Data_Sheet_1_A Nonlinear Simulation Framework Supports Adjusting for Age When Analyzing BrainAGE.docx

Several imaging modalities, including T1-weighted structural imaging, diffusion tensor imaging, and functional MRI can show chronological age related changes. Employing machine learning algorithms, an individual's imaging data can predict their age with reasonable accuracy. While details vary according to modality, the general strategy is to: (1) extract image-related features, (2) build a model on a training set that uses those features to predict an individual's age, (3) validate the model on a test dataset, producing a predicted age for each individual, (4) define the “Brain Age Gap Estimate” (BrainAGE) as the difference between an individual's predicted age and his/her chronological age, (5) estimate the relationship between BrainAGE and other variables of interest, and (6) make inferences about those variables and accelerated or delayed brain aging. For example, a group of individuals with overall positive BrainAGE may show signs of accelerated aging in other variables as well. There is inevitably an overestimation of the age of younger individuals and an underestimation of the age of older individuals due to “regression to the mean.” The correlation between chronological age and BrainAGE may significantly impact the relationship between BrainAGE and other variables of interest when they are also related to age. In this study, we examine the detectability of variable effects under different assumptions. We use empirical results from two separate datasets [training = 475 healthy volunteers, aged 18–60 years (259 female); testing = 489 participants including people with mood/anxiety, substance use, eating disorders and healthy controls, aged 18–56 years (312 female)] to inform simulation parameter selection. Outcomes in simulated and empirical data strongly support the proposal that models incorporating BrainAGE should include chronological age as a covariate. We propose either including age as a covariate in step 5 of the above framework, or employing a multistep procedure where age is regressed on BrainAGE prior to step 5, producing BrainAGE Residualized (BrainAGER) scores.</p

Power as a multiple of current effective sample size for Crohn’s disease and schizophrenia.

<p>Black line displays estimated proportion of additive genetic variance due to large effects for CD data, using a GWAS significance threshold of 5 × 10⁻⁸, current sample size (log₂ 32 = 0) to 64 times current sample size (log₂ 32 = 5). Red line displays same quantities for schizophrenia data.</p

Empirical and model-based replication rates for schizophrenia.

<p>Empirical (black lines) and model-based (red lines) finite sample replication estimates. Left panel displays the average replication proportion conditional on discovery sample <i>z</i>-scores, for 30% of the overall sample apportioned to discovery sample, with the remainder apportioned to the replication sample. Red lines are computed from best fitting scale mixture of two normals. The middle panel displays the same for 50%, and the right panel for 70% of the overall sample apportioned to the training sample.</p

Replication proportions and predicted replication probabilities.

<p>Local fdr estimate are shown on the x-axis (binned from 0 to 1 in increments of 0.10), with discovery fdr computed on 26 randomly selected sub-studies in the PGC schizophrenia data consisting of 17,691 cases and 24,683 controls on <i>N</i> = 129,973 SNPs pruned to pairwise LD ≤ 0:20. For the independent replication sample we computed the meta-analysis <i>z</i>-scores using the remaining 26 studies, with 17,785 cases and 22,156 controls. Replication was defined as: (i) discovery and replication <i>z</i>-scores have same sign, and (ii) replication <i>z</i>-score associated with one-tailed <i>p</i>-value ≤ 0:05. Black squares show actual replication proportions for each bin, whereas red squares show mean predicted replication probabilities given in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005717#pgen.1005717.e087" target="_blank">Eq (15)</a>.</p

Empirical and model-based posterior expectations and variances for schizophrenia and Crohn’s disease.

<p><i>Upper left panel</i>: Schizophrenia empirical conditional mean of split-half replication <i>z</i>-scores (purple line) and fitted effect sizes from scale mixture of normals model (yellow line). <i>Lower left panel</i>: Schizophrenia empirical conditional variance of split-half replication <i>z</i>-scores (purple line) and fitted variances from scale mixture of normals model (yellow line). <i>Upper right panel</i>: Crohn’s disease empirical conditional mean of split-half replication <i>z</i>-scores (purple line) and fitted effect sizes from scale mixture of normals model (yellow line). <i>Lower right panel</i>: Crohn’s disease empirical conditional variance of split-half replication <i>z</i>-scores (purple line) and fitted variances from scale mixture of normals model (yellow line).</p

Cross-tissue eQTLs in the loci with genome-wide significant association with schizophrenia.

Cross-tissue eQTLs in the loci with genome-wide significant association with schizophrenia.</p

Schizophrenia association enrichment in eQTLs.

Q-Q and fold enrichment plots for adipose, epidermal, LCL and whole blood eQTLs. The baseline is determined by respectively matched control SNP sets. The fold enrichment is displayed in logarithmic scale.</p

Schizophrenia association enrichment of eQTLs with different Roadmap functional annotations.

Chi-squared general linear model coefficients for eQTLs of different tissues (adipose, epidermal, lymphoblastoid cell lines (LCL), whole blood) and location (proximal, distal) affiliated to different Roadmap functional elements. “All” stands for all eQTLs (* p p < 0.001).</p

Enrichment statistics and general linear model coefficients for squared schizophrenia association z-scores differences between adipose tissue, epidermal tissue, lymphoblastoid cell lines (LCL) and whole blood eQTLs, and matching control variants.

Enrichment statistics and general linear model coefficients for squared schizophrenia association z-scores differences between adipose tissue, epidermal tissue, lymphoblastoid cell lines (LCL) and whole blood eQTLs, and matching control variants.</p

Relationship between polygenicity and eQTL association enrichment across different GWASes.

Differences (Mann-Whitney test p-values) in association p-values between eQTLs and control variants of various types as functions of the estimated proportions of non-null associations. The GWAS names or acronyms are color-coded to represent different categories (azure = anthropometric [height]; red = cardiovascular, systolic blood pressure [SBP]; green = immune, rheumatoid arthritis [RA]; gold = metabolic, body mass index [BMI], type-II diabetes [T2D]; black = schizophrenia) and their sizes are proportional to the respective chi-squared linear model coefficients (* p p < 0.001).</p