Volume 18, Issue 6

The Dirichlet Process (DP) mixture model has become a popular choice for model-based clustering, largely because it allows the number of clusters to be inferred. The sequential updating and greedy search (SUGS) algorithm (Wang & Dunson, 2011) was proposed as a fast method for performing approximate Bayesian inference in DP mixture models, by posing clustering as a Bayesian model selection (BMS) problem and avoiding the use of computationally costly Markov chain Monte Carlo methods. Here we consider how this approach may be extended to permit variable selection for clustering, and also demonstrate the benefits of Bayesian model averaging (BMA) in place of BMS. Through an array of simulation examples and well-studied examples from cancer transcriptomics, we show that our method performs competitively with the current state-of-the-art, while also offering computational benefits. We apply our approach to reverse-phase protein array (RPPA) data from The Cancer Genome Atlas (TCGA) in order to perform a pan-cancer proteomic characterisation of 5157 tumour samples. We have implemented our approach, together with the original SUGS algorithm, in an open-source R package named sugsvarsel, which accelerates analysis by performing intensive computations in C++ and provides automated parallel processing. The R package is freely available from: https://github.com/ococrook/sugsvarsel

DNA methylation and gene expression are interdependent and both implicated in cancer development and progression, with many individual biomarkers discovered. A joint analysis of the two data types can potentially lead to biological insights that are not discoverable with separate analyses. To optimally leverage the joint data for identifying perturbed genes and classifying clinical cancer samples, it is important to accurately model the interactions between the two data types. Here, we present EBADIMEX for jointly identifying differential expression and methylation and classifying samples. The moderated t-test widely used with empirical Bayes priors in current differential expression methods is generalised to a multivariate setting by developing: (1) a moderated Welch t-test for equality of means with unequal variances; (2) a moderated F-test for equality of variances; and (3) a multivariate test for equality of means with equal variances. This leads to parametric models with prior distributions for the parameters, which allow fast evaluation and robust analysis of small data sets. EBADIMEX is demonstrated on simulated data as well as a large breast cancer (BRCA) cohort from TCGA. We show that the use of empirical Bayes priors and moderated tests works particularly well on small data sets.

Partial least squares regression – or PLS regression – is a multivariate method in which the model parameters are estimated using either the SIMPLS or NIPALS algorithm. PLS regression has been extensively used in applied research because of its effectiveness in analyzing relationships between an outcome and one or several components. Note that the NIPALS algorithm can provide estimates parameters on incomplete data. The selection of the number of components used to build a representative model in PLS regression is a central issue. However, how to deal with missing data when using PLS regression remains a matter of debate. Several approaches have been proposed in the literature, including the Q 2 criterion, and the AIC and BIC criteria. Here we study the behavior of the NIPALS algorithm when used to fit a PLS regression for various proportions of missing data and different types of missingness. We compare criteria to select the number of components for a PLS regression on incomplete data set and on imputed data set using three imputation methods: multiple imputation by chained equations, k -nearest neighbour imputation, and singular value decomposition imputation. We tested various criteria with different proportions of missing data (ranging from 5% to 50%) under different missingness assumptions. Q 2 -leave-one-out component selection methods gave more reliable results than AIC and BIC -based ones.

Recent studies have found that the microbiome in both gut and mouth are associated with diseases of the gut, including cancer. If resident microbes could be found to exhibit consistent patterns between the mouth and gut, disease status could potentially be assessed non-invasively through profiling of oral samples. Currently, there exists no generally applicable method to test for such associations. Here we present a Bayesian framework to identify microbes that exhibit consistent patterns between body sites, with respect to a phenotypic variable. For a given operational taxonomic unit (OTU), a Bayesian regression model is used to obtain Markov-Chain Monte Carlo estimates of abundance among strata, calculate a correlation statistic, and conduct a formal test based on its posterior distribution. Extensive simulation studies demonstrate overall viability of the approach, and provide information on what factors affect its performance. Applying our method to a dataset containing oral and gut microbiome samples from 77 pancreatic cancer patients revealed several OTUs exhibiting consistent patterns between gut and mouth with respect to disease subtype. Our method is well powered for modest sample sizes and moderate strength of association and can be flexibly extended to other research settings using any currently established Bayesian analysis programs.