[Paper Review] Survival analysis of DNA mutation motifs with penalized proportional hazards

Jean Feng, D A Shaw+3 more|arXiv (Cornell University)|Nov 11, 2017

RNA and protein synthesis mechanisms47 references3 citations

TL;DR

This paper introduces SAMM, a novel lasso-penalized proportional hazards model to infer DNA mutation motifs and their effects on somatic hypermutation in B-cell receptors. By using a Monte Carlo EM algorithm to handle unobserved mutation order and high-dimensional motif features, SAMM achieves more parsimonious and accurate models than existing methods, particularly in high-dimensional, sparse settings with complex context-dependent mutation patterns.

ABSTRACT

Antibodies, an essential part of our immune system, develop through an intricate process to bind a wide array of pathogens. This process involves randomly mutating DNA sequences encoding these antibodies to find variants with improved binding, though mutations are not distributed uniformly across sequence sites. Immunologists observe this nonuniformity to be consistent with "mutation motifs", which are short DNA subsequences that affect how likely a given site is to experience a mutation. Quantifying the effect of motifs on mutation rates is challenging: a large number of possible motifs makes this statistical problem high dimensional, while the unobserved history of the mutation process leads to a nontrivial missing data problem. We introduce an $\ell_1$-penalized proportional hazards model to infer mutation motifs and their effects. In order to estimate model parameters, our method uses a Monte Carlo EM algorithm to marginalize over the unknown ordering of mutations. We show that our method performs better on simulated data compared to current methods and leads to more parsimonious models. The application of proportional hazards to mutation processes is, to our knowledge, novel and formalizes the current methods in a statistical framework that can be easily extended to analyze the effect of other biological features on mutation rates.

Motivation & Objective

• To develop a statistically rigorous framework for estimating the effects of DNA sequence motifs on mutation rates in B-cell receptor somatic hypermutation.
• To address the high-dimensional, missing-data problem arising from unobserved mutation order and the large number of potential motifs.
• To improve model parsimony and interpretability compared to existing methods that use ad-hoc or restrictive assumptions.
• To formalize the use of survival analysis in mutation process modeling, enabling extension to other biological features.
• To provide a scalable, data-adaptive method that selects relevant motifs while stabilizing estimates in high-dimensional settings.

Proposed method

• Proposes a semiparametric Cox proportional hazards model where mutations are treated as failure events, and motif context is a time-varying covariate.
• Applies l1-penalization (Lasso) to perform feature selection among the 1024 possible 5-mers, promoting sparse, interpretable models.
• Uses a Monte Carlo EM (MCEM) algorithm to handle missing data from unobserved mutation order, with Gibbs sampling in the E-step to approximate the intractable expectation.
• Marginalizes over all possible mutation orderings by integrating the likelihood using MCMC, enabling maximum likelihood estimation despite unobserved history.
• Employs a data-adaptive approach to select degrees of freedom for the model, avoiding overfitting in high-dimensional settings.
• Extends the framework to allow modeling of arbitrary biological features beyond sequence motifs, such as position or structural context.

Experimental results

Research questions

• RQ1 How can we accurately estimate the mutability of DNA motifs in the presence of unobserved mutation order and high dimensionality?
• RQ2 Can a penalized proportional hazards model outperform existing methods in identifying biologically relevant mutation motifs?
• RQ3 How does the inclusion of mutation order uncertainty affect model accuracy and parameter estimation in somatic hypermutation analysis?
• RQ4 To what extent can l1-penalization improve model parsimony and interpretability in high-dimensional motif analysis?
• RQ5 Can this framework be generalized to model other biological processes involving sequential events with hidden histories?

Key findings

• SAMM estimated only 137 unique motif parameters out of 1024 possible 5-mers, demonstrating superior model parsimony compared to SHazaM (1015) and logistic regression (485).
• On simulated data, SAMM outperformed current state-of-the-art methods in identifying true mutation motifs, especially under high mutation rates and complex context dependencies.
• The method produced visually similar hot- and cold-spot patterns to other models but with a sparser, more interpretable structure, indicating better feature selection.
• Uncertainty intervals from SAMM were close to nominal coverage levels when sufficient data were available, though they are not guaranteed confidence intervals.
• SAMM’s likelihood is computationally intractable to evaluate directly, limiting direct comparison with likelihood-based methods, but simulations support its robustness.
• The approach is generalizable and can be extended to model other biological processes, such as SNP rates or transcription factor binding, by incorporating additional covariates.