Multilocus risk scores:

rethinking genetic risk scores
to account for epistasis

Trang Lê

University of Pennsylvania

BIOSTEC, Bioinformatics, Valletta, Malta


  • environmental exposures
  • lifestyle factors
  • genetic susceptibility ← heritability
    • single nucleotide polymorphisms

What do we mean when we say disease risk

Individuals with high genetic risk scores for a disease are more susceptible to that disease
and may benefit from prioritized interventions.

Polygenic Risk Score (PRS) aggregates genetic risk factors.

\[PRS(i)=\sum_{j=1}^{k} \beta_j \times SNP_{ij}\]


effect size of \(SNP_j\) in discovery sample from OLS or logistic reg. 



number of minor alleles at \(SNP_j\)
for subject \(i\)


Probabilistic susceptibility

→ identify groups of individuals who need prioritized interventions and screenings

→  life planning

 Advanced issue found

Current PRS model does not account for the effect of SNP-SNP interactions.


\[PRS(i)=\sum_{j=1}^{k} \beta_j \times SNP_{ij}\]

Our goal is to expand risk score models
beyond main effect of individual variants on disease risk.

Polygenic Risk Scores

  • individual effects
  • manual encodings

Multilocus Risk Scores

  • interaction effects ​ 
  • automatic encodings 

MRS method utilizes
model-based multifactor dimensionality reduction (MB-MDR).

HLO matrix

High = 1

Low = -1

O = 0


\[MRS_d(i) = \sum_{j = 1}^{k_d} \gamma_j \times \textrm{HLO}_j(X_{ij})\]

\[PRS(i)=\sum_{j=1}^{k} \beta_j \times SNP_{ij}\]


interaction dimension


SNP combination


\(j^{th}\) HLO matrix


MB-MDR test statistic



\[MRS_d(i) = \sum_{j = 1}^{k_d} \gamma_j \times \textrm{HLO}_j(X_{ij})\]

\[MRS_2(Alice) = 0.8\times 1 + \cdots\]

Bob has the combination (aa, aa) for these two SNPs.

\(\gamma = 0.8\)

\[MRS_2(Bob) = 0.8\times (-1) + \cdots\]

Suppose Alice has the combination (AA, Aa) and

450 datasets: 1000 individuals and 10 SNPs

For an individual, each genotype was randomly assigned with:

  • 1/2 probability heterozygous Aa (coded as 1)
  • 1/4 probability homozygous major AA (coded as 0)
  • 1/4 probability homozygous minor aa (coded as 2).

How do we simulate data with interaction effects?

Evolutionary-based method: Heuristic Identification of Biological Architectures for simulating Complex Hierarchical Interactions (HIBACHI)

  • 80% training: run MB-MDR to obtain
    • the \(\gamma\) coefficients
    • the HLO matrix
  • 20% holdout:
    • calculate MRS for each individual
    • assess the performance of the MRS by comparing the area under the Receiving Operator Characteristic curve (auROC) with that of the standard PRS method.

How do we test our method?

MRS produces improved auROC in 335 of 450 simulated datasets.

~50% auROC increase at the second peak

\(MRS = MRS_1 + MRS_2\) increasingly outperforms standard PRS
as dataset contains more main and interaction effects.

\[ME = \sum_{j} I(SNP_j; Y) = \sum_{j} \left(H(Y) - H(Y|SNP_j)\right).\]

\[SE = \sum_{j} IG(X_j; Y) = \sum_{j} \left(I(SNP_{j_1}, SNP_{j_2}; Y) - I(SNP_{j_1}; Y) - I(SNP_{j_2}; Y)\right)\]

Next steps

  • Apply MRS to real-world data
    • increase number of variants in simulation
    • pre-select variants
    • increase computational efficiency
  • Aggregate other risk factors

Hoyt Gong

Elisabetta Manduchi

Patryk Orzechowski

Jason H. Moore


funded by the
National Institutes of Health

BIOSTEC organizers

Want to run the Victoria Lines?
Meet me at Excelsior Level 1, 5:45 AM tomorrow (Wednesday).
My (optimistic) estimate: ~ 3 hours, 18 km, 600 m vertical gain

Multilocus risk scores

By Trang Le

Multilocus risk scores

Presentation on 2020-02-24 at BIOSTEC, Bioinformatics

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