Dale Bowman

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...

ESTIMATING VARIANCE FUNCTIONS IN DEVELOPMENTAL TOXICITY STUDIES

The presence of intralitter correlation is a well known issue for analysis of the developmental toxicology data. The intralitter correlation coefficients observed in developmental toxicology data are generally different across dose groups. In this paper we use a generalized estimating equation procedure to model jointly the mean parameters and the intralitter correlation coefficients as functions of dose levels. Our procedure is similar to that used by Prentice and Zhao (1991, Biometrics 47, 825-839) for estimating the mean and variance parameters.

Effects of correlation in modeling clustered binary data

A simulation study is conducted to determine the effects of varying correlation structures on two estimation procedures used to model clustered binary data; a parametric model, the beta-binomial, and a non-parametric model, the exchangeable binary. The simulations detected bias in estimation of the mean response parameter and the correlation parameter when assuming a parametric model. In addition it was found that variance parameters can be severely underestimated if the correlation structure is considered strictly a nuisance parameter.

A parametric independence test for clustered binary data

This paper proposes an independence test for a set of clustered binary observations, such as might be encountered in developmental toxicity studies. An exchangeable binary model is employed, under an assumption of exchangeability among cluster elements, to model probability of positive response. With a Weibull form assumed for response, the independence test is equivalent to testing whether a parameter value is unity. This Weibull form also allows for parametric tests for a covariate-response relationship and for covariate effects on correlation. The procedure is illustrated using data obtained from a developmental toxicity study.

Phylogenetic tree construction using trinucleotide usage profile (TUP)

BackgroundIt has been a challenging task to build a genome-wide phylogenetic tree for a large group of species containing a large number of genes with long nucleotides sequences. The most popular method, called feature frequency profile (FFP-k), finds the frequency distribution for all words of certain length k over the whole genome sequence using (overlapping) windows of the same length. For a satisfactory result, the recommended word length (k) ranges from 6 to 15 and it may not be a multiple of 3 (codon length). The total number of possible words needed for FFP-k can range from 46=4096 to 415.ResultsWe propose a simple improvement over the popular FFP method using only a typical word length of 3. A new method, called Trinucleotide Usage Profile (TUP), is proposed based only on the (relative) frequency distribution using non-overlapping windows of length 3. The total number of possible words needed for TUP is 43=64, which is much less than the total count for the recommended optimal “resolution” for FFP. To build a phylogenetic tree, we propose first representing each of the species by a TUP vector and then using an appropriate distance measure between pairs of the TUP vectors for the tree construction. In particular, we propose summarizing a DNA sequence by a matrix of three rows corresponding to three reading frames, recording the frequency distribution of the non-overlapping words of length 3 in each of the reading frame. We also provide a numerical measure for comparing trees constructed with various methods.ConclusionsCompared to the FFP method, our empirical study showed that the proposed TUP method is more capable of building phylogenetic trees with a stronger biological support. We further provide some justifications on this from the information theory viewpoint. Unlike the FFP method, the TUP method takes the advantage that the starting of the first reading frame is (usually) known. Without this information, the FFP method could only rely on the frequency distribution of overlapping words, which is the average (or mixture) of the frequency distributions of three possible reading frames. Consequently, we show (from the entropy viewpoint) that the FFP procedure could dilute important gene information and therefore provides less accurate classification.

A Bayesian approach for inducing sparsity in generalized linear models with multi-category response

BackgroundThe dimension and complexity of high-throughput gene expression data create many challenges for downstream analysis. Several approaches exist to reduce the number of variables with respect to small sample sizes. In this study, we utilized the Generalized Double Pareto (GDP) prior to induce sparsity in a Bayesian Generalized Linear Model (GLM) setting. The approach was evaluated using a publicly available microarray dataset containing 99 samples corresponding to four different prostate cancer subtypes.ResultsA hierarchical Sparse Bayesian GLM using GDP prior (SBGG) was developed to take into account the progressive nature of the response variable. We obtained an average overall classification accuracy between 82.5% and 94%, which was higher than Support Vector Machine, Random Forest or a Sparse Bayesian GLM using double exponential priors. Additionally, SBGG outperforms the other 3 methods in correctly identifying pre-metastatic stages of cancer progression, which can prove extremely valuable for therapeutic and diagnostic purposes. Importantly, using Geneset Cohesion Analysis Tool, we found that the top 100 genes produced by SBGG had an average functional cohesion p-value of 2.0E-4 compared to 0.007 to 0.131 produced by the other methods.ConclusionsUsing GDP in a Bayesian GLM model applied to cancer progression data results in better subclass prediction. In particular, the method identifies pre-metastatic stages of prostate cancer with substantially better accuracy and produces more functionally relevant gene sets.

Bayesian bootstrap methods for developmental toxicity studies

Estimates of mean response for a developmental toxicity study are developed using the techniques of Bayesian bootstrap. Using this method, a joint posterior distribution of mean response is simulated, providing a means for determining estimated variance and confidence statements. The approach allows for effects on litter size to be taken into consideration in the estimation of mean response. In addition a method is given for the incorporation of prior information into the analysis. The prior information may be information about mean response and about the litter size distribution as well. Results are compared with likelihood based estimates.

Likelihood estimation for exchangeable multinomial data

ABSTRACT In this article, maximum likelihood estimates of an exchangeable multinomial distribution using a parametric form to model the parameters as functions of covariates are derived. The non linearity of the exchangeable multinomial distribution and the parametric model make direct application of Newton Rahpson and Fishers scoring algorithms computationally infeasible. Instead parameter estimates are obtained as solutions to an iterative weighted least-squares algorithm. A completely monotonic parametric form is proposed for defining the marginal probabilities that results in a valid probability model.

Modeling developmental data using U-shaped threshold dose-response curves

Abstract This paper develops threshold models for developmental toxicity data. The distinguishing feature of these threshold models is their flexibility in modeling data below threshold with a U-shaped function if the data warrants. The method is applied to actual data from a developmental study which exhibits U-shaped behavior in early dose groups. Results from a simulation study demonstrate the flexibility of the threshold model to pick up on U-shaped trends in the data. In addition, the simulation study reveals important considerations in design of developmental studies.