BACKGROUND: Single-cell transcriptome sequencing (scRNA-Seq) has allowed new types of investigations at unprecedented levels of resolution. Among the primary goals of scRNA-Seq is the classification of cells into distinct types. Many approaches build on existing clustering literature to develop tools specific to single-cell. However, almost all of these methods rely on heuristics or user-supplied parameters to control the number of clusters. This affects both the resolution of the clusters within the original dataset as well as their replicability across datasets. While many recommendations exist, in general, there is little assurance that any given set of parameters will represent an optimal choice in the trade-off between cluster resolution and replicability. For instance, another set of parameters may result in more clusters that are also more replicable. RESULTS: Here, we propose Dune, a new method for optimizing the trade-off between the resolution of the clusters and their replicability. Our method takes as input a set of clustering results-or partitions-on a single dataset and iteratively merges clusters within each partitions in order to maximize their concordance between partitions. As demonstrated on multiple datasets from different platforms, Dune outperforms existing techniques, that rely on hierarchical merging for reducing the number of clusters, in terms of replicability of the resultant merged clusters as well as concordance with ground truth. Dune is available as an R package on Bioconductor: https://www.bioconductor.org/packages/release/bioc/html/Dune.html . CONCLUSIONS: Cluster refinement by Dune helps improve the robustness of any clustering analysis and reduces the reliance on tuning parameters. This method provides an objective approach for borrowing information across multiple clusterings to generate replicable clusters most likely to represent common biological features across multiple datasets.

Single-cell RNA-Sequencing (scRNA-seq) is the most widely used high-throughput technology to measure genome-wide gene expression at the single-cell level. One of the most common analyses of scRNA-seq data detects distinct subpopulations of cells through the use of unsupervised clustering algorithms. However, recent advances in scRNA-seq technologies result in current datasets ranging from thousands to millions of cells. Popular clustering algorithms, such as k-means, typically require the data to be loaded entirely into memory and therefore can be slow or impossible to run with large datasets. To address this problem, we developed the mbkmeans R/Bioconductor package, an open-source implementation of the mini-batch k-means algorithm. Our package allows for on-disk data representations, such as the common HDF5 file format widely used for single-cell data, that do not require all the data to be loaded into memory at one time. We demonstrate the performance of the mbkmeans package using large datasets, including one with 1.3 million cells. We also highlight and compare the computing performance of mbkmeans against the standard implementation of k-means and other popular single-cell clustering methods. Our software package is available in Bioconductor at https://bioconductor.org/packages/mbkmeans.

We consider the properties of the bootstrap as a tool for inference concerning the eigenvalues of a sample covariance matrix computed from an n x p data matrix X. We focus on the modern framework where p/n is not close to 0 but remains bounded as n and p tend to infinity. Through a mix of numerical and theoretical considerations, we show that the non-parametric bootstrap is not in general a reliable inferential tool in the setting we consider. However, in the case where the population covariance matrix is well-approximated by a finite rank matrix, the non-parametric bootstrap performs as it does in finite dimension.

We consider the performance of the bootstrap in high-dimensions for the setting of linear regression, where $p\lt n$ but $p/n$ is not close to zero. We consider ordinary least-squares as well as robust regression methods and adopt a minimalist performance requirement: can the bootstrap give us good confidence intervals for a single coordinate of $\beta$ (where $\beta$ is the true regression vector)? We show through a mix of numerical and theoretical work that the bootstrap is fraught with problems. Both of the most commonly used methods of bootstrapping for regression–residual bootstrap and pairs bootstrap–give very poor inference on $\beta$ as the ratio $p/n$ grows. We find that the residual bootstrap tend to give anti-conservative estimates (inflated Type I error), while the pairs bootstrap gives very conservative estimates (severe loss of power) as the ratio $p/n$ grows. We also show that the jackknife resampling technique for estimating the variance of $\hat{\beta}$ severely overestimates the variance in high dimensions. We contribute alternative procedures based on our theoretical results that result in dimensionality adaptive and robust bootstrap methods.

Clustering of genes and/or samples is a common task in gene expression analysis. The goals in clustering can vary, but an important scenario is that of finding biologically meaningful subtypes within the samples. This is an application that is particularly appropriate when there are large numbers of samples, as in many human disease studies. With the increasing popularity of single-cell transcriptome sequencing (RNA-Seq), many more controlled experiments on model organisms are similarly creating large gene expression datasets with the goal of detecting previously unknown heterogeneity within cells. It is common in the detection of novel subtypes to run many clustering algorithms, as well as rely on subsampling and ensemble methods to improve robustness. We introduce a Bioconductor R package, clusterExperiment, that implements a general and flexible strategy we entitle Resampling-based Sequential Ensemble Clustering (RSEC). RSEC enables the user to easily create multiple, competing clusterings of the data based on different techniques and associated tuning parameters, including easy integration of resampling and sequential clustering, and then provides methods for consolidating the multiple clusterings into a final consensus clustering. The package is modular and allows the user to separately apply the individual components of the RSEC procedure, i.e., apply multiple clustering algorithms, create a consensus clustering or choose tuning parameters, and merge clusters. Additionally, clusterExperiment provides a variety of visualization tools for the clustering process, as well as methods for the identification of possible cluster signatures or biomarkers. The R package clusterExperiment is publicly available through the Bioconductor Project, with a detailed manual (vignette) as well as well documented help pages for each function.

MOTIVATION: Tumors acquire many chromosomal amplifications, and those acquired early in the lifespan of the tumor may be not only important for tumor growth but also can be used for diagnostic purposes. Many methods infer the order of the accumulation of abnormalities based on their occurrence in a large cohort of patients. Recently, Durinck et al. (2011) and Greenman et al. (2012) developed methods to order a single tumor's chromosomal amplifications based on the patterns of mutations accumulated within those regions. This method offers an unprecedented opportunity to assess the etiology of a single tumor sample, but has not been widely evaluated. RESULTS: We show that the model for timing chromosomal amplifications is limited in scope, particularly for regions with high levels of amplification. We also show that the estimation of the order of events can be sensitive for events that occur early in the progression of the tumor and that the partial maximum likelihood method of Greenman et al. (2012) can give biased estimates, particularly for moderate read coverage or normal contamination. We propose a maximum-likelihood estimation procedure that fully accounts for sequencing variability and show that it outperforms the partial maximum-likelihood estimation method. We also propose a Bayesian estimation procedure that stabilizes the estimates in certain settings. We implement these methods on a small number of ovarian tumors, and the results suggest possible differences in how the tumors acquired amplifications. AVAILABILITY AND IMPLEMENTATION: We provide implementation of these methods in an R package cancerTiming, which is available from the Comprehensive R Archive Network (CRAN) at http://CRAN.R-project.org/.

BACKGROUND: High-throughput sequencing technologies, such as the Illumina Genome Analyzer, are powerful new tools for investigating a wide range of biological and medical questions. Statistical and computational methods are key for drawing meaningful and accurate conclusions from the massive and complex datasets generated by the sequencers. We provide a detailed evaluation of statistical methods for normalization and differential expression (DE) analysis of Illumina transcriptome sequencing (mRNA-Seq) data. RESULTS: We compare statistical methods for detecting genes that are significantly DE between two types of biological samples and find that there are substantial differences in how the test statistics handle low-count genes. We evaluate how DE results are affected by features of the sequencing platform, such as, varying gene lengths, base-calling calibration method (with and without phi X control lane), and flow-cell/library preparation effects. We investigate the impact of the read count normalization method on DE results and show that the standard approach of scaling by total lane counts (e.g., RPKM) can bias estimates of DE. We propose more general quantile-based normalization procedures and demonstrate an improvement in DE detection. CONCLUSIONS: Our results have significant practical and methodological implications for the design and analysis of mRNA-Seq experiments. They highlight the importance of appropriate statistical methods for normalization and DE inference, to account for features of the sequencing platform that could impact the accuracy of results. They also reveal the need for further research in the development of statistical and computational methods for mRNA-Seq.