilateral HV percentile of 41% (±30%), Mild Cognitive Impairment (MCI) participants ( = 391) had 25% (±29%), and Alzheimer's Disease (AD) participants ( = 121) had 4% (±10%). Visual inspection revealed that while CN participants were spread across the quantiles, AD participants lay mostly below the 2.5% quantile, and MCI participants spanned the range of both CN and AD participants ( Figure 4).
Bisecting the samples by PGS showed that high PGS CN samples had averaged percentiles of 48% (±31%) and low PGS averaged 33% (±30%). When comparing the same samples against the PGS adjusted nomograms instead, high PGS CN samples averaged 45% (±31%) and low PGS averaged 36% (±31%). Thus, reducing the gap between high and low PGS CN participants by 6% (from 15% to 9%). Similar analysis showed a reduction in the gap between the high and low PGS MCI participants by 5%, and 1% for AD participants. The above effects persisted across most strata (i.e., sex and hemisphere) (Supplementary Table   2).

Longitudinal Evaluation
We also investigated whether genetically adjusted nomograms provided additional accuracy in distinguishing stable ( = 299) from progressing MCI subjects ( = 83). With the nonadjusted nomogram, progressing MCI participants had a mean HV percentile of 11% and stable participants had 29% (Supplementary Figure S5). Using the genetically adjusted nomograms, they had 10% and 28%, respectively. Cox proportional hazards models of percentiles obtained using both nomograms revealed little difference between the two in terms of clinical conversion: both models resulted in a hazard ratio of 0.97 for percentile in nomogram (beta of -0.03 at -value < 4e-06); confirming that participants within lower HV percentiles where more likely to convert earlier.

Discussion
We hypothesized that inclusion of genetic information associated with regional brain volume may substantially affect normative models. Indeed, the PGS for HV was significantly positively correlated with estimated HV from MRI; translating into a shift of around 100 mm 3 in nomograms based on PGS stratification (high vs low PGS). Importantly, this magnitude corresponds to ~3 years' worth of HV loss during normal aging. While previous studies have examined the impact of disease associated variants, such as APOE status, on HV 32; 33 our study relied on genetic variants influencing HV in healthy subjects. This is an important difference: the APOE genotype is associated with present or future AD status rather than having a direct influence on HV in healthy populations. Indeed, GWAS studies of the hippocampus that exclude dementia patients find little influence of AD associated SNPs 15 . By design, nomograms are intended to model healthy progression and to simplify spotting disease related outliers. Therefore, accounting for the genetics of overall HV (rather than APOE) should enable earlier detection of AD-related HV decline in older APOE-e4 carriers. Consequently, stratifying by APOE-e4 status when creating HV nomograms charts the different HV trajectories among APOE genotypes, however, at the same time masks the pathological decline and thus does not increase the sensitivity to HV decline.
Subjects with extreme PGS scores account for significant amounts of the variance as indicated by the S-shape in the quantile plots (e.g., Figure 3). This has been observed in other PGS-trait combinations 19; 20; 49 . Furthermore, we noted a bimodal distribution of R 2 values across PGS thresholds. This reflects two types of genetic effects: the first is that few SNPs account for a substantial portion of the total variance in HV because of their high effect size (oligogenic effect) and the second is the combined effect of all common genetic variants on HV (polygenic effect). This type of effect has been reported in other studies of dementia 50 .
In addition to demonstrating the clear effect of genetics on normative models, we have shown GPR to be effective for estimating nomograms. Using a model-based method allows us to generate accurate nomograms across the entire age range of the dataset. In fact, our GPR model can even be accurately extended beyond those limits (Supplementary Figure S6).  (Figure 2). Therefore, using separate GWASs for each of these strata would potentially give the PGS more accuracy. A second limitation of this study is the reliability of HV estimates. There is a significant difference between manual and automated segmentation of the hippocampus 28; 56; 57 ; more so than other brain regions 58; 59 , and Freesurfer is known to consistently overestimate HV 60 . Therefore, other brain regions with higher heritability like the cerebellum or whole brain volume 14 may show more sensitivity on nomograms. Lastly, a recent study of PGS uncertainty revealed large variance in PGS estimates 61 , which may undermine PGS based stratification; hence a more sophisticated method of building PGS or stratification may improve results further.
In conclusion, our study demonstrated that PGS for HV was significantly positively correlated with HV, translating into a shift in the nomograms corresponding to ~3 years' worth of normal aging HV loss. We have additionally shown that this effect can be observed in an independent dataset. And while more work in this direction is needed, successful integration of polygenic effects on multiple brain regions may help improve measures of the brain age gap 62 , and therefore improve sensitivity to detect early disease processes.

Code Availability
The scripts and code used in this study have been made publicly available and can be found at: https://github.com/Mo-Janahi/NOMOGRAMS