A Survival-Adjusted Quantal-Response Test for Analysis of Tumor Incidence Rates in Animal Carcinogenicity Studies

In rodent cancer bioassays, groups of animals are exposed to different doses of a chemical of interest and followed for tumor occurrence. The resulting tumor rates are commonly analyzed using a survival-adjusted Cochran-Armitage (CA) trend test. The CA trend test has reasonable power when the tumor-response curve is linear in dose, but it may be underpowered for a nonlinear response. An alternative survival-adjusted test procedure based on isotonic regression methodology has previously been proposed. Although this alternative procedure performs well when the tumor response is nonlinear in dose, it has less power than the CA trend test when the response is linear in dose. Here, we introduce a new survival-adjusted test procedure that makes use of both the CA trend test and the isotonic regression-based trend test. Using a broad range of experimental conditions typical of National Toxicology Program (NTP) bioassays, we conducted extensive computer simulations to compare the false-positive error rate and power of the proposed procedure with the survival-adjusted CA trend test. The new procedure competes well with the survival-adjusted CA trend test when observed tumor rates are linear in dose and performs substantially better when observed tumor rates are nonlinear in dose. Further, the proposed trend test almost always has a smaller false-positive rate than does the survival-adjusted CA trend test. We also developed an order-restricted inference-based procedure for performing multiple pairwise comparisons between each of the dose groups and the control group. The trend test and the multiple pairwise comparisons test are demonstrated using an example from a study conducted by the NTP

Entropy inequalities for some multivariate distributions

AbstractIn this paper, we derive some monotonicity properties of generalized entropy functionals of various multivariate distributions. These include the distributions of random eigenvalues arising in many hypothesis testing problems in multivariate analysis; the multivariate Liouville distributions; and the noncentral Wishart distributions

CLME: An R Package for Linear Mixed Effects Models under Inequality Constraints

In many applications researchers are typically interested in testing for inequality constraints in the context of linear fixed effects and mixed effects models. Although there exists a large body of literature for performing statistical inference under inequality constraints, user friendly statistical software implementing such methods is lacking, especially in the context of linear fixed and mixed effects models. In this article we introduce CLME, a package in the R language that can be used for testing a broad collection of inequality constraints. It uses residual bootstrap based methodology which is reasonably robust to non-normality as well as heteroscedasticity. The package is illustrated using two data sets. The package also contains a graphical user interface built using the shiny package

A multiple testing procedure for multi-dimensional pairwise comparisons with application to gene expression studies

Figure S1. A graphical display of various hypotheses of interest. (TIFF 149 kb

Phase analysis of circadian-related genes in two tissues

BACKGROUND: Recent circadian clock studies using gene expression microarray in two different tissues of mouse have revealed not all circadian-related genes are synchronized in phase or peak expression times across tissues in vivo. Instead, some circadian-related genes may be delayed by 4–8 hrs in peak expression in one tissue relative to the other. These interesting biological observations prompt a statistical question regarding how to distinguish the synchronized genes from genes that are systematically lagged in phase/peak expression time across two tissues. RESULTS: We propose a set of techniques from circular statistics to analyze phase angles of circadian-related genes in two tissues. We first estimate the phases of a cycling gene separately in each tissue, which are then used to estimate the paired angular difference of the phase angles of the gene in the two tissues. These differences are modeled as a mixture of two von Mises distributions which enables us to cluster genes into two groups; one group having synchronized transcripts with the same phase in the two tissues, the other containing transcripts with a discrepancy in phase between the two tissues. For each cluster of genes we assess the association of phases across the tissue types using circular-circular regression. We also develop a bootstrap methodology based on a circular-circular regression model to evaluate the improvement in fit provided by allowing two components versus a one-component von-Mises model. CONCLUSION: We applied our proposed methodologies to the circadian-related genes common to heart and liver tissues in Storch et al. [2], and found that an estimated 80% of circadian-related transcripts common to heart and liver tissues were synchronized in phase, and the other 20% of transcripts were lagged about 8 hours in liver relative to heart. The bootstrap p-value for being one cluster is 0.063, which suggests the possibility of two clusters. Our methodologies can be extended to analyze peak expression times of circadian-related genes across more than two tissues, for example, kidney, heart, liver, and the suprachiasmatic nuclei (SCN) of the hypothalamus