arXiv subjects

Lorenzo Trippa

Publications and source records attributed to Lorenzo Trippa.

29 records · Page 2Linked to original sources

arXiv2018

Multi-study Factor Analysis

We introduce a novel class of factor analysis methodologies for the joint analysis of multiple studies. The goal is to separately identify and estimate 1) common factors shared across multiple studies, and 2) study-specific factors. We develop a fast Expectation Conditional-Maximization algorithm for parameter estimates and we provide a procedure for choosing the common and specific factor. We present simulations evaluating the performance of the method and we illustrate it by applying it to gene expression data in ovarian cancer. In both cases, we clarify the benefits of a joint analysis compared to the standard factor analysis. We hope to have provided a valuable tool to accelerate the pace at which we can combine unsupervised analysis across multiple studies, and understand the cross-study reproducibility of signal in multivariate data.

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arXiv2018

Bayesian Multi-study Factor Analysis for High-throughput Biological Data

This paper presents a new modeling strategy for joint unsupervised analysis of multiple high-throughput biological studies. As in Multi-study Factor Analysis, our goals are to identify both common factors shared across studies and study-specific factors. Our approach is motivated by the growing body of high-throughput studies in biomedical research, as exemplified by the comprehensive set of expression data on breast tumors considered in our case study. To handle high-dimensional studies, we extend Multi-study Factor Analysis using a Bayesian approach that imposes sparsity. Specifically, we generalize the sparse Bayesian infinite factor model to multiple studies. We also devise novel solutions for the identification of the loading matrices: we recover the loading matrices of interest ex-post, by adapting the orthogonal Procrustes approach. Computationally, we propose an efficient and fast Gibbs sampling approach. Through an extensive simulation analysis, we show that the proposed approach performs very well in a range of different scenarios, and outperforms standard Factor analysis in all the scenarios identifying replicable signal in unsupervised genomic applications. The results of our analysis of breast cancer gene expression across seven studies identified replicable gene patterns, clearly related to well-known breast cancer pathways. An R package is implemented and available on GitHub.

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arXiv2017

Bayesian Nonparametric Ordination for the Analysis of Microbial Communities

Human microbiome studies use sequencing technologies to measure the abundance of bacterial species or Operational Taxonomic Units (OTUs) in samples of biological material. Typically the data are organized in contingency tables with OTU counts across heterogeneous biological samples. In the microbial ecology community, ordination methods are frequently used to investigate latent factors or clusters that capture and describe variations of OTU counts across biological samples. It remains important to evaluate how uncertainty in estimates of each biological sample's microbial distribution propagates to ordination analyses, including visualization of clusters and projections of biological samples on low dimensional spaces. We propose a Bayesian analysis for dependent distributions to endow frequently used ordinations with estimates of uncertainty. A Bayesian nonparametric prior for dependent normalized random measures is constructed, which is marginally equivalent to the normalized generalized Gamma process, a well-known prior for nonparametric analyses. In our prior the dependence and similarity between microbial distributions is represented by latent factors that concentrate in a low dimensional space. We use a shrinkage prior to tune the dimensionality of the latent factors. The resulting posterior samples of model parameters can be used to evaluate uncertainty in analyses routinely applied in microbiome studies. Specifically, by combining them with multivariate data analysis techniques we can visualize credible regions in ecological ordination plots. The characteristics of the proposed model are illustrated through a simulation study and applications in two microbiome datasets.

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arXiv2016

Robust Lineage Reconstruction from High-Dimensional Single-Cell Data

Single-cell gene expression data provide invaluable resources for systematic characterization of cellular hierarchy in multi-cellular organisms. However, cell lineage reconstruction is still often associated with significant uncertainty due to technological constraints. Such uncertainties have not been taken into account in current methods. We present ECLAIR, a novel computational method for the statistical inference of cell lineage relationships from single-cell gene expression data. ECLAIR uses an ensemble approach to improve the robustness of lineage predictions, and provides a quantitative estimate of the uncertainty of lineage branchings. We show that the application of ECLAIR to published datasets successfully reconstructs known lineage relationships and significantly improves the robustness of predictions. In conclusion, ECLAIR is a powerful bioinformatics tool for single-cell data analysis. It can be used for robust lineage reconstruction with quantitative estimate of prediction accuracy.

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arXiv2015

Bayesian nonparametric cross-study validation of prediction methods

We consider comparisons of statistical learning algorithms using multiple data sets, via leave-one-in cross-study validation: each of the algorithms is trained on one data set; the resulting model is then validated on each remaining data set. This poses two statistical challenges that need to be addressed simultaneously. The first is the assessment of study heterogeneity, with the aim of identifying a subset of studies within which algorithm comparisons can be reliably carried out. The second is the comparison of algorithms using the ensemble of data sets. We address both problems by integrating clustering and model comparison. We formulate a Bayesian model for the array of cross-study validation statistics, which defines clusters of studies with similar properties and provides the basis for meaningful algorithm comparison in the presence of study heterogeneity. We illustrate our approach through simulations involving studies with varying severity of systematic errors, and in the context of medical prognosis for patients diagnosed with cancer, using high-throughput measurements of the transcriptional activity of the tumor's genes.

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arXiv2015

Looking-backward probabilities for Gibbs-type exchangeable random partitions

Gibbs-type random probability measures and the exchangeable random partitions they induce represent the subject of a rich and active literature. They provide a probabilistic framework for a wide range of theoretical and applied problems that are typically referred to as species sampling problems. In this paper, we consider the class of looking-backward species sampling problems introduced in Lijoi et al. (Ann. Appl. Probab. 18 (2008) 1519-1547) in Bayesian nonparametrics. Specifically, given some information on the random partition induced by an initial sample from a Gibbs-type random probability measure, we study the conditional distributions of statistics related to the old species, namely those species detected in the initial sample and possibly re-observed in an additional sample. The proposed results contribute to the analysis of conditional properties of Gibbs-type exchangeable random partitions, so far focused mainly on statistics related to those species generated by the additional sample and not already detected in the initial sample.

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arXiv2014

Subgroup-Based Adaptive (SUBA) Designs for Multi-Arm Biomarker Trials

Targeted therapies based on biomarker profiling are becoming a mainstream direction of cancer research and treatment. Depending on the expression of specific prognostic biomarkers, targeted therapies assign different cancer drugs to subgroups of patients even if they are diagnosed with the same type of cancer by traditional means, such as tumor location. For example, Herceptin is only indicated for the subgroup of patients with HER2+ breast cancer, but not other types of breast cancer. However, subgroups like HER2+ breast cancer with effective targeted therapies are rare and most cancer drugs are still being applied to large patient populations that include many patients who might not respond or benefit. Also, the response to targeted agents in human is usually unpredictable. To address these issues, we propose SUBA, subgroup-based adaptive designs that simultaneously search for prognostic subgroups and allocate patients adaptively to the best subgroup-specific treatments throughout the course of the trial. The main features of SUBA include the continuous reclassification of patient subgroups based on a random partition model and the adaptive allocation of patients to the best treatment arm based on posterior predictive probabilities. We compare the SUBA design with three alternative designs including equal randomization, outcome-adaptive randomization and a design based on a probit regression. In simulation studies we find that SUBA compares favorably against the alternatives.

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arXiv2013

Hierarchical Bayesian analysis of somatic mutation data in cancer

Identifying genes underlying cancer development is critical to cancer biology and has important implications across prevention, diagnosis and treatment. Cancer sequencing studies aim at discovering genes with high frequencies of somatic mutations in specific types of cancer, as these genes are potential driving factors (drivers) for cancer development. We introduce a hierarchical Bayesian methodology to estimate gene-specific mutation rates and driver probabilities from somatic mutation data and to shed light on the overall proportion of drivers among sequenced genes. Our methodology applies to different experimental designs used in practice, including one-stage, two-stage and candidate gene designs. Also, sample sizes are typically small relative to the rarity of individual mutations. Via a shrinkage method borrowing strength from the whole genome in assessing individual genes, we reinforce inference and address the selection effects induced by multistage designs. Our simulation studies show that the posterior driver probabilities provide a nearly unbiased false discovery rate estimate. We apply our methods to pancreatic and breast cancer data, contrast our results to previous estimates and provide estimated proportions of drivers for these two types of cancer.

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arXiv2013

Defining Predictive Probability Functions for Species Sampling Models

We review the class of species sampling models (SSM). In particular, we investigate the relation between the exchangeable partition probability function (EPPF) and the predictive probability function (PPF). It is straightforward to define a PPF from an EPPF, but the converse is not necessarily true. In this paper we introduce the notion of putative PPFs and show novel conditions for a putative PPF to define an EPPF. We show that all possible PPFs in a certain class have to define (unnormalized) probabilities for cluster membership that are linear in cluster size. We give a new necessary and sufficient condition for arbitrary putative PPFs to define an EPPF. Finally, we show posterior inference for a large class of SSMs with a PPF that is not linear in cluster size and discuss a numerical method to derive its PPF.

stat.ME↗

arXiv2013

Bayesian nonparametric analysis of reversible Markov chains

We introduce a three-parameter random walk with reinforcement, called the $(θ,α,β)$ scheme, which generalizes the linearly edge reinforced random walk to uncountable spaces. The parameter $β$ smoothly tunes the $(θ,α,β)$ scheme between this edge reinforced random walk and the classical exchangeable two-parameter Hoppe urn scheme, while the parameters $α$ and $θ$ modulate how many states are typically visited. Resorting to de Finetti's theorem for Markov chains, we use the $(θ,α,β)$ scheme to define a nonparametric prior for Bayesian analysis of reversible Markov chains. The prior is applied in Bayesian nonparametric inference for species sampling problems with data generated from a reversible Markov chain with an unknown transition kernel. As a real example, we analyze data from molecular dynamics simulations of protein folding.

math.ST↗

arXiv2011

False discovery rates in somatic mutation studies of cancer

The purpose of cancer genome sequencing studies is to determine the nature and types of alterations present in a typical cancer and to discover genes mutated at high frequencies. In this article we discuss statistical methods for the analysis of somatic mutation frequency data generated in these studies. We place special emphasis on a two-stage study design introduced by Sjöblom et al. [Science 314 (2006) 268--274]. In this context, we describe and compare statistical methods for constructing scores that can be used to prioritize candidate genes for further investigation and to assess the statistical significance of the candidates thus identified. Controversy has surrounded the reliability of the false discovery rates estimates provided by the approximations used in early cancer genome studies. To address these, we develop a semiparametric Bayesian model that provides an accurate fit to the data. We use this model to generate a large collection of realistic scenarios, and evaluate alternative approaches on this collection. Our assessment is impartial in that the model used for generating data is not used by any of the approaches compared. And is objective, in that the scenarios are generated by a model that fits data. Our results quantify the conservative control of the false discovery rate with the Benjamini and Hockberg method compared to the empirical Bayes approach and the multiple testing method proposed in Storey [J. R. Stat. Soc. Ser. B Stat. Methodol. 64 (2002) 479--498]. Simulation results also show a negligible departure from the target false discovery rate for the methodology used in Sjöblom et al. [Science 314 (2006) 268--274].

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