Yaning Yang

With the increasing amount of data generated in molecular genetics laboratories, it is often difficult to make sense of results because of the vast number of different outcomes or variables studied. Examples include expression levels for large numbers of genes and haplotypes at large numbers of loci. It is then natural to group observations into smaller numbers of classes that allow for an easier overview and interpretation of the data. This grouping is often carried out in multiple steps with the aid of hierarchical cluster analysis, each step leading to a smaller number of classes by combining similar observations or classes. At each step, either implicitly or explicitly, researchers tend to interpret results and eventually focus on that set of classes providing the "best" (most significant) result. While this approach makes sense, the overall statistical significance of the experiment must include the clustering process, which modifies the grouping structure of the data and often removes variation. For hierarchically clustered data, we propose considering the strongest result or, equivalently, the smallest p-value as the experiment-wise statistic of interest and evaluating its significance level for a global assessment of statistical significance. We apply our approach to datasets from haplotype association and microarray expression studies where hierarchical clustering has been used. In all of the cases we examine, we find that relying on one set of classes in the course of clustering leads to significance levels that are too small when compared with the significance level associated with an overall statistic that incorporates the process of clustering. In other words, relying on one step of clustering may furnish a formally significant result while the overall experiment is not significant.

The efficiency of single-nucleotide polymorphism haplotype analysis may be increased by DNA pooling, which can dramatically reduce the number of genotyping assays. We develop a method for obtaining maximum likelihood estimates of haplotype frequencies for different pool sizes, assess the accuracy of these estimates, and show that pooling DNA samples is efficient in estimating haplotype frequencies. Although poolingKindividuals increases ambiguities, at least for small pool sizeKand small numbers of loci, the uncertainty of estimation increases <Ktimes that of unpooled DNA. We also develop the asymptotic variance-covariance of maximum likelihood estimates and evaluate the accuracy of variance estimates by Monte Carlo methods. When the sample size of pools is moderately large, the asymptotic variance estimates are rather accurate. Completely or partially missing genotyping information is allowed for in our analysis. Finally, our methods are applied to single-nucleotide polymorphisms in the angiotensinogen gene.

Expression levels in oligonucleotide microarray experiments depend on a potentially large number of factors, for example, treatment conditions, different probes, different arrays, and so on. To dissect the effects of these factors on expression levels, fixed-effects ANOVA methods have previously been proposed. Because we are not necessarily interested in estimating the specific effects of different probes and arrays, we propose to treat these as random effects. Then we only need to estimate their means and variances but not the effect of each of their levels; that is, we can work with a much reduced number of parameters and, consequently, higher precision for estimating expression levels. Thus, we developed a mixed-effects ANOVA model with some random and some fixed effects. It automatically accounts for local normalization between different arrays and for background correction. The method was applied to each of the 6,584 genes investigated in a microarray experiment on two mouse cell lines, PA6/S and PA6/8, where PA6/S enhances proliferation of Pre B cells in vitro but PA6/8 does not. To detect a set of differentially expressed genes (multiple testing problem), we applied the method of controlling the false discovery rate (FDR), which successfully identified 207 genes with significantly different expression levels.