Zeros (i.e. events that do not happen) are the source of two common phenomena in count data: overdispersion and zero‐inflation. Zeros have multiple origins in a dataset: false zeros occur due to errors in the experimental design or the observer; structural zeros are related to the ecological or evolutionary restrictions of the system under study; and random zeros are the result of the sampling variability. Identifying the type of zeros and their relation with overdispersion and/or zero inflation is key to select the most appropriate statistical model. Here we review the different modelling options in relation to the presence of overdispersion and zero inflation, tested through the dispersion and zero inflation indices. We then examine the theory of the zero‐inflated (ZI) models and the use of the score tests to assess overdispersion and zero inflation over a model. In order to choose an adequate model when analysing count data we suggest the following protocol: Step 1) classify the zeros and minimize the presence of false zeros; Step 2) identify suitable covariates; Step 3) test the data for overdispersion and zero‐inflation and Step 4) choose the most adequate model based on the results of step 3 and use score tests to determine whether more complex models should be implemented. We applied the recommended protocol on a real dataset on plant–herbivore interactions to evaluate the suitability of six different models (Poisson, NB and their zero‐inflated versions—ZIP, ZINB). Our data were overdispersed and zero‐inflated, and the ZINB was the model with the best fit, as predicted. Ignoring overdispersion and/or zero inflation during data analyses caused biased estimates of the statistical parameters and serious errors in the interpretation of the results. Our results are a clear example on how the conclusions of an ecological hypothesis can change depending on the model applied. Understanding how zeros arise in count data, for example identifying the potential sources of structural zeros, is essential to select the best statistical design. A good model not only fits the data correctly but also takes into account the idiosyncrasies of the biological system.

In this work, we deal with correlated under-reported data through INAR(1)-hidden Markov chain models. These models are very flexible and can be identified through its autocorrelation function, which has a very simple form. A naïve method of parameter estimation is proposed, jointly with the maximum likelihood method based on a revised version of the forward algorithm. The most-probable unobserved time series is reconstructed by means of the Viterbi algorithm. Several examples of application in the field of public health are discussed illustrating the utility of the models. Copyright © 2016 John Wiley & Sons, Ltd.

BackgroundHigh-throughput RNA sequencing (RNA-seq) offers unprecedented power to capture the real dynamics of gene expression. Experimental designs with extensive biological replication present a unique opportunity to exploit this feature and distinguish expression profiles with higher resolution. RNA-seq data analysis methods so far have been mostly applied to data sets with few replicates and their default settings try to provide the best performance under this constraint. These methods are based on two well-known count data distributions: the Poisson and the negative binomial. The way to properly calibrate them with large RNA-seq data sets is not trivial for the non-expert bioinformatics user.ResultsHere we show that expression profiles produced by extensively-replicated RNA-seq experiments lead to a rich diversity of count data distributions beyond the Poisson and the negative binomial, such as Poisson-Inverse Gaussian or Pólya-Aeppli, which can be captured by a more general family of count data distributions called the Poisson-Tweedie. The flexibility of the Poisson-Tweedie family enables a direct fitting of emerging features of large expression profiles, such as heavy-tails or zero-inflation, without the need to alter a single configuration parameter. We provide a software package for R called implementing a new test for differential expression based on the Poisson-Tweedie family. Using simulations on synthetic and real RNA-seq data we show that yields P-values that are equally or more accurate than competing methods under different configuration parameters. By surveying the tiny fraction of sex-specific gene expression changes in human lymphoblastoid cell lines, we also show that accurately detects differentially expressed genes in a real large RNA-seq data set with improved performance and reproducibility over the previously compared methodologies. Finally, we compared the results with those obtained from microarrays in order to check for reproducibility.ConclusionsRNA-seq data with many replicates leads to a handful of count data distributions which can be accurately estimated with the statistical model illustrated in this paper. This method provides a better fit to the underlying biological variability; this may be critical when comparing groups of RNA-seq samples with markedly different count data distributions. The package forms part of the Bioconductor project and it is available for download at http://www.bioconductor.org.

We present a model based on two-order integer-valued autoregressive time series to analyze the number of hospital emergency service arrivals caused by diseases that present seasonal behavior. We also introduce a method to describe this seasonality, on the basis of Poisson innovations with monthly means. We show parameter estimation by maximum likelihood and model validation and show several methods for forecasting, on the basis of long-time means and short-time and long-time prediction regions. We analyze an application to model the number of hospital admissions per week caused by influenza.

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