Volume 13, Issue 6

Menzerath’s law, the tendency of Z (the mean size of the parts) to decrease as X (the number of parts) increases, is found in language, music and genomes. Recently, it has been argued that the presence of the law in genomes is an inevitable consequence of the fact that Z = Y / X , which would imply that Z scales with X as Z ∼1/ X . That scaling is a very particular case of Menzerath-Altmann law that has been rejected by means of a correlation test between X and Y in genomes, being X the number of chromosomes of a species, Y its genome size in bases and Z the mean chromosome size. Here we review the statistical foundations of that test and consider three non-parametric tests based upon different correlation metrics and one parametric test to evaluate if Z ∼1/ X in genomes. The most powerful test is a new non-parametric one based upon the correlation ratio, which is able to reject Z ∼1/ X in nine out of 11 taxonomic groups and detect a borderline group. Rather than a fact, Z ∼1/ X is a baseline that real genomes do not meet. The view of Menzerath-Altmann law as inevitable is seriously flawed.

It has been proposed recently that differentially variable CpG methylation (DVC) may contribute to transcriptional aberrations in human diseases. In large scale epigenetic studies, potential confounders could affect the observed methylation variabilities and need to be accounted for. In this paper, we develop a robust statistical model for differential variability DVC analysis that accounts for potential confounding covariates by utilizing the propensity score method. Our method is based on a weighted score test on strata generated propensity score stratification. To the best of our knowledge, this is the first proposed statistical method for detecting DVCs that adjusts for confounding covariates. We show that this method is robust against model misspecification and achieves good operating characteristics based on extensive simulations and a case study.

Conservative statistical tests are often used in complex multiple testing settings in which computing the type I error may be difficult. In such tests, the reported p -value for a hypothesis can understate the evidence against the null hypothesis and consequently statistical power may be lost. False Discovery Rate adjustments, used in multiple comparison settings, can worsen the unfavorable effect. We present a computationally efficient and test-agnostic calibration technique that can substantially reduce the conservativeness of such tests. As a consequence, a lower sample size might be sufficient to reject the null hypothesis for true alternatives, and experimental costs can be lowered. We apply the calibration technique to the results of DESeq, a popular method for detecting differentially expressed genes from RNA sequencing data. The increase in power may be particularly high in small sample size experiments, often used in preliminary experiments and funding applications.

In genetic association studies, detecting disease-genotype association is a primary goal. We study seven robust test statistics for such association when the underlying genetic model is unknown, for data on disease status (case or control) and genotype (three genotypes of a biallelic genetic marker). In such studies, p -values have predominantly been calculated by asymptotic approximations or by simulated permutations. We consider an exact method, conditional enumeration. When the number of simulated permutations tends to infinity, the permutation p -value approaches the conditional enumeration p -value, but calculating the latter is much more efficient than performing simulated permutations. We have studied case-control sample sizes with 500–5000 cases and 500–15,000 controls, and significance levels from 5×10 –8 to 0.05, thus our results are applicable to genetic association studies with only a few genetic markers under study, intermediate follow-up studies, and genome-wide association studies. Our main findings are: (i) If all monotone genetic models are of interest, the best performance in the situations under study is achieved for the robust test statistics based on the maximum over a range of Cochran-Armitage trend tests with different scores and for the constrained likelihood ratio test. (ii) For significance levels below 0.05, for the test statistics under study, asymptotic approximations may give a test size up to 20 times the nominal level, and should therefore be used with caution. (iii) Calculating p -values based on exact conditional enumeration is a powerful, valid and computationally feasible approach, and we advocate its use in genetic association studies.

We explore the probabilistic structure of DNA in a number of bacterial genomes and conclude that a form of Markovianness is present at the boundaries between coding and non-coding regions, that is, the sequence of START and STOP codons annotated for the bacterial genome. This sequence is shown to satisfy a conditional independence property which allows its governing Markov chain to be uniquely identified from the abundances of START and STOP codons. Furthermore, we show that the annotated sequence of STARTs and STOPs complies with Chargaff’s second parity rule.

The literature shows that classifiers perform differently across datasets and that correlations within datasets affect the performance of classifiers. The question that arises is whether the correlation structure within datasets differ significantly across diseases. In this study, we evaluated the homogeneity of correlation structures within and between datasets of six etiological disease categories; inflammatory, immune, infectious, degenerative, hereditary and acute myeloid leukemia (AML). We also assessed the effect of filtering; detection call and variance filtering on correlation structures. We downloaded microarray datasets from ArrayExpress for experiments meeting predefined criteria and ended up with 12 datasets for non-cancerous diseases and six for AML. The datasets were preprocessed by a common procedure incorporating platform-specific recommendations and the two filtering methods mentioned above. Homogeneity of correlation matrices between and within datasets of etiological diseases was assessed using the Box’s M statistic on permuted samples. We found that correlation structures significantly differ between datasets of the same and/or different etiological disease categories and that variance filtering eliminates more uncorrelated probesets than detection call filtering and thus renders the data highly correlated.