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Several doses and a control group can be compared under order restriction using the Williams procedure for normally distributed endpoints assuming variance homogeneity. Comparison of the survival functions represents a secondary endpoint in long-term in vivo bioassays of carcinogenicity. Therefore, a Williams-type procedure for the comparison of survival functions is proposed for the assumption of the Cox proportional hazards model or the general frailty Cox model to allow a joint analysis over sex and strains. Interpretation according to both statistical significance and biological relevance is possible with simultaneous confidence intervals for hazard ratios. Related survival data can be analyzed using the R packages survival, coxme, and multcomp. Together with the R packages MCPAN and nparcomp, Dunnett- or Williams-type procedures are now available for the statistical analysis of the following endpoint types in toxicology: (i) normally distributed, (ii) non-normally distributed, (iii) score (ordered categorical) data, (iv) crude proportions, (v) survival functions, and (vi) time-to-tumor data with and without cause-of-death information., (Copyright © 2012 Elsevier Inc. All rights reserved.)

The analysis of dose-response relationships is a common problem in pre-clinical studies. For example, proportions such as mortality rates and histopathological findings are of particular interest in repeated toxicity studies. Commonly applied designs consist of an untreated control group and several, possibly unequally spaced, dosage groups. The Williams test can be formulated as a multiple contrast test and is a powerful option to evaluate such data. In this paper, we consider simultaneous inference for Williams-type multiple contrasts when the response variable is binomial and sample sizes are only moderate. Approximate simultaneous confidence limits can be constructed using the quantiles of a multivariate normal distribution taking the correlation into account. Alternatively, multiplicity-adjusted p-values can be calculated as well. A simulation study shows that a simple correction based on adding pseudo observations leads to acceptable performance for moderate sample sizes, such as 40 per group. In addition, the calculation of adjusted p-values and approximate power is presented. Finally, the proposed methods are applied to example data from two toxicological studies; the methods are available in an R-package.

This paper proposes a general approach for handling multiple contrast tests for normally distributed data in the presence of heteroscedasticity. Three candidate procedures are described and compared by simulations. Only the procedure with both comparison-specific degrees of freedom and a correlation matrix depending on sample variances maintains the alpha-level over all situations. Other approaches may fail notably as the variances differ more. Furthermore, related approximate simultaneous confidence intervals are given. The approach will be applied to a toxicological experiment.

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).

Recent biotechnology advances allow for multiple types of omics data, such as transcriptomic, proteomic or metabolomic data sets to be integrated. The problem of feature selection has been addressed several times in the context of classification, but needs to be handled in a specific manner when integrating data. In this study, we focus on the integration of two-block data that are measured on the same samples. Our goal is to combine integration and simultaneous variable selection of the two data sets in a one-step procedure using a Partial Least Squares regression (PLS) variant to facilitate the biologists' interpretation. A novel computational methodology called ;;sparse PLS" is introduced for a predictive analysis to deal with these newly arisen problems. The sparsity of our approach is achieved with a Lasso penalization of the PLS loading vectors when computing the Singular Value Decomposition. Sparse PLS is shown to be effective and biologically meaningful. Comparisons with classical PLS are performed on a simulated data set and on real data sets. On one data set, a thorough biological interpretation of the obtained results is provided. We show that sparse PLS provides a valuable variable selection tool for highly dimensional data sets.

Trend tests for monotone trend or umbrella trend (monotone upward changing to monotone downward or vise versa) in count data are proposed when the data exhibit extra-Poisson variability. The proposed tests, which are called the GS1 test and the GS2 test, are constructed by applying an orthonormal score vector to a generalized score test under an rth-order log-linear model. These tests are compared by simulation with the Cochran-Armitage test and the quasi-likelihood test of Piegorsch and Bailer (1997, Statistics for Environmental Biology and Toxicology). It is shown that the Cochran-Armitage test should not be used under the existence of extra-Poisson variability; that, for detecting monotone trend, the GS1 test is superior to the others; and that the GS2 test has high power to detect an umbrella response.

Preclinical animal carcinogenicity studies are usually concerned with testing the statistical significance of a dose-response relationship. When the response consists of a rare event such as the development of a certain type of tumor, exact statistical methods are often employed. The exact randomization trend test based on the multivariate hypergeometric distribution is less powerful in the presence of treatment-related risks other than the specified response. Particularly, the loss of power becomes more pronounced when competing risks cause progressively higher mortality rates with increasing dose, which is usual in practice. An age-adjusted form of the randomization test is proposed to adjust for this effect. Permutational distribution for Peto's cause-of-death (COD) test is also explored and compared with its asymptotic counterpart by simulation. The use of COD information has been a controversial issue due to the subjectivity in the pathologists' determinations as well as for economic reasons. The proposed age-adjusted exact test does not require COD, and it is shown to compare favorably to the COD tests via an extensive Monte Carlo simulation. Applications of the methods to two real data sets are included.

The problem of testing a dose-response relationship in the presence of exchangeably correlated binary data has been addressed using a variety of models. Most commonly used approaches are derived from likelihood or generalized estimating equations and rely on large-sample theory to justify their inferences. However, while earlier work has determined that these methods may perform poorly for small or sparse samples, there are few alternatives available to those faced with such data. We propose an exact trend test for exchangeably correlated binary data when groups of correlated observations are ordered. This exact approach is based on an exponential model derived by Molenberghs and Ryan (1999) and Ryan and Molenberghs (1999) and provides natural analogues to Fisher's exact test and the binomial trend test when the data are correlated. We use a graphical method with which one can efficiently compute the exact tail distribution and apply the test to two examples.

We consider identifying the minimum effective dose (MED) in a dose-response study, where the MED is defined to be the lowest dose level producing an effect over that of the zero-dose control. Proposed herein is a nonparametric procedure based on the Mann-Whitney statistic incorporated with the step-down closed testing scheme. A numerical example demonstrates the feasibility of the proposed nonparametric procedure. Finally, the comparative results of a Monte Carlo level and power study for small sample sizes are presented and discussed.

The extent of drug availability is often measured by the area under the concentration-time curve. In animal studies, experimental constraints can limit the number of observations available on each animal. Estimation of area under the curve and its standard error are straightforward when each animal is measured at each time point. Bailer and Nedelman et al., have described techniques for estimating the area under the curve and its standard error when each animal is measured once. Yeh has described a technique for the hybrid case where animals are measured more than once, but not at all time points. We describe a method for estimating area under the curve and its standard error which is applicable to all three types of designs. We give formulas for testing treatment differences, including dose trends and dose proportionality, in area under the curve for designs containing an arbitrary number of treatments. A jackknife estimator is also described.

This paper develops regression models for ordinal data with nonzero control response probabilities. The models are especially useful in dose-response studies where the spontaneous or natural response rate is nonnegligible and the dosage is logarithmic. These models generalize Abbott's formula, which has been commonly used to model binary data with nonzero background observations. We describe a biologically plausible latent structure and develop an EM algorithm for fitting the models. The EM algorithm can be implemented using standard software for ordinal regression. A toxicology data set where the proposed model fits the data but a more conventional model fails is used to illustrate the methodology.

The problem of identifying the lowest dose level for which the mean response differs from that at the zero dose level is considered. A general framework for stepwise testing procedures that use contrasts among the dose level means is proposed. Using this framework, several new procedures are derived. These and some existing procedures, including that of Williams (1971, Biometrics 27, 103-117; 1972, Biometrics 28, 519-531), are compared analytically and by an extensive simulation study for the normal theory balanced one-way layout case. It is pointed out that the procedures based on the so-called step and basin contrasts proposed by Ruberg (1989, Journal of American Statistical Association 84, 816-822) have excessively high type I familywise error rates (FWEs) and, hence, they should not be used. Some findings of the simulation study are as follows: For monotone dose mean configurations, Williams' procedure and two step-down test procedures based on Helmert and linear contrasts offer the best performance. For nonmonotone dose mean configurations, the performance of Williams' procedure does degrade somewhat, but the other two procedures are still the best. For more complex designs, a simple step-down test procedure that uses any alpha-level tests (not necessarily t-tests) to compare each dose level with the zero dose level controls the FWE and is the only alternative available, but its power is rather low, especially under nonmonotone configurations. Step-up procedures are generally dominated by step-down procedures when the same contrasts are used although the differences are not great.

Historical control data can often aid in the interpretation of the results from laboratory dose-response experiments. For example, formal statistical methods for using historical data are well established for carcinogenicity studies. In that case, a score test derived from a beta-binomial model yields a simple modification of the standard Cochran-Armitage test for trend. However, this test cannot be used for developmental toxicity studies since it does not allow for the additional correlation structure induced by the presence of litter effects. In this paper, quasi-likelihood methods are used to incorporate historical control information into a trend test for the types of correlated binary outcomes that typically arise in developmental toxicity studies. The proposed test is asymptotically equivalent to the beta-binomial score test in the special case when all the litter sizes are equal to 1. Malformation data from a series of developmental toxicity studies illustrate the results.

The applied statistician often encounters the need to compare two or more groups with respect to more than one outcome or response. Several options are generally available, including reducing the dimension of the problem by averaging or summarizing the outcomes, using Bonferroni or other adjustments for multiple comparisons, or applying a global test based on a suitable multivariate model. For normally distributed data, it is well established that global tests tend to be significantly more sensitive than other procedures. While global tests have also been proposed for multiple binary outcomes, their properties have not been well studied nor have they been widely discussed in the context of clustered data. In this paper, we derive a class of quasi-likelihood score tests for multiple binary outcomes, and show that special cases of this class correspond to other tests that have been proposed. We discuss extensions to allow for clustered data, and compare the results to the simple approach of collapsing the data to a single binary outcome, indicating the presence or absence of at least one response. The asymptotic relative efficiencies of the tests are shown to depend not only on the correlation between the outcomes, but also on the response probabilities. Although global tests based on a multivariate model are generally recommended, our findings suggest that a test based on the collapsed data can maintain surprisingly high efficiency, especially when the outcomes of interest are rare. Data from several developmental toxicity studies illustrate our results.