Estimating misclassification error with small samples via bootstrap cross-validation

MOTIVATION: Estimation of misclassification error has received increasing attention in clinical diagnosis and bioinformatics studies, especially in small sample studies with microarray data. Current error estimation methods are not satisfactory because they either have large variability (such as leave-one-out cross-validation) or large bias (such as resubstitution and leave-one-out bootstrap). While small sample size remains one of the key features of costly clinical investigations or of microarray studies that have limited resources in funding, time and tissue materials, accurate and easy-to-implement error estimation methods for small samples are desirable and will be beneficial. RESULTS: A bootstrap cross-validation method is studied. It achieves accurate error estimation through a simple procedure with bootstrap resampling and only costs computer CPU time. Simulation studies and applications to microarray data demonstrate that it performs consistently better than its competitors. This method possesses several attractive properties: (1) it is implemented through a simple procedure; (2) it performs well for small samples with sample size, as small as 16; (3) it is not restricted to any particular classification rules and thus applies to many parametric or non-parametric methods.     

Interactions among genomic structure, function, and evolution revealed by comprehensive analysis of the Arabidopsis thaliana genome

The genome in a higher organism consists of a number of types of nucleotide sequence-specialized components, with each having tens of thousands of members or elements. It is crucial for our understanding of how a genome as an entity is organized, functions, and evolves to determine how these components are organized in the genome and how they relate with each other; however, no such knowledge is available. Here, we report a comprehensive analysis of the organization and interaction of all 40 components constituting the genome of the plant model species, Arabidopsis thaliana, at the whole-genome and chromosome levels. The 40 components include (i) 6 genome structural components consisting of GC%, genes, retrotransposons, DNA transposons, simple repeats, and low complex repeats; (ii) 3 evolutionarily critical features consisting of recombination rate, nucleotide substitutions, and nucleotide insertions/deletions; and (iii) 31 categories of genes with different functions and numbers of functions. We show that the distributions of 39 of the 40 components of the genome (excepting GC%) deviate significantly from the random distribution model and different types of the genome components are significantly correlated. These results remained to be true even when the genomic regions, such as centromeric regions, where transposable and repeat elements are abundant were excluded from the analyses. These findings suggest that DNA molecules contained in the Arabidopsis genome are each organized and structured from their constituting components in an unambiguous manner and that different types of the components that constitute or characterize the genome interact. The analysis also showed that each chromosome consists of a similar set of the components at similar densities, suggesting that the unique organization and interaction pattern of the components in each chromosome may represent, at least in part, the identity of a chromosome or a genome at the genome level, thus partly accounting for the phenotypic variation among different species. The data also provide comprehensive and new insights into many phenomena significant in genome biology, with which we particularly discuss the variation of genetic recombination. The variation of genetic recombination rate along a chromosomal arm is shaped, not only by the distribution of simple repeats, retrotransposons, DNA transposons, and nucleotide substitutions, but also by the functions of genes contained, especially those with multiple functions, suggesting that variation of genetic recombination along a chromosomal arm is the result of interactions among the components constituting local genome structure, function, and evolution.     

Confidence intervals for the difference in the success rates of two treatments in the analysis of correlated binary responses

In clinical studies, we often compare the success rates of two treatment groups where post‐treatment responses of subjects within clusters are usually correlated. To estimate the difference between the success rates, interval estimation procedures that do not account for this intraclass correlation are likely inappropriate. To address this issue, we propose three interval procedures by direct extensions of recently proposed methods for independent binary data based on the concepts of design effect and effective sample size used in sample surveys. Each of them is then evaluated with four competing variance estimates. We also extend three existing methods recommended for complex survey data using different weighting schemes required for those three existing methods. An extensive simulation study is conducted for the purposes of evaluating and comparing the performance of the proposed methods in terms of coverage and expected width. The interval estimation procedures are illustrated using three examples in clinical and social science studies. Our analytic arguments and numerical studies suggest that the methods proposed in this work may be useful in clustered data analyses.