Impact of unequal censoring and insufficient follow-up on comparing survival outcomes: Applications to clinical studies.

Clinical trials with survival endpoints are typically designed to enroll patients for a specified number of years, (usually 2-3 years) with another specified duration of follow-up (usually 2-3 years). Under this scheme, patients who are alive or free of the event of interest at the termination of the study are censored. Consequently, a patient may be censored due to insufficient follow-up duration or due to being lost to follow-up. Potentially, this process could lead to unequal censoring in the treatment arms and lead to inaccurate and adverse conclusions about treatment effects. In this article, using extensive simulation studies, we assess the impact of such censorings on statistical procedures (the generalized logrank tests) for comparing two survival distributions and illustrate our observations by revisiting Mukherjee et al.'s1 findings of cardiovascular events in patients who took Rofecoxib (Vioxx).

POST: A framework for set-based association analysis in high-dimensional data.

Evaluating the differential expression of a set of genes belonging to a common biological process or ontology has proven to be a very useful tool for biological discovery. However, existing gene-set association methods are limited to applications that evaluate differential expression across k⩾2 treatment groups or biological categories. This limitation precludes researchers from most effectively evaluating the association with other phenotypes that may be more clinically meaningful, such as quantitative variables or censored survival time variables. Projection onto the Orthogonal Space Testing (POST) is proposed as a general procedure that can robustly evaluate the association of a gene-set with several different types of phenotypic data (categorical, ordinal, continuous, or censored). For each gene-set, POST transforms the gene profiles into a set of eigenvectors and then uses statistical modeling to compute a set of z-statistics that measure the association of each eigenvector with the phenotype. The overall gene-set statistic is the sum of squared z-statistics weighted by the corresponding eigenvalues. Finally, bootstrapping is used to compute a p-value. POST may evaluate associations with or without adjustment for covariates. In simulation studies, it is shown that the performance of POST in evaluating the association with a categorical phenotype is similar to or exceeds that of existing methods. In evaluating the association of 875 biological processes with the time to relapse of pediatric acute myeloid leukemia, POST identified the well-known oncogenic WNT signaling pathway as its top hit. These results indicate that POST can be a very useful tool for evaluating the association of a gene-set with a variety of different phenotypes. We have developed an R package named POST which is freely available in Bioconductor.

On exchangeable multinomial distributions.

We derive an expression for the joint distribution of exchangeable multinomial random variables, which generalizes the multinomial distribution based on independent trials while retaining some of its important properties. Unlike de Finneti's representation theorem for a binary sequence, the exchangeable multinomial distribution derived here does not require that the finite set of random variables under consideration be a subset of an infinite sequence. Using expressions for higher moments and correlations, we show that the covariance matrix for exchangeable multinomial data has a different form from that usually assumed in the literature, and we analyse data from developmental toxicology studies. The proposed analyses have been implemented in R and are available on CRAN in the CorrBin package.

Integer sparse distributed memory: analysis and results.

Sparse distributed memory is an auto-associative memory system that stores high dimensional Boolean vectors. Here we present an extension of the original SDM, the Integer SDM that uses modular arithmetic integer vectors rather than binary vectors. This extension preserves many of the desirable properties of the original SDM: auto-associativity, content addressability, distributed storage, and robustness over noisy inputs. In addition, it improves the representation capabilities of the memory and is more robust over normalization. It can also be extended to support forgetting and reliable sequence storage. We performed several simulations that test the noise robustness property and capacity of the memory. Theoretical analyses of the memory's fidelity and capacity are also presented.

An empirical Bayes approach for analysis of diverse periodic trends in time-course gene expression data.

MOTIVATION: There is a substantial body of works in the biology literature that seeks to characterize the cyclic behavior of genes during cell division. Gene expression microarrays made it possible to measure the expression profiles of thousands of genes simultaneously in time-course experiments to assess changes in the expression levels of genes over time. In this context, the commonly used procedures for testing include the permutation test by de Lichtenberg et al. and the Fisher's G-test, both of which are designed to evaluate periodicity against noise. However, it is possible that a gene of interest may have expression that is neither cyclic nor just noise. Thus, there is a need for a new test for periodicity that can identify cyclic patterns against not only noise but also other non-cyclic patterns such as linear, quadratic or higher order polynomial patterns. RESULTS: To address this weakness, we have introduced an empirical Bayes approach to test for periodicity and compare its performance in terms of sensitivity and specificity with that of the permutation test and Fisher's G-test through extensive simulations and by application to a set of time-course experiments on the Schizosaccharomyces pombe cell-cycle gene expression. We use 'conserved' and 'cycling' genes by Lu et al. to assess the sensitivity and CESR genes by Chenet al. to assess the specificity of our new empirical Bayes method. AVAILABILITY AND IMPLEMENTATION: The SAS Macro for our empirical Bayes test for periodicity is included in the supplementary materials along with a sample run of the MACRO program. CONTACT: mkocak1@uthsc.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Literature aided determination of data quality and statistical significance threshold for gene expression studies.

BACKGROUND: Gene expression data are noisy due to technical and biological variability. Consequently, analysis of gene expression data is complex. Different statistical methods produce distinct sets of genes. In addition, selection of expression p-value (EPv) threshold is somewhat arbitrary. In this study, we aimed to develop novel literature based approaches to integrate functional information in analysis of gene expression data. METHODS: Functional relationships between genes were derived by Latent Semantic Indexing (LSI) of Medline abstracts and used to calculate the function cohesion of gene sets. In this study, literature cohesion was applied in two ways. First, Literature-Based Functional Significance (LBFS) method was developed to calculate a p-value for the cohesion of differentially expressed genes (DEGs) in order to objectively evaluate the overall biological significance of the gene expression experiments. Second, Literature Aided Statistical Significance Threshold (LASST) was developed to determine the appropriate expression p-value threshold for a given experiment. RESULTS: We tested our methods on three different publicly available datasets. LBFS analysis demonstrated that only two experiments were significantly cohesive. For each experiment, we also compared the LBFS values of DEGs generated by four different statistical methods. We found that some statistical tests produced more functionally cohesive gene sets than others. However, no statistical test was consistently better for all experiments. This reemphasizes that a statistical test must be carefully selected for each expression study. Moreover, LASST analysis demonstrated that the expression p-value thresholds for some experiments were considerably lower (p < 0.02 and 0.01), suggesting that the arbitrary p-values and false discovery rate thresholds that are commonly used in expression studies may not be biologically sound. CONCLUSIONS: We have developed robust and objective literature-based methods to evaluate the biological support for gene expression experiments and to determine the appropriate statistical significance threshold. These methods will assist investigators to more efficiently extract biologically meaningful insights from high throughput gene expression experiments.

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 (IC(50)) values for inhibition of CYP1A2. The rank order of inhibitor potency was OLT >> TBD >> D3T, with IC(50) values estimated as 0.2, 12.8 and >100 microM, 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.

Multiple comparisons model-based clustering and ternary pattern tree numerical display of gene response to treatment: procedure and application to the preclinical evaluation of chemopreventive agents.

Microarray technology has greatly aided the identification of genes that are expressed differentially. Statistical analysis of such data by multiple comparisons procedures has been slow to develop, in part, because methods to cluster the results of such comparisons in biologically meaningful ways have not been available. We isolated and analyzed, by Northern blot and GeneChip, replicate liver RNA samples (n = 4/group) from rats fed with control diet or diet containing one of three chemopreventive compounds, selected because their pharmacological activities, including RNA expression response, are relatively well understood. We report on a classification tree, based on the results of nonparametric multiple comparisons, which results in the bipolar hierarchical clustering of genes in relation to their response to treatment. In addition to identifying treatment-responsive genes, application of this procedure to our test study identified the known pharmacological relationships among the treatment groups without supervision. Also, small treatment-specific subsets of genes were identified that may be indicative of additional pharmacophores present in the test compounds.