RICE (polygenic Risk predictions Integrating Common and rarE variants)
Summary¶
RICE is a unified multi-ancestry polygenic risk scoring framework that integrates common variants (MAF $> 0.01$) and rare variants (MAF $\le 0.01$) into a joint predictive model.[1] Trained and validated on whole-exome (WES), imputed, and whole-genome sequencing (WGS) data from up to 361,939 individuals across 6 major continental ancestries in the UK Biobank and All of Us Research Program, RICE captures rare-variant burden signals that are missed by standard common-variant PRSs.[1] For traits with strong oligogenic rare-variant components — such as blood lipid levels — adding RICE-RV yields $R^2$ improvements of up to $11.2\%$ in European ancestries and up to $60.7\%$ in non-European populations, identifying extreme-risk individuals who are misclassified as average-risk by common-variant PRSs alone.[1]
Mathematical Formulation & Three-Step Workflow¶
RICE operates across three strictly independent sub-samples: a training set (for computing GWAS summary statistics, rare-variant $p$-values, and base PRS models), a tuning set (for optimizing hyperparameter penalties and ensemble blending weights), and a validation set (for unbiased performance reporting).[1]
┌─────────────────────────────────────────┐
│ Independent Input Biobank │
└────────────────────┬────────────────────┘
│
┌──────────────────────────────┴──────────────────────────────┐
▼ ▼
┌──────────────────────────┐ ┌──────────────────────────┐
│ RICE-CV Branch │ │ RICE-RV Branch │
│ (Common: MAF > 0.01) │ │ (Rare: MAF <= 0.01) │
└─────────────┬────────────┘ └─────────────┬────────────┘
│ │
┌─────────────┴────────────┐ ┌─────────────┴────────────┐
│ Single-Ancestry / Multi- │ │ Covariate & RICE-CV │
│ Ancestry Base Models │ │ Residualization Step │
│ (CT, LDpred2, JointPRS, │ │ (Y ~ 10 PCs + Age + Sex │
│ PROSPER, CT-SLEB) │ │ + RICE-CV) │
└─────────────┬────────────┘ └─────────────┬────────────┘
│ │
┌─────────────┴────────────┐ ┌─────────────┴────────────┐
│ LASSO / Ridge Ensemble │ │ STAARpipeline Burden │
│ Optimization (Tuning) │ │ Set Test (p < 10^-3) │
└─────────────┬────────────┘ └─────────────┬────────────┘
│ │
│ ┌─────────────┴────────────┐
│ │ Collapsed Burden Scores │
│ │ + LASSO/Ridge Ensemble │
│ └─────────────┬────────────┘
│ │
└──────────────────────────────┬──────────────────────────────┘
│
▼
┌─────────────────────────────┐
│ Joint Regression Model │
│ Y = β_CV*PRS_CV + β_RV*... │
└─────────────────────────────┘
Step 1: Common Variant Ensemble (RICE-CV)¶
In the training set, common variants are evaluated to compute summary statistics. Multiple base PRS models are generated across tuning parameters: - Single-Ancestry datasets: Clumping and Thresholding (C+T), LDpred2 (infinitesimal, auto, and grid models), and Lassosum2.[1] - Multi-Ancestry datasets: CT-SLEB, JointPRS, and PROSPER.[1]
In the tuning set, RICE-CV combines candidate PRSs into a single optimized score $\text{PRS}{\text{CV}}$ using penalized regression as base learners:[1] $$\text{PRS}_m$$ where $w_m$ represents ensemble weights estimated via LASSO ($\ell_1$) and ridge ($\ell_2$) cross-validation, and $\hat{S}_m$ are standardized candidate PRSs.}} = \sum_{m \in \mathcal{M}} w_m \hat{S
Step 2: Conditional Rare Variant Burden Ensemble (RICE-RV)¶
To isolate rare-variant signals that provide additive information beyond common-variant polygenic risk, RICE-RV fits a baseline residualization model in the training set:[1]
$$Y = \alpha_0 + \mathbf{X}\boldsymbol{\alpha} + \gamma \text{PRS}_{\text{CV}} + \epsilon$$
where $\mathbf{X}$ includes the top 10 genetic principal components (PCs), sex, age, and age$^2$. Working on the residuals $\hat{\epsilon}$, RICE-RV conducts multi-category rare-variant burden tests via the STAARpipeline framework.[1] Variant sets are constructed across protein-coding genes (WES) or coding plus non-coding regulatory elements (WGS) across 7 annotation channels: coding, promoter, enhancer, UTR, evolutionary conserved, and non-coding RNA peaks.[1]
Gene-annotation sets with a STAAR-Burden $p$-value $< 1 \times 10^{-3}$ are retained and collapsed into individual burden vectors $B_j \approx \sum_{k} G_{jk}$ (representing combined rare allele counts).[1] In the tuning dataset, burden scores are jointly trained under penalization to yield $\text{PRS}{\text{RV}}$:[1] $$\text{PRS} \theta_j B_j$$ where $\theta_j$ are joint effect weights optimized via LASSO/ridge regression.}} = \sum_{j \in \mathcal{S}
Step 3: Joint Predictive Evaluation¶
In the validation set, the pre-trained and fixed weights of $\text{PRS}{\text{CV}}$ and $\text{PRS}$ are jointly fitted in a final regression model:[1] $$g(\mathbb{E}[Y]) = \beta_0 + \mathbf{X}\boldsymbol{\delta} + \beta_{\text{CV}} \text{PRS}}{\text{CV}} + \beta}} \text{PRS{\text{RV}}$$ Performance is reported using three complementary metrics: 1. Standardized Effect Size ($\beta$ per SD): The change in standardized outcome per standard deviation increase in PRS ($\beta$.[1] 2. }}$ or $\beta_{\text{RV}}$ for continuous traits; log odds ratio per SD for binary traits). This metric directly equals $\sqrt{h^2_{\text{PRS}}Absolute Predictive Accuracy ($R^2$ / AUC): Total variance explained ($R^2$) or area under the ROC curve (AUC).[1] 3. Quantile Stratification Metrics: Disease odds ratios or trait means comparing top and bottom PRS deciles/percentiles.[1]
Empirical Performance Across 11 Complex Traits & 6 Ancestries¶
RICE was systematically evaluated on 11 traits in the UK Biobank (UKB) and All of Us (AoU) sequencing cohorts across African (AFR), Admixed American/Latino (AMR), East Asian (EAS), European (EUR), Middle Eastern (MID), and South Asian (SAS) populations:[1]
| Trait Category | Traits Analyzed | Primary Sourced Findings & Variance Explained ($R^2$ / AUC) | RICE-RV Significance ($\beta_{\text{RV}}$ per SD) |
|---|---|---|---|
| Lipid Traits | HDL, LDL, log(TG), Total Cholesterol (TC) | Full model (CV+RV) improved $R^2$ in EUR by $4.9\%$--$11.2\%$. Non-EUR gains reached $+60.7\%$ for log(TG) in AFR, $+29.8\%$ for TC in AFR, $+43.2\%$ for HDL in EAS, and $+25.9\%$ for log(TG) in AMR.[1] | $p < 0.05$ across EUR, AFR, AMR, EAS, MID, and SAS.[1] |
| Anthropometric | Height, BMI | RICE-RV achieved statistically significant gains for Height in EUR ($\beta_{\text{RV}} = 0.039$) and AMR ($\beta_{\text{RV}} = 0.038$), boosting $R^2$ by $+7.5\%$ to $+14.2\%$. BMI showed negligible rare-variant gains due to highly polygenic, small-effect architecture.[1] | Height: $p < 0.05$ (EUR, AFR, AMR, EAS). BMI: non-significant across most populations.[1] |
| Binary Diseases | Asthma, Breast Cancer, CAD, Prostate Cancer, T2D | RICE-CV matched or exceeded top multi-ancestry methods (JointPRS, PROSPER). RICE-RV additions yielded no statistically significant AUC increase, limited by current biobank case sample sizes.[1] | Non-significant for binary disease traits at current biobank sample sizes.[1] |
Key Sourced Metrics (UKB & AoU)¶
- HDL Cholesterol (UKB EUR Validation, $N=13,839$): Standardized effect for $\text{PRS}{\text{CV}}$ was $\beta_1 = 0.389$ ($p < 10^{-300}$), while $\text{PRS}$).[1] Approximately $8.1\%$ of individuals exhibited RICE-RV values $> 5$ units above the population mean.[1]}}$ contributed an independent effect of $\beta_2 = 0.107$ ($p < 10^{-45
- Genome-Wide Gene Drivers: Signal in RICE-RV for lipid traits was concentrated in well-defined metabolic genes:[1]
- APOC3: Aggregated weight for HDL = $0.516$ ($3.8$ standard deviations above average gene burden weight).[1]
- LDLR, APOB, PCSK9, LPA, LCAT: Contributed robust, non-overlapping risk prediction weights across non-European cohorts.[1]
- Beyond Monogenic Risk Genes: RICE-RV evaluated against a gene-restricted baseline containing only LDLR, APOB, and PCSK9 demonstrated a $196\%$ higher standardized effect size ($\beta_{\text{RV}}$ per SD) in Europeans, confirming that hundreds of modest-effect rare-variant sets across the genome contribute aggregate polygenic risk beyond established familial hypercholesterolemia loci.[1]
Clinical Risk Stratification & Misclassification¶
Cross-classifying validation individuals into four joint risk strata based on common-variant risk (RICE-CV top $10\%$ vs. bottom $90\%$) and rare-variant risk (RICE-RV top $5\%$ vs. bottom $95\%$) demonstrated that common-variant PRSs systematically miss high-risk patients:[1]
┌─────────────────────────────────────────────────────────┐
│ RICE-RV Top 5% (High Rare Risk) │
│ Mean Standardized HDL: +0.32 SD above population mean │
└────────────────────────────┬────────────────────────────┘
│
┌──────────────────────────┴──────────────────────────┐
▼ ▼
┌──────────────────────────────┐ ┌──────────────────────────────┐
│ Low CV / High RV (6.3%) │ │ High CV / High RV (1.9%) │
│ - Bottom 90% Common PRS │ │ - Top 10% Common PRS │
│ - Top 5% Rare Burden Score │ │ - Top 5% Rare Burden Score │
│ - Standardized HDL: +0.28 SD │ │ - Standardized HDL: +0.48 SD │
│ (p = 3.41 x 10^-14 vs Low) │ │ (p = 9.51 x 10^-140 vs Low)│
└──────────────────────────────┘ └──────────────────────────────┘
- Identification of Discrepant High-Risk Patients: Among individuals in the top decile of observed HDL phenotype, $6.3\%$ belonged to the Low-CV / High-RV stratum.[1] These individuals carried severe lipid perturbations driven entirely by rare variants despite having an unexceptional or low common-variant polygenic risk score.[1]
- Phenotypic Gradient: The Low-CV / High-RV group exhibited significantly elevated HDL compared to the double-low reference group ($p = 3.41 \times 10^{-14}$).[1]
Cross-Dataset Portability & WGS vs WES Scaling¶
- Cross-Biobank Transferability: RICE models trained exclusively on All of Us (AoU) data ($N=155,611$) and evaluated in the UK Biobank validation set demonstrated high portability.[1] Average standardized effect sizes were $\beta_{\text{CV}} = 0.241$ in AoU vs. $0.247$ in UKB, and $\beta_{\text{RV}} = 0.059$ in AoU vs. $0.053$ in UKB.[1] Validation $R^2$ values were on average $45.0\%$ higher in UKB, reflecting phenotype measurement uniformity in UKB.[1]
- WGS vs WES Coding Saturation: Expanding common variants from $1.48$ million (imputed HapMap3/TOPMed) to $5.47$ million (WGS) yielded no additional predictive gains.[1] Similarly, expanding rare variants from $17$ million (WES coding) to $734$ million (WGS non-coding) did not increase $R^2$, demonstrating that functional rare-variant predictive signal is overwhelmingly concentrated in protein-coding regions.[1]
Computational Efficiency & Resource Requirements¶
- Runtime Profile: Total CPU time for RICE ensemble learning averaged $1.73$ compute hours per trait ($\sim 1.1\%$ of total pipeline compute time).[1]
- Bottlenecks: Rare-variant association testing via
STAARpipelinerequired $106.7$ compute hours ($68.6\%$ of total, split across $381$ parallel jobs), followed by base common-variant PRS generation ($28.4$ hours, $18.9\%$).[1]
Code & Data Availability¶
- Model Weights: Pre-trained multi-ancestry RICE-CV and RICE-RV model weights for all 11 complex traits are hosted on Harvard Dataverse at doi.org/10.7910/DVN/RICE_WEIGHTS.[1]
- Pipeline Implementation: STAARpipeline rare-variant burden set generation and LASSO/ridge ensemble scripts follow standard R and C++ dependencies specified in Williams et al. (2026).[1]
See Also¶
- Burden Heritability Regression (BHR) — empirical method establishing the $1:12$ rare-to-common heritability ratio used to benchmark RICE simulations.
- JointPRS — multi-ancestry common-variant PRS integration method used as a core constituent within RICE-CV.
- Genome-Wide Fine-Mapping (GWFM) — complementary Bayesian approach for mapping causal variants across common and rare allele frequency spectra.
- Distinct Genetic Architecture in Trait Tails — conceptual framework explaining why common-variant PRSs fail in phenotypic tails where rare-variant burden dominates.
Citations¶
[1] Williams, J., Chen, T., Hua, X., Wong, W., Yu, K., Kraft, P., Li, X., Zhang, H. (2026). Integrating common and rare variants improves polygenic risk prediction across diverse populations. Nature Communications, 17, 5772. Supports: RICE three-step mathematical formulation; multi-ancestry metrics across 11 traits; $6.3\%$ capture of top-decile HDL individuals in Low-CV/High-RV stratum; $196\%$ gain over monogenic gene baseline; cross-biobank portability metrics; WGS vs WES coding saturation. Location: Abstract; Results ("Method overview", "Evaluation of prediction performance", "Simulation Study Results", "UKB imputed + WES and WGS results", "All of Us results", "Evaluation of AoU PRS on UKB"); Figures 1--8; Supplementary Figures 1--21.