Weibull regression with Bayesian variable selection to identify prognostic tumour markers of breast cancer survival

Hi-C and capture Hi-C (CHi-C) are used to map physical contacts between chromatin regions in cell nuclei using high-throughput sequencing. Analysis typically proceeds considering the evidence for contacts between each possible pair of fragments independent from other pairs. This can produce long runs of fragments which appear to all make contact with the same baited fragment of interest. We hypothesised that these long runs could result from a smaller subset of direct contacts and propose a new method, based on a Bayesian sparse variable selection approach, which attempts to fine map these direct contacts.Our model is conceptually novel, exploiting the spatial pattern of counts in CHi-C data, and prioritises fragments with biological properties that would be expected of true contacts. For bait fragments corresponding to gene promoters, we identify contact fragments with active chromatin and contacts that correspond to edges found in previously defined enhancer-target networks; conversely, for intergenic bait fragments, we identify contact fragments corresponding to promoters for genes expressed in that cell type. We show that long runs of apparently co-contacting fragments can typically be explained using a subset of direct contacts consisting of < 10% of the number in the full run, suggesting that greater resolution can be extracted from existing datasets. Our results appear largely complementary to the those from a per-fragment analytical approach, suggesting that they provide an additional level of interpretation that may be used to increase resolution for mapping direct contacts in CHi-C experiments.

show abstract

“…We fit the model using an RJMCMC sampler, R2BGLiMS (Newcombe et al, 2014). For each bait b, the distribution of sampled coefficients β b1 , .…”

Section: Inference Of Bait-prey Interactionsmentioning

confidence: 99%

Fine mapping chromatin contacts in capture Hi-C data

Eijsbouts

Burren

Newcombe

et al. 2018

Preprint

View full text Add to dashboard Cite

show abstract

“…

σ_{β}^{2}

may be interpreted as the variance among the “true” genetic effects. To estimate this crucial parameter largely from the data, we assign a vague hyper‐prior (rather than choosing a fixed value), which we have used previously in an ′omics setting (Newcombe et al, ):

σ_{β} ~ italic italicUnif (0.05, 2)

…”

Section: Methodsmentioning

confidence: 99%

A flexible and parallelizable approach to genome‐wide polygenic risk scores

Newcombe

Nelson

Samani

et al. 2019

Genetic Epidemiology

View full text Add to dashboard Cite

The heritability of most complex traits is driven by variants throughout the genome. Consequently, polygenic risk scores, which combine information on multiple variants genome‐wide, have demonstrated improved accuracy in genetic risk prediction. We present a new two‐step approach to constructing genome‐wide polygenic risk scores from meta‐GWAS summary statistics. Local linkage disequilibrium (LD) is adjusted for in Step 1, followed by, uniquely, long‐range LD in Step 2. Our algorithm is highly parallelizable since block‐wise analyses in Step 1 can be distributed across a high‐performance computing cluster, and flexible, since sparsity and heritability are estimated within each block. Inference is obtained through a formal Bayesian variable selection framework, meaning final risk predictions are averaged over competing models. We compared our method to two alternative approaches: LDPred and lassosum using all seven traits in the Welcome Trust Case Control Consortium as well as meta‐GWAS summaries for type 1 diabetes (T1D), coronary artery disease, and schizophrenia. Performance was generally similar across methods, although our framework provided more accurate predictions for T1D, for which there are multiple heterogeneous signals in regions of both short‐ and long‐range LD. With sufficient compute resources, our method also allows the fastest runtimes.

show abstract

“…Consider a high‐dimensional generalized linear model setting, where response Y is linked to X via the linear predictor η = X β . Moreover, β j is endowed with a spike‐and‐slab prior of the form

(β_{j} | ξ_{j} = 0) \sim F_{0}, (β_{j} | ξ_{j} = 1) \sim F_{1}, ξ_{j} \sim Bern (ν_{j}), j = 1, …, p,

where, typically, F 0 is concentrated around zero or even F 0 = δ 0 , and F 1 is more dispersed, for example, Gaussian (Newcombe et al, ) or Laplace (Ročková & George, ). The alternative mixture prior representation is obtained by marginalization over the latent variables ξ j .…”

Section: Application Of Eb When Using Co‐datamentioning

confidence: 99%

“…where, typically, F 0 is concentrated around zero or even F 0 = 0 , and F 1 is more dispersed, for example, Gaussian (Newcombe et al, 2014) or Laplace (Ročková & George, 2014). The alternative mixture prior representation is obtained by marginalization over the latent variables j .…”

Section: Mcmc Eb For Spike-and-slab Modelsmentioning

confidence: 99%

“…Other Bayesian sparse regression models like the Bayesian elastic net (see Section 3) can also be represented as (scale) mixtures but with a remaining dependency of on plus a more complex dependency of the mixture proportions on . While conceptually simple, the algorithm above is computationally demanding, requiring efficient implementations of spike-and-slab MCMC (such as those by Peltola, Marttinen, &Vehtari, 2012, andNewcombe et al, 2014). Variational Bayes approximations may be an alternative (Carbonetto & Stephens, 2012) in combination with an EM-type maximization (Beal & Ghahramani, 2003).…”

Section: Mcmc Eb For Spike-and-slab Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Learning from a lot: Empirical Bayes for high‐dimensional model‐based prediction

Wiel

Beest

Münch

2018

Scandinavian J Statistics

View full text Add to dashboard Cite

Empirical Bayes is a versatile approach to “learn from a lot” in two ways: first, from a large number of variables and, second, from a potentially large amount of prior information, for example, stored in public repositories. We review applications of a variety of empirical Bayes methods to several well‐known model‐based prediction methods, including penalized regression, linear discriminant analysis, and Bayesian models with sparse or dense priors. We discuss “formal” empirical Bayes methods that maximize the marginal likelihood but also more informal approaches based on other data summaries. We contrast empirical Bayes to cross‐validation and full Bayes and discuss hybrid approaches. To study the relation between the quality of an empirical Bayes estimator and p , the number of variables, we consider a simple empirical Bayes estimator in a linear model setting. We argue that empirical Bayes is particularly useful when the prior contains multiple parameters, which model a priori information on variables termed “co‐data”. In particular, we present two novel examples that allow for co‐data: first, a Bayesian spike‐and‐slab setting that facilitates inclusion of multiple co‐data sources and types and, second, a hybrid empirical Bayes–full Bayes ridge regression approach for estimation of the posterior predictive interval.

show abstract

Weibull regression with Bayesian variable selection to identify prognostic tumour markers of breast cancer survival

Cited by 29 publications

References 79 publications

Fine mapping chromatin contacts in capture Hi-C data

Fine mapping chromatin contacts in capture Hi-C data

A flexible and parallelizable approach to genome‐wide polygenic risk scores

Learning from a lot: Empirical Bayes for high‐dimensional model‐based prediction

Contact Info

Product

Resources

About