Choosing Smoothness Parameters for Smoothing Splines by Minimizing and Estimate of Risk

Smoothing splines are a popular approach for non-parametric regression problems. We use periodic smoothing splines to fit a periodic signal plus noise model to data for which we assume there are underlying circadian patterns. In the smoothing spline methodology, choosing an appropriate smoothness parameter is an important step in practice. In this paper, we draw a connection between smoothing splines and REACT estimators that provides motivation for the creation of criteria for choosing the smoothness parameter. The new criteria are compared to three existing methods, namely cross-validation, generalized cross-validation, and generalization of maximum likelihood criteria, by a Monte Carlo simulation and by an application to the study of circadian patterns. For most of the situations presented in the simulations, including the practical example, the new criteria out-perform the three existing criteria

A Statistical Framework for the Analysis of Microarray Probe-Level Data

Microarrays are an example of the powerful high through-put genomics tools that are revolutionizing the measurement of biological systems. In this and other technologies, a number of critical steps are required to convert the raw measures into the data relied upon by biologists and clinicians. These data manipulations, referred to as preprocessing, have enormous influence on the quality of the ultimate measurements and studies that rely upon them. Many researchers have previously demonstrated that the use of modern statistical methodology can substantially improve accuracy and precision of gene expression measurements, relative to ad-hoc procedures introduced by designers and manufacturers of the technology. However, further substantial improvements are possible. Microarrays are now being used to measure diverse high genomic endpoints including yeast mutant representations, the presence of SNPs, presence of deletions/insertions, and protein binding sites by chromatin immunoprecipitation (known as ChIP-chip). In each case, the genomic units of measurement are relatively short DNA molecules referred to as probes. Without appropriate understanding of the bias and variance of these measurements, biological inferences based upon probe analysis will be compromised. Standard operating procedure for microarray researchers is to use preprocessed data as the starting point for the statistical analyses that produce reported results. This has prevented many researchers from carefully considering their choice of preprocessing methodology. Furthermore, the fact that the preprocessing step greatly affects the stochastic properties of the final statistical summaries is ignored. In this paper we propose a statistical framework that permits the integration of preprocessing into the standard statistical analysis flow of microarray data. We demonstrate its usefulness by applying the idea in three different applications of the technology

A statistical framework for the analysis of microarray probe-level data

In microarray technology, a number of critical steps are required to convert the raw measurements into the data relied upon by biologists and clinicians. These data manipulations, referred to as preprocessing, influence the quality of the ultimate measurements and studies that rely upon them. Standard operating procedure for microarray researchers is to use preprocessed data as the starting point for the statistical analyses that produce reported results. This has prevented many researchers from carefully considering their choice of preprocessing methodology. Furthermore, the fact that the preprocessing step affects the stochastic properties of the final statistical summaries is often ignored. In this paper we propose a statistical framework that permits the integration of preprocessing into the standard statistical analysis flow of microarray data. This general framework is relevant in many microarray platforms and motivates targeted analysis methods for specific applications. We demonstrate its usefulness by applying the idea in three different applications of the technology.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS116 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multiple Lab Comparison of Microarray Platforms

Microarray technology is a powerful tool able to measure RNA expression for thousands of genes at once. Various studies have been published comparing competing platforms with mixed results: some find agreement, others do not. As the number of researchers starting to use microarrays and the number of crossplatform meta-analysis studies rapidly increase, appropriate platform assessments become more important. Here we present results from a comparison study that offers important improvements over those previously described in the literature. In particular, we notice that none of the previously published papers consider differences between labs. For this paper, a consortium of ten labs from the Washington DC/Baltimore (USA) area was formed to compare three heavily used platforms using identical RNA samples: Appropriate statistical analysis demonstrates that relatively large differences exist between labs using the same platform, but that the results from the best performing labs agree rather well. Supplemental material is available from http://www.biostat.jhsph.edu/~ririzarr/techcomp

MODEL-BASED QUALITY ASSESSMENT AND BASE-CALLING FOR SECOND-GENERATION SEQUENCING DATA

Second-generation sequencing (sec-gen) technology can sequence millions of short fragments of DNA in parallel, and is capable of assembling complex genomes for a small fraction of the price and time of previous technologies. In fact, a recently formed international consortium, the 1,000 Genomes Project, plans to fully sequence the genomes of approximately 1,200 people. The prospect of comparative analysis at the sequence level of a large number of samples across multiple populations may be achieved within the next five years. These data present unprecedented challenges in statistical analysis. For instance, analysis operates on millions of short nucleotide sequences, or reads—strings of A,C,G, or T’s, between 30-100 characters long—which are the result of complex processing of noisy continuous fluorescence intensity measurements known as base-calling. The complexity of the base-calling discretization process results in reads of widely varying quality within and across sequence samples. This variation in processing quality results in infrequent but systematic errors that we have found to mislead downstream analysis of the discretized sequence read data. For instance, a central goal of the 1000 Genomes Project is to quantify across-sample variation at the single nucleotide level. At this resolution, small error rates in sequencing prove significant, especially for rare variants. Sec-gen sequencing is a relatively new technology for which potential biases and sources of obscuring variation are not yet fully understood. Therefore, modeling and quantifying the uncertainty inherent in the generation of sequence reads is of utmost importance. In this paper we present a simple model to capture uncertainty arising in the base-calling procedure of the Illumina/Solexa GA platform. Model parameters have a straightforward interpretation in terms of the chemistry of base-calling allowing for informative and easily interpretable metrics that capture the variability in sequencing quality. Our model provides these informative estimates readily usable in quality assessment tools while significantly improving base-calling performance

Accounting for cellular heterogeneity is critical in epigenome-wide association studies

Background: Epigenome-wide association studies of human disease and other quantitative traits are becoming increasingly common. A series of papers reporting age-related changes in DNA methylation profiles in peripheral blood have already been published. However, blood is a heterogeneous collection of different cell types, each with a very different DNA methylation profile. Results: Using a statistical method that permits estimating the relative proportion of cell types from DNA methylation profiles, we examine data from five previously published studies, and find strong evidence of cell composition change across age in blood. We also demonstrate that, in these studies, cellular composition explains much of the observed variability in DNA methylation. Furthermore, we find high levels of confounding between age-related variability and cellular composition at the CpG level. Conclusions: Our findings underscore the importance of considering cell composition variability in epigenetic studies based on whole blood and other heterogeneous tissue sources. We also provide software for estimating and exploring this composition confounding for the Illumina 450k microarray

Stochastic Models Based on Molecular Hybridization Theory for Short Oligonucleotide Microarrays

High density oligonucleotide expression arrays are a widely used tool for the measurement of gene expression on a large scale. Affymetrix GeneChip arrays appear to dominate this market. These arrays use short oligonucleotides to probe for genes in an RNA sample. Due to optical noise, non-specific hybridization, probe-specific effects, and measurement error, ad-hoc measures of expression, that summarize probe intensities, can lead to imprecise and inaccurate results. Various researchers have demonstrated that expression measures based on simple statistical models can provide great improvements over the ad-hoc procedure offered by Affymetrix. Recently, physical models based on molecular hybridization theory, have been proposed as useful tools for prediction of, for example, non-specific hybridization. These physical models show great potential in terms of improving existing expression measures. In this paper we demonstrate that the system producing the measured intensities is too complex to be fully described with these relatively simple physical models and we propose empirically motivated stochastic models that compliment the above mentioned molecular hybridization theory to provide a comprehensive description of the data. We discuss how the proposed model can be used to obtain improved measures of expression useful for the data analysts

FEATURE-LEVEL EXPLORATION OF THE CHOE ET AL. AFFYMETRIX GENECHIP CONTROL DATASET

We describe why the Choe et al. control dataset should not be used to assess GeneChip expression measures

Using the R Package crlmm for Genotyping and Copy Number Estimation

Genotyping platforms such as Affymetrix can be used to assess genotype-phenotype as well as copy number-phenotype associations at millions of markers. While genotyping algorithms are largely concordant when assessed on HapMap samples, tools to assess copy number changes are more variable and often discordant. One explanation for the discordance is that copy number estimates are susceptible to systematic differences between groups of samples that were processed at different times or by different labs. Analysis algorithms that do not adjust for batch effects are prone to spurious measures of association. The R package crlmm implements a multilevel model that adjusts for batch effects and provides allele-specific estimates of copy number. This paper illustrates a workflow for the estimation of allele-specific copy number and integration of the marker-level estimates with complimentary Bioconductor software for inferring regions of copy number gain or loss. All analyses are performed in the statistical environment R.

Comparison of Affymetrix GeneChip Expression Measures

Affymetrix GeneChip expression array technology has become a standard tool in medical science and basic biology research. In this system, preprocessing occurs before one obtains expression level measurements. Because the number of competing preprocessing methods was large and growing, in the summer of 2003 we developed a benchmark to help users of the technology identify the best method for their application. In conjunction with the release of a Bioconductor R package (affycomp), a webtool was made available for developers of preprocessing methods to submit them to a benchmark for comparison. There have now been over 30 methods compared via the webtool. Results: Background correction, one of the main steps in preprocessing, has the largest effect on performance. In particular, background correction appears to improve accuracy but, in general, worsen precision. The benchmark results put this balance in perspective. Furthermore, we have improved some of the original benchmark metrics to provide more detailed information regarding accuracy and precision. A handful of methods stand out as maintaining a useful balance. The affycomp package, now version 1.5.2, continues to be available as part of the Bioconductor project (http://www.bioconductor.org). The webtool continues to be available at http://affycomp.biostat.jhsph.edu