Functional mapping of dynamic traits with robust t-distribution

Functional mapping has been a powerful tool in mapping quantitative trait loci (QTL) underlying dynamic traits of agricultural or biomedical interest. In functional mapping, multivariate normality is often assumed for the underlying data distribution, partially due to the ease of parameter estimation. The normality assumption however could be easily violated in real applications due to various reasons such as heavy tails or extreme observations. Departure from normality has negative effect on testing power and inference for QTL identification. In this work, we relax the normality assumption and propose a robust multivariate t-distribution mapping framework for QTL identification in functional mapping. Simulation studies show increased mapping power and precision with the t distribution than that of a normal distribution. The utility of the method is demonstrated through a real data analysis.     

Generalization of DNA microarray dispersion properties: microarray equivalent of t-distribution

Background

DNA microarrays are a powerful technology that can provide a wealth of gene expression data for disease studies, drug development, and a wide scope of other investigations. Because of the large volume and inherent variability of DNA microarray data, many new statistical methods have been developed for evaluating the significance of the observed differences in gene expression. However, until now little attention has been given to the characterization of dispersion of DNA microarray data.

Results

Here we examine the expression data obtained from 682 Affymetrix GeneChips^® with 22 different types and we demonstrate that the Gaussian (normal) frequency distribution is characteristic for the variability of gene expression values. However, typically 5 to 15% of the samples deviate from normality. Furthermore, it is shown that the frequency distributions of the difference of expression in subsets of ordered, consecutive pairs of genes (consecutive samples) in pair-wise comparisons of replicate experiments are also normal. We describe a consecutive sampling method, which is employed to calculate the characteristic function approximating standard deviation and show that the standard deviation derived from the consecutive samples is equivalent to the standard deviation obtained from individual genes. Finally, we determine the boundaries of probability intervals and demonstrate that the coefficients defining the intervals are independent of sample characteristics, variability of data, laboratory conditions and type of chips. These coefficients are very closely correlated with Student's t-distribution.

Conclusion

In this study we ascertained that the non-systematic variations possess Gaussian distribution, determined the probability intervals and demonstrated that the K _α coefficients defining these intervals are invariant; these coefficients offer a convenient universal measure of dispersion of data. The fact that the K _α distributions are so close to t-distribution and independent of conditions and type of arrays suggests that the quantitative data provided by Affymetrix technology give "true" representation of physical processes, involved in measurement of RNA abundance.

Reviewers

This article was reviewed by Yoav Gilad (nominated by Doron Lancet), Sach Mukherjee (nominated by Sandrine Dudoit) and Amir Niknejad and Shmuel Friedland (nominated by Neil Smalheiser).     

A note on the use of the non-central t-distribution in setting numerical microbiological specifications for foods

An exact procedure is described and used to determine k values and probabilities of rejection used in the application of variables sampling plans to foods. Comparison of quantities so obtained to those calculated by Kilsby et al. (1979), who used an approximation procedure, reveals that for small samples the approximation can lead to probabilities of rejection which are larger than those obtained using the exact procedure. It is recommended that the exact procedure be used in the application of these plans.     

A note on the use of the non-central t-distribution in setting numerical microbiological specifications for foods

O rdonez , J.A. S anz , B. H ernandez , P.E. L opez -L orenzo , P 1984, A note on the effect of combined ultrasonic and heat treatments on the survival of thermoduric streptococci. Journal of Applied Bacteriology , 56 , 175–177.
The combined destructive effect of ultrasonic waves and heating on microorganisms has been investigated using as a model two species of thermoduric streptococci. Ultrasonic and heat treatments applied simultaneously were much more destructive than the additive effect of the two agents considered independently. Compared with heat alone, the simultaneous application of ultrasonic vibration and heat reduced the resistance of the organisms 6–11.fold.     

Comparison of gaussian and t-distribution densities for modeling fluorescence dispersion in flow cytometric DNA histograms

In this paper, we have analyzed, on an experimental basis, the behaviour of the standardized t-distribution with three degrees of freedom versus the gaussian model, when employed for describing the fluorescence dispersion effect in flow cytometric DNA measurements. The comparison has been performed by employing two different objective criteria based on a computer analysis for fitting DNA histograms and on a parameter related to the peak distribution shape. The results indicate that, when the peak variance is not particularly small, the two models are substantially equivalent. In the case of experimental data with very sharp peaks, the t-distribution performs better than the gaussian density.     

HLA and the probability of paternity.

In cases of disputed paternity, blood tests are often used to obtain an estimate of the probability that the accused male is the true father. The interpretation of the genetic data is usually based upon a statistic called the paternity index. This paper shows that the paternity index method cannot be applied to data from compound loci in the absence of information on linkage phase. Since phenotypic data from compound loci, such as HLA, MNSs, and Rh, are often useful in disputed paternity proceedings, they should be analyzed with available alternative statistics.     

Chromatin looping and the probability of transcription

Recent studies of several multigene clusters have shown that gene activation by a remote enhancer is associated with chromatin loop formation. It is not fully understood how a chromatin loop forms in a nucleus or how it is involved in gene regulation. In this article, we propose that the major feature that determines loop formation is the flexibility of chromatin, and that this flexibility is modulated by histone acetylation (and other modifications). Thus, histone modifications will modulate distribution of the preferential looping site in chromatin, which, in turn, determines the probability of interaction between a remote enhancer and the cognate genes. This model can explain gene expression changes in the Hoxd gene cluster and the beta-globin locus.     

The relationship between species detection probability and local extinction probability

In community-level ecological studies, generally not all species present in sampled areas are detected. Many authors have proposed the use of estimation methods that allow detection probabilities that are <1 and that are heterogeneous among species. These methods can also be used to estimate community-dynamic parameters such as species local extinction probability and turnover rates (Nichols et al. Ecol Appl 8:1213–1225; Conserv Biol 12:1390–1398). Here, we present an ad hoc approach to estimating community-level vital rates in the presence of joint heterogeneity of detection probabilities and vital rates. The method consists of partitioning the number of species into two groups using the detection frequencies and then estimating vital rates (e.g., local extinction probabilities) for each group. Estimators from each group are combined in a weighted estimator of vital rates that accounts for the effect of heterogeneity. Using data from the North American Breeding Bird Survey, we computed such estimates and tested the hypothesis that detection probabilities and local extinction probabilities were negatively related. Our analyses support the hypothesis that species detection probability covaries negatively with local probability of extinction and turnover rates. A simulation study was conducted to assess the performance of vital parameter estimators as well as other estimators relevant to questions about heterogeneity, such as coefficient of variation of detection probabilities and proportion of species in each group. Both the weighted estimator suggested in this paper and the original unweighted estimator for local extinction probability performed fairly well and provided no basis for preferring one to the other.