Are methylation beta-values simplex distributed?

DNA methylation plays an important role in the development and progression of disease. Beta-values are the standard methylation measures. Different statistical methods have been proposed to assess differences in methylation between conditions. However, most of them do not completely account for the distribution of beta-values. The simplex distribution can accommodate beta-values data. We hypothesize that simplex is a quite flexible distribution which is able to model methylation data.To test our hypothesis, we conducted several analyses using four real data sets obtained from microarrays and sequencing technologies. Standard data distributions were studied and modelled in comparison to the simplex. Besides, some simulations were conducted in different scenarios encompassing several distribution assumptions, regression models and sample sizes. Finally, we compared DNA methylation between females and males in order to benchmark the assessed methodologies under different scenarios.According to the results obtained by the simulations and real data analyses, DNA methylation data are concordant with the simplex distribution in many situations. Simplex regression models work well in small sample size data sets. However, when sample size increases, other models such as the beta regression or even the linear regression can be employed to assess group comparisons and obtain unbiased results. Based on these results, we can provide some practical recommendations when analyzing methylation data: 1) use data sets of at least 10 samples per studied condition for microarray data sets or 30 in NGS data sets, 2) apply a simplex or beta regression model for microarray data, 3) apply a linear model in any other case.

Estimation for finite mixture of simplex models: applications to biomedical data

Simplex distribution has been proved useful for modelling double-bounded variables in data directly. Yet, it is not sufficient for multimodal distributions. This article addresses the problem of estimating a density when data is restricted to the (0,1) interval and contains several modes. Particularly, we propose a simplex mixture model approach to model this kind of data. In order to estimate the parameters of the model, an Expectation Maximization (EM) algorithm is developed. The parameter estimation performance is evaluated through simulation studies. Models are explored using two real datasets: i) gene expressions data of patients’ survival times and the relation to adenocarcinoma and ii) magnetic resonant images (MRI) with a view in segmentation. In the latter case, given that data contains zeros, the main model is modified to consider the zero-inflated setting.

Singhiella simplex. [Distribution map].

A new disrtibution map is provided for Singhiella simplex (Singh). Hemiptera: Aleyrodidae. Hosts: Ficus spp. Information is given on the geographical distribution in Europe (Cyprus), Asia (China, India, Bihar and Myanmar), North America (Mexico, USA, California and Florida), Central America and Caribbean (Barbados, Cayman Islands, Dominican Republic, Jamaica, Panama and Puerto Rico) and South America (Brazil, Minas Gerais, Rio de Janeiro, Sao Paulo and Colombia).

MAXIMUM LIKELIHOOD ESTIMATION FOR SIMPLEX DISTRIBUTION NONLINEAR MIXED MODELS VIA AN EM ALGORITHM

Longitudinal continuous proportional data is common in many fields such as biomedical research, psychological research and so on. As shown in [16], such data can be fitted with simplex models. Based on the original models of [16] which assumed a fixed effect for every subject, this paper extends the models by adding random effects and proposes simplex distribution nonlinear mixed models which are one kind of nonlinear reproductive dispersion mixed models. By treating the random effects in the models as hypothetical missing data and applying Metropolis–Hastings (M–H) algorithm, this paper develops an EM algorithm with Markov chain Monte–Carlo method for maximum likelihood estimation in the models. The method is illustrated with the same data from an ophthalmology study on the use of intraocular gas in retinal surgeries in [16] for ease of comparison.

Anura, Bufonidae, Melanophryniscus simplex: distribution extension

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Butterfly-Shaped Mark: A Variant Form of Nevus Flammeus Simplex

A red-violet, rhomboid-shaped mark on the sacrum of 25 children is described. It is recognized, for the first time, as a part of the nevus flammeus simplex distribution; it is less common than the erythema nuchae or the facial salmon patch. It has the tendency to disappear more slowly than other forms of nevus flammeus simplex. No further investigations seem indicated.

Thrips simplex. [Distribution map].

A new distribution map is provided for Thrips simplex (Morison) [Thysanoptera: Thripidae] Gladiolus thrips. Attacks gladiolus and carnation. Information is given on the geographical distribution in EUROPE, Austria, Bulgaria, Czechoslovakia, France, Germany, East Hungary, Netherlands, Norway, Romania, Sweden, United Kingdom, USSR, AFRICA, Angola, Egypt, Ethiopia, Kenya, Lesotho, Mauritius, Morocco St. Helena, South Africa, Uganda, Zimbabwe, ASIA, Burma, Hongkong, India, Indonesia, Israel, Malaysia, Saudi Arabia, AUSTRALASIA, AND PACIFIC ISLANDS, Australia, Hawaii, New Caledonia, New Zealand, Papua New Guinea, Tasmania, NORTH AMERICA, Canada, USA, Mexico.