Random effects modeling of multiple binomial responses using the multivariate binomial logit-normal distribution

The multivariate binomial logit-normal distribution is a mixture distribution for which, (i) conditional on a set of success probabilities and sample size indices, a vector of counts is independent binomial variates, and (ii) the vector of logits of the parameters has a multivariate normal distribution. We use this distribution to model multivariate binomial-type responses using a vector of random effects. The vector of logits of parameters has a mean that is a linear function of explanatory variables and has an unspecified or partly specified covariance matrix. The model generalizes and provides greater flexibility than the univariate model that uses a normal random effect to account for positive correlations in clustered data. The multivariate model is useful when different elements of the response vector refer to different characteristics, each of which may naturally have its own random effect. It is also useful for repeated binary measurement of a single response when there is a nonexchangeable association structure, such as one often expects with longitudinal data or when negative association exists for at least one pair of responses. We apply the model to an influenza study with repeated responses in which some pairs are negatively associated and to a developmental toxicity study with continuation-ratio logits applied to an ordinal response with clustered observations.     

Approximate simultaneous confidence intervals for multiple contrasts of binomial proportions

Simultaneous confidence intervals for contrasts of means in a one-way layout with several independent samples are well established for Gaussian distributed data. Procedures addressing different hypotheses are available, such as all pairwise comparisons or comparisons to control, comparison with average, or different tests for order-restricted alternatives. However, if the distribution of the response is not Gaussian, corresponding methods are usually not available or not implemented in software. For the case of comparisons among several binomial proportions, we extended recently proposed confidence interval methods for the difference of two proportions or single contrasts to multiple contrasts by using quantiles of the multivariate normal distribution, taking the correlation into account. The small sample performance of the proposed methods was investigated in simulation studies. The simple adjustment of adding 2 pseudo-observations to each sample estimate leads to reasonable coverage probabilities. The methods are illustrated by the evaluation of real data examples of a clinical trial and a toxicological study. The proposed methods and examples are available in the R package MCPAN. ((c) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim).     

On testing departure from the binomial and multinomial assumptions

This paper is concerned with testing the multinomial (binomial) assumption against the Dirichlet-multinomial (beta-binomial) alternatives. In particular, we discuss the distribution of the asymptotic likelihood ratio (LR) test and obtain the C(alpha) goodness-of-fit test statistic. The inadequacy of the regular chi-square approximation to the LR test is supported by some Monte Carlo experiments. The C(alpha) test is recommended based on empirical significance level and power and also computational simplicity. Two examples are given.     

Note on a binomial test against sectoral preference of circular observations

A binomial test is proposed to test the nullhypothesis of uniform distribution of circular observations against the alternative of sectoral preference where the sector in which the observations are expected to cluster must be chosen prior to sampling. This binomial test against sectoral preference is illustrated by an example from psychopharmacology. The method is modified for comparing the sectoral proportions of two independent as well as two paired samples of circular observations.     

On the inhibitory power of some further pyrazole derivatives of horse liver alcohol dehydrogenase

We found in 1969 (1) that the inhibitory power of pyrazole on LADH was greatly increased by methyl substitution in the 4-position. In this paper we have studied the effect of increasing the size of this side chain. The inhbitory power was found to increase by a factor of two for each methyl group added in a normal side chain. Some other side chains were tested. Already the 4-butyl and 4-pentyl pyrazoles were so active that for the calculation of their true inhibition constants these had to be corrected for the concentration of the enzyme (0.0005 μN). To our knowledge this never happened before.     

On the power for linkage detection using a test based on scan statistics

We analyze some aspects of scan statistics, which have been proposed to help for the detection of weak signals in genetic linkage analysis. We derive approximate expressions for the power of a test based on moving averages of the identity by descent allele sharing proportions for pairs of relatives at several contiguous markers. We confirm these approximate formulae by simulation. The results show that when there is a single trait-locus on a chromosome, the test based on the scan statistic is slightly less powerful than that based on the customary allele sharing statistic. On the other hand, if two genes having a moderate effect on a trait lie close to each other on the same chromosome, scan statistics improve power to detect linkage.     

Using group testing to estimate a proportion, and to test the binomial model

Group testing has been extensively studied as an efficient way to classify units as defective or satisfactory when the proportion (p) of defectives is small. It can also be used to estimate p, often substantially reducing the mean squared error (MSE) of p and cost per unit information. Group testing is useful for larger p in the estimation problem than in the classification problem, but for larger p more care must be taken in choosing the group size (k); k being too large not only increases MSE (p), but adversely affects the robustness of p to both errors in testing (misclassification) and errors in the assumed binomial model. Procedures that retest units from defective groups, if even feasible, are shown to reduce cost per unit information very little in the estimation problem, but can provide useful information for testing the model. Methods are given for using data from tests of unequal-sized groups to estimate p and for testing the validity of the binomial model.