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Synthetic Phenotype Assisted Linear Mixed Models Improve Proteome-Wide Genetic Discovery in Incomplete Biobank Data

The paper introduces Syn-PALM, a robust and scalable linear mixed model framework that leverages machine learning-predicted synthetic proteomic data to significantly enhance statistical power and genetic discovery in genome-wide association studies despite substantial missingness in biobank datasets.

Original authors: Xihong Lin, Haoyu Yang, Ruoyu Wang, Shuang Song

Published 2026-07-30

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CC BY 4.0

Original authors: Xihong Lin, Haoyu Yang, Ruoyu Wang, Shuang Song

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine you are a detective trying to solve a massive mystery: how do our genes shape the tiny machines inside our bodies that keep us alive? These machines are called proteins, and they are the actual workers that genes hire to build muscles, fight infections, and digest food. To solve the mystery, scientists need to look at the "blueprints" (our DNA) and the "workers" (our proteins) at the same time. This is called a Genome-Wide Association Study, or GWAS. It's like trying to match a specific instruction in a book to a specific action in a factory.

But there's a huge problem. While we have a giant library of blueprints for half a million people, actually measuring the workers (proteins) is incredibly expensive and difficult. It's like having a map of every house in a city, but only being able to peek inside the windows of a few thousand of them. For the rest, the curtains are drawn. Because so much data is missing, traditional detective work often misses clues or gets confused by fake ones. Scientists have tried to guess what's behind the curtains using computer programs, but if those guesses are slightly wrong, the whole investigation can go off the rails, leading to false accusations against innocent genes.

This is where a new method called Syn-PALM comes in, proposed by researchers Xihong Lin, Haoyu Yang, Ruoyu Wang, and Shuang Song. Think of Syn-PALM as a super-smart detective who doesn't just guess what's behind the curtains but creates a "synthetic" version of the room for every single house in the city. Here's how it works: First, the team uses the few houses they can see to teach a computer how to predict what the rooms look like based on the outside (like the color of the door or the size of the garden). Then, they use this computer to generate a "fake" but highly accurate picture of the interior for every house, even the ones with closed curtains.

The magic trick isn't just making these fake pictures; it's how they use them. Instead of throwing away the real data and only trusting the fake pictures, or mixing them together in a messy pile, Syn-PALM looks at the real data and the fake data together at the same time. It's like having a team of two detectives: one who only looks at the few houses they can actually enter, and another who has a perfect 3D model of every house in the city. They work together, cross-checking each other. If the 3D model is a little bit wrong, the real detective corrects it. If the real data is too noisy, the 3D model helps smooth it out.

The paper shows that this team-up is a game-changer. In their tests, Syn-PALM was able to find many more genetic clues than the old methods, especially when the missing data was huge (like 90% of the houses). Even better, it didn't get tricked by bad guesses; if the computer's prediction model was imperfect, Syn-PALM still found the truth without making false alarms. They tested this on real data from the UK Biobank, looking at nearly 3,000 different proteins. The result? Syn-PALM discovered thousands more connections between genes and proteins than the standard method could find. It even found new clues for diseases like heart issues and inflammation that were previously hidden.

One of the coolest parts is that Syn-PALM works even when everyone is related, like a giant family reunion where cousins and siblings are all in the mix. Old methods often had to kick out the relatives to avoid confusion, throwing away a third of the data. Syn-PALM keeps everyone in the room, using the family connections to make the clues even sharper. The researchers confirmed their findings by checking against known medical records and by splitting their data in half to see if the results held up, and they did. They even built a public website where anyone can explore these new discoveries.

In short, Syn-PALM is a new, robust way to solve the puzzle of how our genes build our bodies, even when we only have a tiny fraction of the pieces. It turns a massive gap in our knowledge into a strength, using smart predictions to fill in the blanks without losing the plot. By combining real observations with synthetic guesses in a clever statistical dance, it helps us see the full picture of human biology with much greater clarity than ever before.

Technical Summary: Synthetic Phenotype Assisted Linear Mixed Models (Syn-PALM)

Problem Statement
Proteome-wide genetic discovery is critical for understanding disease mechanisms and drug development, yet it faces a significant barrier in large-scale biobanks like the UK Biobank. While the UK Biobank Pharma Proteomics Project (UKB-PPP) has generated plasma proteomic data for 54,219 participants, approximately 90% of the cohort lacks these measurements due to the high cost and technical complexity of proteomic assays. Traditional approaches to handle this missingness—such as restricting analysis to observed samples (reducing statistical power) or using imputation/proxy methods (which can introduce bias and false positives if prediction models are misspecified)—are insufficient. Furthermore, existing methods that utilize synthetic phenotypes, such as Synthetic Surrogate (SynSurr), fail to account for cryptic relatedness among participants, limiting their application to independent samples and discarding a substantial portion of the cohort's genetic information.

Methodology
The authors propose Synthetic Phenotype Assisted Linear Mixed Models (Syn-PALM), a robust framework designed to perform Genome-Wide Association Studies (GWAS) on partially observed phenotypes while explicitly modeling sample relatedness. The method operates in three primary stages:

Prediction Model Training: A machine learning model (specifically Random Forests in the application) is trained on a labeled subset of the data (the training dataset) to predict the target phenotype (e.g., protein levels) using fully observed surrogate variables (e.g., demographics, clinical history, polygenic risk scores).
Synthetic Phenotype Generation: The trained model is applied to the entire GWAS analysis dataset to generate "synthetic phenotypes" ( $\hat{Y}$ ) for all individuals, including those with missing observed measurements ( $Y$ ) and those with observed measurements.
Joint Linear Mixed Modeling: Syn-PALM conducts a joint GWAS analysis by regressing both the partially observed phenotypes ( $Y_{obs}$ $Y_{o b s}$ ) and the complete synthetic phenotypes ( $\hat{Y}$ $\hat{Y}$ ) on genotypes and covariates. This is achieved through a unified Linear Mixed Model (LMM) that:
- Accounts for cryptic relatedness and population structure using sparse Genetic Relatedness Matrices (GRMs) and ancestry Principal Components (PCs).
- Models the target and synthetic phenotypes jointly, allowing their regression coefficients to differ. This feature ensures robustness against prediction model misspecification; the method does not assume the synthetic phenotype is a perfect substitute for the observed one.
- Utilizes a computationally efficient Method of Moments (MoM) approach to estimate variance components under the global null hypothesis, avoiding the iterative optimization required by Restricted Maximum Likelihood (REML) methods and enabling scalability to biobank-sized datasets.

Key Contributions

Robustness to Misspecification: Unlike traditional imputation or proxy GWAS, Syn-PALM provides valid statistical inference (controlled Type I error) even when the phenotype prediction model is misspecified. It treats the synthetic phenotype as a correlated, auxiliary data source rather than a direct replacement.
Handling Relatedness: Syn-PALM is the first synthetic phenotype-assisted method to explicitly incorporate linear mixed models with sparse GRMs. This allows the inclusion of related individuals (e.g., siblings, parent-child pairs), which constitute roughly one-third of the UK Biobank, thereby recovering statistical power lost by methods restricted to independent samples.
Computational Scalability: By estimating variance components once under the null and pre-computing matrix quantities, Syn-PALM achieves high computational efficiency, making it feasible for proteome-wide scans across hundreds of thousands of samples.
Power Gains in Full Data: Uniquely, the authors demonstrate that Syn-PALM can improve statistical power over standard GWAS even when phenotypes are fully observed, provided the samples are related. The synthetic phenotype helps "denoise" random effects by leveraging shared genetic structure among relatives.

Results
The authors validated Syn-PALM through extensive simulations and real-world analysis of UKB-PPP data:

Simulation Studies: Syn-PALM consistently controlled Type I error rates across varying degrees of missingness, prediction model accuracy, and sample relatedness. In contrast, methods like POP-GWAS exhibited Type I error inflation in the presence of relatedness. Syn-PALM demonstrated superior statistical power compared to standard GWAS (Obs-GWAS) and SynSurr, with power gains increasing as missingness rates and prediction accuracy rose.
Ablation Study (Height): Using height as a proxy phenotype with known ground truth, the authors showed that Syn-PALM recovered a higher proportion of genome-wide significant associations than standard GWAS as missingness increased. Notably, even with 0% missingness, Syn-PALM identified more associations (9,233 vs. 9,206) than the standard Oracle-GWAS, attributed to the exploitation of relatedness.
Proteome-Wide GWAS (UKB-PPP): Applied to 2,916 plasma proteins, Syn-PALM identified 53,304 significant SNPs, a 1.25-fold increase over the 42,626 identified by standard GWAS restricted to observed samples.
- The method discovered novel associations supported by enrichment in protein-related gene sets and strong overlap with the GWAS Catalog.
- Specific examples included the identification of four additional loci for GDF15 (RPL22, MDM4, IRF5, CRLF1) that were missed by standard GWAS, with biological plausibility linked to stress response and immune pathways.
- External validation against the GWAS Catalog and internal split-sample replication confirmed the robustness and reproducibility of the findings.

Significance
The paper claims that Syn-PALM represents a significant methodological advance for genetic discovery in biobanks with incomplete phenotypic data. By jointly modeling observed and synthetic phenotypes within a mixed-model framework, it overcomes the trade-off between statistical power and inference validity. The method enables the utilization of the full biobank cohort, including related individuals, to uncover genetic associations that would otherwise remain undetected due to missing data or methodological limitations. The authors emphasize that this approach is broadly applicable to other expensive or technically challenging phenotypes (e.g., imaging, metabolomics) and facilitates downstream analyses such as Mendelian randomization and colocalization. The authors have made the summary statistics available via an interactive web portal and the software as an R package to facilitate community use.

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