E. Olusegun George

A full likelihood procedure for analysing exchangeable binary data.

A full-likelihood procedure is proposed for analyzing correlated binary data under the assumption of exchangeability. The binomial and beta-binomial models are shown to occur as special cases correspondingly, respectively, to the choice of degenerate and beta-mixing distributions. For a finite exchangeable binary sequence of random variables, expressions for the joint distribution, moments, and correlations of all orders are derived. Maximum likelihood estimates of the moments of all orders are computed and used to estimate correlations and the distribution of the number of responses in a cluster. In an application to developmental toxicology data analysis, the procedure introduced is compared with a beta-binomial and a generalized estimating equation procedure in which mean response and intralitter correlation are linked to dose.

A Saturated Model for Analyzing Exchangeable Binary Data: Applications to Clinical and Developmental Toxicity Studies

Abstract Correlated binary data occur very frequently in statistical practice. In many applications, it is reasonable to assume that data from the same cluster are exchangeable. Such data are commonly encountered in cluster sample surveys, teratological experiments, ophthalmologic and otolaryngologic studies, and other clinical trials. The standard methods of analyzing these data include the use of beta-binomial models and generalized estimating equations with third and fourth moments specified by “working matrices.” The focus of these procedures is an estimation of the mean and variance parameters. More information can be obtained when data are exchangeable. By expressing the joint distribution of a set of exchangeable binary random variables in terms of the probability of similar response within cluster, this article introduces a procedure for obtaining maximum likelihood estimates of population parameters such as the marginal means, moments, and correlations of orders two and higher. Applications are m...

The effect of time after treatment, treatment schedule and animal age on the frequency of 6-thioguanine-resistant T-lymphocytes induced in Fischer 344 rats by N-ethyl-N-nitrosourea

The persistence of 6-thioguanine-resistant (TGr) T-lymphocytes was investigated in Fischer 344 rats treated with N-ethyl-N-nitrosourea (ENU) using two schedules. Male rats, aged 3 months, were given i.p. injections containing a total of 0, 50 or 100 mg ENU/kg either as a single treatment (single-dose group) or divided among 10 weekly treatments (split-dose group). At 1, 3, 5, 10, 20, 30 and 50 weeks after the single-dose treatment, and 10, 20, 30 and 50 weeks after beginning the split-dose regimen, animals were assayed for the frequency of TGr spleen lymphocytes. ENU produced significant dose- and time-dependent responses in the single- and the split-dose treatment groups. Although a few of the 50 mg/kg split-dose treatments were significantly higher than the comparative single-dose groups, the number of TGr lymphocytes produced by the two dosing regimens were generally similar. The frequency of TGr cells for control animals increased with the age of the animals. The mode of ENU administration did not greatly influence the percent cloning efficiency (%CE) of the non-selection cultures, although the %CE declined in animals over 10 months of age. To investigate the relationship between the frequency of TGr cells and the age of the animals at the time of ENU administration, additional rats aged 17 months were treated with a single dose of ENU and at 1, 5 and 10 weeks following exposure, the frequencies of TGr cells were determined from the isolated lymphocytes. No difference in mutagen sensitivity between rats treated at 3 months of age and those treated at 17 months of age was detected at the time points evaluated. The data demonstrate the persistence of ENU-induced TGr T-lymphocytes in the rat and suggest that the dose and possibly the treatment schedule, but not the age of the animal at the time of treatment, affect the response.

On stochastic inequalities and comparisons of reliability measures for weighted distributions

Inequalities, relations and stochastic orderings, as well as useful ageing notions for weighted distributions are established. Also presented are preservation and stability results and comparisons for weighted and length-biased distributions. Relations for length-biased and equilibrium distributions as examples of weighted distributions are also presented.

Generation of Uniform Variates from Several Nearly Uniformly Distributed Variables

A very useful result for generating random numbers is that the fractional part of a sum of independent U(0,1) random variables is also a U(0,l) random variable. In this paper we show that a more general result is true: the fractional part of a sum of n independent random variables, one of which is U(0,l), is also U(0,l). Moreover, we show that the fractional part of a sum of independent near-uniform variables is closer in distribution to a U(0,l) variate than each of the component near-uniform variables. These results are used to characterize the uniform distribution and to give some justification for an algorithm of Wichmann and Hill(1982). In addition, we show how the property of “closeness” carries over to the generation of any random variable.

ON A GENERALIZATION OF THE LOGISTIC DISTRIBUTION

SummaryExpressions for the moment generating functions, cumulants and coefficients of kurtosis of a generalization of the logistic distribution are derived and used to show that any symmetric version of this distribution can be closely and simply approximated by a Studentt distribution. Related approximation of the distribution of the logistic sample median is discussed.

Tests of Independence, Treatment Heterogeneity Dose-Related Trend with Exchangeable Binary Data

Abstract Existing methods of testing for treatment effects for clustered binary data include the beta-binomial, quasilikelihood GEE procedures. All of these methods revolve around the mean response and the second-order correlation. However, these two parameters alone do not fully determine the effect of treatment. This article develops nonparametric likelihood ratio procedures to test for independence, heterogeneity dose-related trend in dose—response studies involving exchangeable binary data. The hypotheses of independence, heterogeneity trend are expressed in terms of joint probabilities of similar responses among cluster mates. Constrained maximum likelihood estimates of these probabilities are computed and used to construct test statistics. Unlike the test statistics for independence and heterogeneity, the asymptotic distribution of the likelihood ratio test for trend is not exactly a chi-square. However, an upper bound of its p value is obtained by using a chi-squared distribution. A set of clustere...

Chemical genomics of cancer chemopreventive dithiolethiones

3H-1,2-dithiole-3-thione (D3T) and its analogues 4-methyl-5-pyrazinyl-3H-1,2-dithiole-3-thione (OLT) and 5-tert-butyl-3H-1,2-dithiole-3-thione (TBD) are chemopreventive agents that block or diminish early stages of carcinogenesis by inducing activities of detoxication enzymes. While OLT has been used in clinical trials, TBD has been shown to be more efficacious and possibly less toxic than OLT in animals. Here, we utilize a robust and high-resolution chemical genomics procedure to examine the pharmacological structure–activity relationships of these compounds in livers of male rats by microarray analyses. We identified 226 differentially expressed genes that were common to all treatments. Functional analysis identified the relation of these genes to glutathione metabolism and the nuclear factor, erythroid derived 2-related factor 2 pathway (Nrf2) that is known to regulate many of the protective actions of dithiolethiones. OLT and TBD were shown to have similar efficacies and both were weaker than D3T. In addition, we identified 40 genes whose responses were common to OLT and TBD, yet distinct from D3T. As inhibition of cytochrome P450 (CYP) has been associated with the effects of OLT on CYP expression, we determined the half maximal inhibitory concentration (IC50) values for inhibition of CYP1A2. The rank order of inhibitor potency was OLT ≫ TBD ≫ D3T, with IC50 values estimated as 0.2, 12.8 and >100 μM, respectively. Functional analysis revealed that OLT and TBD, in addition to their effects on CYP, modulate liver lipid metabolism, especially fatty acids. Together, these findings provide new insight into the actions of clinically relevant and lead dithiolethione analogues.

ANALYZING MICROARRAY DATA WITH TRANSITIVE DIRECTED ACYCLIC GRAPHS

Post hoc assignment of patterns determined by all pairwise comparisons in microarray experiments with multiple treatments has been proven to be useful in assessing treatment effects. We propose the usage of transitive directed acyclic graphs (tDAG) as the representation of these patterns and show that such representation can be useful in clustering treatment effects, annotating existing clustering methods, and analyzing sample sizes. Advantages of this approach include: (1) unique and descriptive meaning of each cluster in terms of how genes respond to all pairs of treatments; (2) insensitivity of the observed patterns to the number of genes analyzed; and (3) a combinatorial perspective to address the sample size problem by observing the rate of contractible tDAG as the number of replicates increases. The advantages and overall utility of the method in elaborating drug structure activity relationships are exemplified in a controlled study with real and simulated data.

Bayesian neural network for microarray data

We propose Bayesian neural networks (BNN) with structural learning for exploring microarray data in gene expressions. The approach employs representative data and regularization to capture correlation among gene expressions and Bayesian techniques to extract gene expression information from noisy data. The performance was verified with stratified cross-validation and multiple iterated runs.