A Cox Model for Biostatistics of the Future

Professor Sir David R. Cox (DRC) is widely acknowledged as among the most important scientists of the second half of the twentieth century. He inherited the mantle of statistical science from Pearson and Fisher, advanced their ideas, and translated statistical theory into practice so as to forever change the application of statistics in many fields, but especially biology and medicine. The logistic and proportional hazards models he substantially developed, are arguably among the most influential biostatistical methods in current practice. This paper looks forward over the period from DRC's 80th to 90th birthdays, to speculate about the future of biostatistics, drawing lessons from DRC's contributions along the way. We consider "Cox's model" of biostatistics, an approach to statistical science that: formulates scientific questions or quantities in terms of parameters gamma in probability models f(y; gamma) that represent in a parsimonious fashion, the underlying scientific mechanisms (Cox, 1997); partition the parameters gamma = theta, eta into a subset of interest theta and other "nuisance parameters" eta necessary to complete the probability distribution (Cox and Hinkley, 1974); develops methods of inference about the scientific quantities that depend as little as possible upon the nuisance parameters (Barndorff-Nielsen and Cox, 1989); and thinks critically about the appropriate conditional distribution on which to base infrences. We briefly review exciting biomedical and public health challenges that are capable of driving statistical developments in the next decade. We discuss the statistical models and model-based inferences central to the CM approach, contrasting them with computationally-intensive strategies for prediction and inference advocated by Breiman and others (e.g. Breiman, 2001) and to more traditional design-based methods of inference (Fisher, 1935). We discuss the hierarchical (multi-level) model as an example of the future challanges and opportunities for model-based inference. We then consider the role of conditional inference, a second key element of the CM. Recent examples from genetics are used to illustrate these ideas. Finally, the paper examines causal inference and statistical computing, two other topics we believe will be central to biostatistics research and practice in the coming decade. Throughout the paper, we attempt to indicate how DRC's work and the "Cox Model" have set a standard of excellence to which all can aspire in the future.

An introduction to low-level analysis methods of DNA microarray data

This article gives an overview over the methods used in the low--level analysis of gene expression data generated using DNA microarrays. This type of experiment allows to determine relative levels of nucleic acid abundance in a set of tissues or cell populations for thousands of transcripts or loci simultaneously. Careful statistical design and analysis are essential to improve the efficiency and reliability of microarray experiments throughout the data acquisition and analysis process. This includes the design of probes, the experimental design, the image analysis of microarray scanned images, the normalization of fluorescence intensities, the assessment of the quality of microarray data and incorporation of quality information in subsequent analyses, the combination of information across arrays and across sets of experiments, the discovery and recognition of patterns in expression at the single gene and multiple gene levels, and the assessment of significance of these findings, considering the fact that there is a lot of noise and thus random features in the data. For all of these components, access to a flexible and efficient statistical computing environment is an essential aspect.

Statistical Analyses and Reproducible Research

For various reasons, it is important, if not essential, to integrate the computations and code used in data analyses, methodological descriptions, simulations, etc. with the documents that describe and rely on them. This integration allows readers to both verify and adapt the statements in the documents. Authors can easily reproduce them in the future, and they can present the document's contents in a different medium, e.g. with interactive controls. This paper describes a software framework for authoring and distributing these integrated, dynamic documents that contain text, code, data, and any auxiliary content needed to recreate the computations. The documents are dynamic in that the contents, including figures, tables, etc., can be recalculated each time a view of the document is generated. Our model treats a dynamic document as a master or ``source'' document from which one can generate different views in the form of traditional, derived documents for different audiences. We introduce the concept of a compendium as both a container for the different elements that make up the document and its computations (i.e. text, code, data, ...), and as a means for distributing, managing and updating the collection. The step from disseminating analyses via a compendium to reproducible research is a small one. By reproducible research, we mean research papers with accompanying software tools that allow the reader to directly reproduce the results and employ the methods that are presented in the research paper. Some of the issues involved in paradigms for the production, distribution and use of such reproducible research are discussed.

Caching and Visualizing Statistical Analyses

We present the cacher and CodeDepends packages for R, which provide tools for (1) caching and analyzing the code for statistical analyses and (2) distributing these analyses to others in an efficient manner over the web. The cacher package takes objects created by evaluating R expressions and stores them in key-value databases. These databases of cached objects can subsequently be assembled into “cache packages” for distribution over the web. The cacher package also provides tools to help readers examine the data and code in a statistical analysis and reproduce, modify, or improve upon the results. In addition, readers can easily conduct alternate analyses of the data. The CodeDepends package provides complementary tools for analyzing and visualizing the code for a statistical analysis and this functionality has been integrated into the cacher package. In this chapter we describe the cacher and CodeDepends packages and provide examples of how they can be used for reproducible research.

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, develops markerand study-level summaries of batch effects, and demonstrates how the marker-level estimates can be integrated with complimentary Bioconductor software for inferring regions of copy number gain or loss. All analyses are performed in the statistical environment R. A compendium for reproducing the analysis is available from the author’s website (http://www.biostat.jhsph.edu/~rscharpf/crlmmCompendium/index.html).