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In co-expression analyses of gene expression data, it is often of interest to interpret clusters of co-expressed genes with respect to a set of external information, such as a potentially incomplete list of functional properties for which a subset of genes may be annotated. Based on the framework of finite mixture models, we propose a model selection criterion that takes into account such external gene annotations, providing an efficient tool for selecting a relevant number of clusters and clustering model. This criterion, called the integrated completed annotated likelihood (ICAL), is defined by adding an entropy term to a penalized likelihood to measure the concordance between a clustering partition and the external annotation information. The ICAL leads to the choice of a model that is more easily interpretable with respect to the known functional gene annotations. We illustrate the interest of this model selection criterion in conjunction with Gaussian mixture models on simulated gene expression data and on real RNA-seq data.

Sample size calculations for gene expression microarray and NGS-RNA-Seq experiments are challenging because the overall power depends on unknown quantities as the proportion of true null hypotheses and the distribution of the effect sizes under the alternative. We propose a two-stage design with an adaptive interim analysis where these quantities are estimated from the interim data. The second stage sample size is chosen based on these estimates to achieve a specific overall power. The proposed procedure controls the power in all considered scenarios except for very low first stage sample sizes. The false discovery rate (FDR) is controlled despite of the data dependent choice of sample size. The two-stage design can be a useful tool to determine the sample size of high-dimensional studies if in the planning phase there is high uncertainty regarding the expected effect sizes and variability.

In association studies of quantitative traits, the association of each genetic marker with the trait of interest is typically tested using the F -test assuming an additive genetic model. In practice, the true model is rarely known, and specifying an incorrect model can lead to a loss of power. For case-control studies, the maximum of test statistics optimal for additive, dominant, and recessive models has been shown to be robust to model misspecification. The approach has later been extended to quantitative traits. However, the existing procedures assume that the trait is normally distributed and may not maintain correct type I error rates and can also have reduced power when the assumption of normality is violated. Here, we introduce a maximum (MAX3) test that is based on ranks and is therefore distribution-free. We examine the behavior of the proposed method using a Monte Carlo simulation with both normal and non-normal data and compare the results to the usual parametric procedures and other nonparametric alternatives. We show that the rank-based maximum test has favorable properties relative to other tests, especially in the case of symmetric distributions with heavy tails. We illustrate the method with data from a real association study of symmetric dimethylarginine (SDMA).

There is a large number of applications where family relationships need to be determined from DNA data. In forensic science, competing ideas are in general verbally formulated as the two hypotheses of a test. For the most common paternity case, the null hypothesis states that the alleged father is the true father against the alternative hypothesis that the father is an unrelated man. A likelihood ratio is calculated to summarize the evidence. We propose an alternative framework whereby a model and the hypotheses are formulated in terms of parameters representing identity-by-descent probabilities. There are several advantages to this approach. Firstly, the alternative hypothesis can be completely general. Specifically, the alternative does not need to specify an unrelated man. Secondly, the parametric formulation corresponds to the approach used in most other applications of statistical hypothesis testing and so there is a large theory of classical statistics that can be applied. Theoretical properties of the test statistic under the null hypothesis are studied. An extension to trios of individuals has been carried out. The methods are exemplified using simulations and a real dataset of 27 Spanish Romani individuals.

This paper presents two simple rare variant (RV) burden tests based on the likelihood ratio test (LRT) and score statistics. LRT is one of the commonly used tests in practical data analysis, and we show here that there is no reason to ignore it in testing RV associations. With the Bartlett correction, we have numerically shown that the LRT-based test can have a reliable distribution. Our simulation study indicates that if the non-null variants are as common as the null variants, then the LRT and score statistics have comparable performance to the C-alpha test, and if the former is rarer than the null variants, then they outperform the C-alpha test.

We are concerned with statistical inference for 2× C × K contingency tables in the context of genetic case-control association studies. Multivariate methods based on asymptotic Gaussianity of vectors of test statistics require information about the asymptotic correlation structure among these test statistics under the global null hypothesis. In the case of C =2, we show that for a wide variety of test statistics this asymptotic correlation structure is given by the standardized linkage disequilibrium matrix of the K loci under investigation. Three popular choices of test statistics are discussed for illustration. In the case of C =3, the standardized composite linkage disequilibrium matrix is the limiting correlation matrix of the K locus-specific Cochran-Armitage trend test statistics.