On a likelihood-based goodness-of-fit test of the beta-binomial model

A new regression model for overdispersed binomial data accounting for outliers and an excess of zeros

Binary outcomes are extremely common in biomedical research. Despite its popularity, binomial regression often fails to model this kind of data accurately due to the overdispersion problem. Many alternatives can be found in the literature, the beta-binomial (BB) regression model being one of the most popular. The additional parameter of this model enables a better fit to overdispersed data. It also exhibits an attractive interpretation in terms of the intraclass correlation coefficient. Nonetheless, in many real data applications, a single additional parameter cannot handle the entire excess of variability. In this study, we propose a new finite mixture distribution with BB components, namely, the flexible beta-binomial (FBB), which is characterized by a richer parameterization. This allows us to enhance the variance structure to account for multiple causes of overdispersion while also preserving the intraclass correlation interpretation. The novel regression model, based on the FBB distribution, exploits the flexibility and large variety of the distribution's possible shapes (which includes bimodality and various tail behaviors). Thus, it succeeds in accounting for several (possibly concomitant) sources of overdispersion stemming from the presence of latent groups in the population, outliers, and excessive zero observations. Adopting a Bayesian approach to inference, we perform an intensive simulation study that shows the superiority of the new regression model over that of the existing ones. Its better performance is also confirmed by three applications to real datasets extensively studied in the biomedical literature, namely, bacteria data, atomic bomb radiation data, and control mice data.

The Validation of a Beta-Binomial Model for Overdispersed Binomial Data

The beta-binomial model has been widely used as an analytically tractable alternative that captures the overdispersion of an intra-correlated, binomial random variable, X. However, the model validation for X has been rarely investigated. As a beta-binomial mass function takes on a few different shapes, the model validation is examined for each of the classified shapes in this paper. Further, the mean square error (MSE) is illustrated for each shape by the maximum likelihood estimator (MLE) based on a beta-binomial model approach and the method of moments estimator (MME) in order to gauge when and how much the MLE is biased.

Differential effect of isoflurane, medetomidine, and urethane on BOLD responses to acute levo-tetrahydropalmatine in the rat

Levo-tetrahydropalmatine (l-THP) has shown significant promise in preclinical and clinical studies to treat drug addiction. Pharmacological MRI methods can elucidate the regional cerebral effects of l-THP, but there are potential confounds from the use of general anesthesia. To investigate the possible anesthetic-drug interactions for the pharmacological MRI result of acute l-THP, we examined acute blood oxygen level-dependent responses of both 5 and 20 mg/kg l-THP in naïve rats during general anesthesia achieved with three agents: isoflurane, medetomidine, and urethane. We found that with acute l-THP administration, isoflurane revealed the smallest blood oxygen level-dependent activation areas. In addition, urethane had the most activation areas; however, they were all negative. Medetomidine showed mixed positive and negative activations. Region-specific interactions were found between the l-THP-induced blood oxygen level-dependent responses and the anesthetic agents.

Responses of dopaminergic, serotonergic and noradrenergic networks to acute levo-tetrahydropalmatine administration in naïve rats detected at 9.4 T

AIM

The aim of this study was to understand the neuropharmacological characteristics of levo-tetrahydropalmatine (l-THP), a recently found potential treatment for drug addiction, and discover its neural correlates and sites of action.

METHODS

High-field pharmacological magnetic resonance imaging (phMRI) was used to detect activation induced by acute l-THP administration in the naïve rat brain at dose levels of 5, 10, 20 and 40 mg/kg.

RESULTS

Interestingly, the pharmacological profile of l-THP selectively binds to the receptors of the dopaminergic, serotonergic and noradrenergic systems. Using the phMRI method, it was demonstrated that l-THP selectively activated the key brain regions of the dopaminergic, serotonergic and noradrenergic systems in a dose-dependent manner.

CONCLUSION

Numerous studies suggest a critical role of monoamines in the behavioral, pharmacological and addictive properties of psychostimulants. It is suggested that l-THP holds great potential to be a therapeutic medication for drug addiction.

Misspecification tests for binomial and beta-binomial models

The IOS test of Presnell and Boss (J. Am. Stat. Assoc. 2004; 99(465):216-227) is a general-purpose goodness-of-fit test based on the ratio of in-sample and out-of-sample likelihoods. For large samples, the IOS statistic can be approximated by a multiplicative contrast between two estimates of the information matrix, and in this way the IOS test is connected to White's (Econometrica 1982; 50:1-26) information matrix test, or IM test, which is based directly on the difference of two estimates of the information matrix. In this paper, we compare the performance of IOS to that of the IM test and of other goodness-of-fit tests for binomial and beta-binomial models, in both examples and simulations. Our findings suggest that IOS is strongly competitive, not only against the IM test but also against tests designed for specific binomial and beta-binomial models.

Pooling overdispersed binomial data to estimate event rate

Background

The beta-binomial model is one of the methods that can be used to validly combine event rates from overdispersed binomial data. Our objective is to provide a full description of this method and to update and broaden its applications in clinical and public health research.

Methods

We describe the statistical theories behind the beta-binomial model and the associated estimation methods. We supply information about statistical software that can provide beta-binomial estimations. Using a published example, we illustrate the application of the beta-binomial model when pooling overdispersed binomial data.

Results

In an example regarding the safety of oral antifungal treatments, we had 41 treatment arms with event rates varying from 0% to 13.89%. Using the beta-binomial model, we obtained a summary event rate of 3.44% with a standard error of 0.59%. The parameters of the beta-binomial model took the values of 1.24 for alpha and 34.73 for beta.

Conclusion

The beta-binomial model can provide a robust estimate for the summary event rate by pooling overdispersed binomial data from different studies. The explanation of the method and the demonstration of its applications should help researchers incorporate the beta-binomial method as they aggregate probabilities of events from heterogeneous studies.