Reproducible Research: A Bioinformatics Case Study

While scientific research and the methodologies involved have gone through substantial technological evolution the technology involved in the publication of the results of these endeavors has remained relatively stagnant. Publication is largely done in the same manner today as it was fifty years ago. Many journals have adopted electronic formats, however, their orientation and style is little different from a printed document. The documents tend to be static and take little advantage of computational resources that might be available. Recent work, Gentleman and Temple Lang (2004), suggests a methodology and basic infrastructure that can be used to publish documents in a substantially different way. Their approach is suitable for the publication of papers whose message relies on computation. Stated quite simply, Gentleman and Temple Lang propose a paradigm where documents are mixtures of code and text. Such documents may be self-contained or they may be a component of a compendium which provides the infrastructure needed to provide access to data and supporting software. These documents, or compendiums, can be processed in a number of different ways. One transformation will be to replace the code with its output -- thereby providing the familiar, but limited, static document. In this paper we apply these concepts to a seminal paper in bioinformatics, namely The Molecular Classification of Cancer, Golub et al. (1999). The authors of that paper have generously provided data and other information that have allowed us to largely reproduce their results. Rather than reproduce this paper exactly we demonstrate that such a reproduction is possible and instead concentrate on demonstrating the usefulness of the compendium concept itself.

A NOVEL AND SIMPLE RULE OF THUMB FOR MULTIPLICITY CONTROL IN EQUIVALENCE TESTING USING TWO ONE-SIDED TESTS

Equivalence testing is growing in use in scientific research outside of its traditional role in the drug approval process. Largely due to its ease of use and recommendation from the United States Food and Drug Administration guidance, the most common statistical method for testing (bio)equivalence is the two one-sided tests procedure (TOST). Like classical point-null hypothesis testing, TOST is subject to multiplicity concerns as more comparisons are made. In this manuscript, a condition that bounds the family-wise error rate (FWER) using TOST is given. This condition then leads to a simple solution for controlling the FWER. Specifically, we demonstrate that if all pairwise comparisons of k independent groups are being evaluated for equivalence, then simply scaling the nominal Type I error rate down by (k - 1) is sufficient to maintain the family-wise error rate at the desired value or less. The resulting rule is much less conservative than the equally simple Bonferroni correction. An example of equivalence testing in a non drug-development setting is given.

PENALIZED FUNCTIONAL REGRESSION

We develop fast fitting methods for generalized functional linear models. An undersmooth of the functional predictor is obtained by projecting on a large number of smooth eigenvectors and the coefficient function is estimated using penalized spline regression. Our method can be applied to many functional data designs including functions measured with and without error, sparsely or densely sampled. The methods also extend to the case of multiple functional predictors or functional predictors with a natural multilevel structure. Our approach can be implemented using standard mixed effects software and is computationally fast. Our methodology is motivated by a diffusion tensor imaging (DTI) study. The aim of this study is to analyze differences between various cerebral white matter tract property measurements of multiple sclerosis (MS) patients and controls. While the statistical developments proposed here were motivated by the DTI study, the methodology is designed and presented in generality and is applicable to many other areas of scientific research. An online appendix provides R implementations of all simulations.