The statistical analysis of the in vitro chromosome aberration assay using Chinese hamster ovary cells

The purpose of the in vitro chromosome aberration assay (ABS) is to determine whether the test compound is a clastogen, i.e. induces structural changes in chromosomes. Details of this assay can be found in Galloway et al. [S.M. Galloway, M. Aardema, M. Ishidate Jr, J.L. Ivett, D.J. Kirkland, M. Takeshi, P. Mosesso, T. Sofuni, Mutation Res. 312 (1994) 241-261]. The standard design consists of a negative control and at least three positive dose groups. At each dose, a sample, say 200, of metaphase cells is examined microscopically and cells exhibiting at least one type of chromosome aberration are identified. Using Chinese hamster ovary cells, Margolin et al. [B.H. Margolin, M.A. Resnick, J.Y. Rimpo, P. Archer, S.M. Galloway, A.D. Bloom, E. Zeiger, Environ. Mutagen. 8 (1986) 183-204] and Richardson et al. [C. Richardson, D.A. Williams, J.A. Allen, G. Amphlett, D.O. Chanter, B. Phillips, Analysis of data from in vitro cytogenetic assays, in: D.J. Kirkland (Ed.), Statistical Evaluation of Mutagenicity Test Data, Cambridge University Press, Cambridge, 1989, pp. 141-154] demonstrated that a binomial sampling model could be used to describe the proportion of cells with chromosome aberrations.Statisticians and toxicologists have also suggested evaluation criteria for the dose response pattern of ABS. Margolin et al. [B.H. Margolin, M.A. Resnick, J.Y. Rimpo, P. Archer, S.M. Galloway, A.D. Bloom, E. Zeiger, Environ. Mutagen. 8 (1986) 183-204] suggested one use the Cochran-Armitage trend test. Sofuni et al. [T. Sofuni, A. Matsuoka, M. Sawada, M. Ishidate Jr, E. Zeiger, M.D. Shelby, Mutation Res. 241 (1990) 175-213] considered the dose response to be (strong) positive if it had two significant doses out of three dose groups and decided it was weakly positive if it had only one significant dose and there was a significant trend. The criterion of Galloway et al. for a positive response was a clear dose-related increase in cells with structural aberrations in one experiment or a reproducible single positive dose [S.M. Galloway, M. Aardema, M. Ishidate Jr, J.L. Ivett, D.J. Kirkland, M. Takeshi, P. Mosesso, T. Sofuni, Mutation Res. 312 (1994) 241-261].We formulate the above three procedures in terms of a Cochran-Armitage trend test and a Dunnett type test. We then compare the performance of these three procedures in terms of a Monte Carlo simulation study. We then develop a software program from the chosen procedure for its ease of use by statisticians and toxicologists.     

Comparability of segmented line regression models

Segmented line regression models, which are composed of continuous linear phases, have been applied to describe changes in rate trend patterns. In this article, we propose a procedure to compare two segmented line regression functions, specifically to test (i) whether the two segmented line regression functions are identical or (ii) whether the two mean functions are parallel allowing different intercepts. A general form of the test statistic is described and then the permutation procedure is proposed to estimate the p-value of the test. The permutation test is compared to an approximate F-test in terms of the p-value estimation and the performance of the permutation test is studied via simulations. The tests are applied to compare female lung cancer mortality rates between two registry areas and also to compare female breast cancer mortality rates between two states.     

Statistical analysis of in vivo rodent micronucleus assay

The in vivo rodent micronucleus assay (MNC) is widely used as a cytogenetic assay to detect the clastogenic activity of a chemical in vivo. MNC is one of three tests in a battery recommended by the fourth International Conference on Harmonization (ICH4) of Genotoxicity Guidelines. As such it has been accepted by many regulatory authorities. However, the determination of a positive result in a genotoxicity test, including MNC, has been an issue of debate among toxicologists and biometricians. In this presentation we compare several statistical procedures that have been suggested for the analysis of MNC data and indicate which one is the most powerful. The standard protocol of MNC has at least three dose levels plus the control dose and uses at least four animals per group. For each animal, 2000 polychromatic erythrocytes (PCE) are counted. Two statistical procedures can be employed, either alone or jointly, for the analysis of the MNC dose-response curve. These are the Cochran-Armitage (C-A) trend test and the Dunnett type test. For performing Dunnett type tests, toxicologists often use negative historical control rate for the estimate of the concurrent negative control rate. Some toxicologists emphasize the reproducibility of assay results instead of the dose-response relationship for the important criterion [J. Ashby, H. Tinwell, Mutat. Res. 327 (1995) 49-55; for the rebuttal see M. Hayashi, T. Sofuni, Mutat. Res. 331 (1995) 173-174]. The following three procedures are currently employed in toxicology labs for the evaluation of MNC result. The assay response is deemed positive if it is detected by (i) the C-A trend test alone, (ii) both the C-A trend test and the Dunnett type test and (iii) either the C-A trend test or the Dunnett type test. Using Monte Carlo simulation, we first find for each procedure, sizes of tests which yield the experiment-wise type I error rate of 0.05 and show that the procedure (ii) is the most powerful against the alternatives of monotone increase. The procedure (ii) which originated from Hayashi's three-step procedure was coded in C and termed 'MNC'. The MNC software program is available in the public domain through the ftp.     

Testing for a trend in tumor prevalence rates: I. Nonlethal tumors

In the analysis of animal carcinogenicity studies, the standard survival-adjusted test for a dose-related trend in the prevalence of nonlethal tumors is the Hoel-Walburg test, which stratifies on age at death by grouping survival times into intervals. An alternative analysis assesses trend on the basis of the likelihood score test under a logistic model for the prevalence function, which adjusts for survival by including age at death as a continuous regression variable. Extensive simulations demonstrate that the test based on modeling the prevalence log-odds as a linear function of age is more powerful than the Hoel-Walburg test, regardless of the intervals used by the latter to stratify the data. Without incorporating a continuity correction, the size of each test often exceeds the nominal level, especially when the mortality patterns differ across dose groups. Corrected versions of the tests operate at conservative levels, where the degree of conservatism varies with the distribution of the data. When the mortality patterns for the dose groups are similar, both tests have essentially the same power to detect a trend in tumor prevalence rates. However, when mortality varies with dose, the logistic regression test with a linear age term is more powerful than the Hoel-Walburg test, and this gain in power increases as the dose-specific mortality patterns become more disparate.     

Exact analysis of dose response for multiple correlated binary outcomes

The neurotoxicity of a substance is often tested using animal bioassays. In the functional observational battery, animals are exposed to a test agent and multiple outcomes are recorded to assess toxicity, using approximately 40 animals measured on up to 30 different items. This design gives rise to a challenging statistical problem: a large number of outcomes for a small sample of subjects. We propose an exact test for multiple binary outcomes, under the assumption that the correlation among these items is equal. This test is based upon an exponential model described by Molenberghs and Ryan (1999, Environmetrics 10, 279-300) and extends the methods developed by Corcoran et al. (2001, Biometrics 57, 941-948) who developed an exact test for exchangeably correlated binary data for groups (clusters) of correlated observations. We present a method that computes an exact p-value testing for a joint dose-response relationship. An estimate of the parameter for dose response is also determined along with its 95% confidence bound. The method is illustrated using data from a neurotoxicity bioassay for the chemical perchlorethylene.     

Efficient p-value evaluation for resampling-based tests

The resampling-based test, which often relies on permutation or bootstrap procedures, has been widely used for statistical hypothesis testing when the asymptotic distribution of the test statistic is unavailable or unreliable. It requires repeated calculations of the test statistic on a large number of simulated data sets for its significance level assessment, and thus it could become very computationally intensive. Here, we propose an efficient p-value evaluation procedure by adapting the stochastic approximation Markov chain Monte Carlo algorithm. The new procedure can be used easily for estimating the p-value for any resampling-based test. We show through numeric simulations that the proposed procedure can be 100-500 000 times as efficient (in term of computing time) as the standard resampling-based procedure when evaluating a test statistic with a small p-value (e.g. less than 10( - 6)). With its computational burden reduced by this proposed procedure, the versatile resampling-based test would become computationally feasible for a much wider range of applications. We demonstrate the application of the new method by applying it to a large-scale genetic association study of prostate cancer.     

Evaluation of Animal Carcinogenicity Studies: Cochran‐Armitage Trend Test vs. Multiple Contrast Tests

Typical animal carcinogenicity studies involve the comparison of several dose groups to a negative control. The uncorrected asymptotic Cochran‐Armitage trend test with equally spaced dose scores is the most frequently used test in such set‐ups. However, this test based on a weighted linear regression on proportions. It is well known that the Cochran‐Armitage test lacks in power for other shapes than the assumed linear one. Therefore, dichotomous multiple contrast tests are introduced. These build the maximum over several single contrasts, where each of them is chosen appropriately to cover a specific dose‐response shape. An extensive power study has been conducted to compare multiple contrast tests with the approaches used so far. Crucial results will be presented in this paper. Moreover, exact tests and continuity corrected versions are introduced and compared to the traditional uncorrected approaches regarding size and power behaviour. A trend test for any shape of the dose‐response relationship for either crude tumour rates or mortality‐ adjusted rates based on the simple Poly‐3 transformation is proposed for evaluation of carcinogenicity studies.     

On testing simultaneously non-inferiority in two multiple primary endpoints and superiority in at least one of them

In a clinical trial with an active treatment and a placebo the situation may occur that two (or even more) primary endpoints may be necessary to describe the active treatment's benefit. The focus of our interest is a more specific situation with two primary endpoints in which superiority in one of them would suffice given that non-inferiority is observed in the other. Several proposals exist in the literature for dealing with this or similar problems, but prove insufficient or inadequate at a closer look (e.g. Bloch et al. (2001, 2006) or Tamhane and Logan (2002, 2004)). For example, we were unable to find a good reason why a bootstrap p-value for superiority should depend on the initially selected non-inferiority margins or on the initially selected type I error alpha. We propose a hierarchical three step procedure, where non-inferiority in both variables must be proven in the first step, superiority has to be shown by a bivariate test (e.g. Holm (1979), O'Brien (1984), Hochberg (1988), a bootstrap (Wang (1998)), or L?uter (1996)) in the second step, and then superiority in at least one variable has to be verified in the third step by a corresponding univariate test. All statistical tests are performed at the same one-sided significance level alpha. From the above mentioned bivariate superiority tests we preferred L?uter's SS test and the Holm procedure for the reason that these have been proven to control the type I error strictly, irrespective of the correlation structure among the primary variables and the sample size applied. A simulation study reveals that the performance regarding power of the bivariate test depends to a considerable degree on the correlation and on the magnitude of the expected effects of the two primary endpoints. Therefore, the recommendation of which test to choose depends on knowledge of the possible correlation between the two primary endpoints. In general, L?uter's SS procedure in step 2 shows the best overall properties, whereas Holm's procedure shows an advantage if both a positive correlation between the two variables and a considerable difference between their standardized effect sizes can be expected.     

The Effect of Stimulus Duration on Frequency-Response Functions in the Pacinian (P) Channel

Psychophysical experiments on human observers and physiological measurements on Pacinian corpuscles (PCs) isolated from cat mesentery were performed to explain certain discrepancies in the psychophysical—physiological model (Bolanowski et al., 1988) for the sense of touch in the vibrotactle Pacinian (P) channel. The model was based on correlations among the psychophysical frequency response obtained on human glabrous skin and physiological frequency-response functions measured on two PC preparations: PC fibers innervating human glabrous skin (Johansson et al., 1982) and PCs isolated from cat mesentery. The three frequency-response functions were qualitatively similar. However, the low-frequency slope for the human PC fibers differed from the slopes for the psychophysical and cat mesentery PC functions by being 3 dB/octave less steep. This discrepancy can be explained theoretically by differences in methodology involving the effect of stimulus duration and the property of temporal summation known to exist in the P channel (i.e., a 3-dB increase in sensitivity per doubling of stimulus duration). To test this, experiments were performed using two methods of stimulation: (1) a constant stimulus duration for different test frequencies, as generally used in this laboratory; and (2) a constant number of stimulus cycles (n = 5) for each test frequency as used by Johansson et al. The method of least squares was used to calculate the low-frequency (50 to 150-Hz) slopes of individual psychophysical and physiological functions. The mean slopes that resulted from using the two methods of stimulation were consistent with the theoretical expectations.     

Semi-parametric differential expression analysis via partial mixture estimation

We develop an approach for microarray differential expression analysis, i.e. identifying genes whose expression levels differ between two or more groups. Current approaches to inference rely either on full parametric assumptions or on permutation-based techniques for sampling under the null distribution. In some situations, however, a full parametric model cannot be justified, or the sample size per group is too small for permutation methods to be valid. We propose a semi-parametric framework based on partial mixture estimation which only requires a parametric assumption for the null (equally expressed) distribution and can handle small sample sizes where permutation methods break down. We develop two novel improvements of Scott's minimum integrated square error criterion for partial mixture estimation [Scott, 2004a,b]. As a side benefit, we obtain interpretable and closed-form estimates for the proportion of EE genes. Pseudo-Bayesian and frequentist procedures for controlling the false discovery rate are given. Results from simulations and real datasets indicate that our approach can provide substantial advantages for small sample sizes over the SAM method of Tusher et al. [2001], the empirical Bayes procedure of Efron and Tibshirani [2002], the mixture of normals of Pan et al. [2003] and a t-test with p-value adjustment [Dudoit et al., 2003] to control the FDR [Benjamini and Hochberg, 1995].     

Biostatistical assessment of mutagenicity studies by including the positive control

Statistical analysis plays a fundamental part in the evaluation of mutagenicity experiments. However, a statistically significant or non-significant test result without incorporating the biological relevance cannot be a valid scientific criterion for concluding a positive or negative effect of the underlying compound (Hauschke et al., 1997). The classification of an experiment as being negative or positive should be based also on the magnitude of the responses in the positive control. We address the problem of determining the maximum safe dose by incorporating a biologically meaningful threshold value, which is expressed as a fraction of the difference between positive and vehicle control.     

A correction for estimating error when using the Local Pooled Error Statistical Test

Jain et al. introduced the Local Pooled Error (LPE) statistical test designed for use with small sample size microarray gene-expression data. Based on an asymptotic proof, the test multiplicatively adjusts the standard error for a test of differences between two classes of observations by pi/2 due to the use of medians rather than means as measures of central tendency. The adjustment is upwardly biased at small sample sizes, however, producing fewer than expected small P-values with a consequent loss of statistical power. We present an empirical correction to the adjustment factor which removes the bias and produces theoretically expected P-values when distributional assumptions are met. Our adjusted LPE measure should prove useful to ongoing methodological studies designed to improve the LPE's; performance for microarray and proteomics applications and for future work for other high-throughput biotechnologies. AVAILABILITY: The software is implemented in the R language and can be downloaded from the Bioconductor project website (http://www.bioconductor.org).     

Linear regression and two-class classification with gene expression data

MOTIVATION: Using gene expression data to classify (or predict) tumor types has received much research attention recently. Due to some special features of gene expression data, several new methods have been proposed, including the weighted voting scheme of Golub et al., the compound covariate method of Hedenfalk et al. (originally proposed by Tukey), and the shrunken centroids method of Tibshirani et al. These methods look different and are more or less ad hoc. RESULTS: We point out a close connection of the three methods with a linear regression model. Casting the classification problem in the general framework of linear regression naturally leads to new alternatives, such as partial least squares (PLS) methods and penalized PLS (PPLS) methods. Using two real data sets, we show the competitive performance of our new methods when compared with the other three methods.     

Fine-mapping using the weighted average method for a case-control study

We present a new method for fine-mapping a disease susceptibility locus using a case-control design. The new method, termed the weighted average (WA) statistic, averages the Cochran-Armitage (CA) trend test statistic and the difference between the Hardy-Weinberg disequilibrium test statistic for cases and controls (the HWD trend). The main characteristics of the WA statistic are that it improves on the weaknesses, and maintains the strengths, of both the CA trend test and the HWD trend test. Data from three different populations in the Genetic Analysis Workshop 14 (GAW14) simulated dataset (Aipotu, Karangar, and Danacaa) were first subjected to model-free linkage analysis to find regions exhibiting linkage. Then, for fine-scale mapping, 140 SNPs within the significant linkage regions were analyzed with the WA test statistic on replicates of the three populations, both separately and combined. The regions that were significant in the multipoint linkage analysis were also significant in this fine-scale mapping. The most significant regions that were obtained using the WA statistic were regions in chromosome 3 (B03T3056-B03T3058, p-value < 1 x 10(-10)) and chromosome 9 (B09T8332-B09T8334, p-value 1 x 10(-6)). Based on the results of the simulated GAW14 data, the WA test statistic showed good performance and could narrow down the region containing the susceptibility locus. However, the strength of the signal depends on both the strength of the linkage disequilibrium and the heterozygosity of the linked marker.     

Positional changes of the frontoparietal ossification centers in perinatal craniosynostotic rabbits.

It has been suggested that craniosynostosis is caused by abnormally located ossification centers (i.e., bony tubers) in the developing skull prior to suture formation [Mathijssen et al., 1996, 1997]. The present study was designed to test this hypothesis in a rabbit model of human familial, nonsyndromic coronal suture (CS) synostosis. Calvariae were taken from 99 New Zealand White rabbit perinates (55 normal controls, 15 with delayed-onset CS synostosis, and 29 with bilateral or unilateral CS synostosis), ranging in age from 23 to 34 days postconception (synostosis occurs at approximately 23 days in this model). Frontoparietal, interfrontal, and interparietal ossification center distances were obtained using a Wild microscope with camera lucida attachment and a 2-D computer digitization technique. Linear regression analysis was used to compare age-related changes in the perinatal ossification centers among groups. Results revealed that frontoparietal ossification center regression line slopes had similar start points (24-day intercepts) with significantly (P < 0.05) diverging slopes over time. Normal and delayed-onset ossification center distance increased more rapidly than in synostosed perinates. No significant (P > 0.05) differences were noted in regression line slopes among groups for interparietal or interfrontal ossification center distances. Results demonstrated that, in synostosed perinates, frontoparietal ossification center location was similar to normals around the time of synostosis and became displaced later. These findings suggest that ossification center (i.e., bony tuber) displacement seen in infants with craniosynostosis is probably a secondary and compensatory, postsynostotic change and not a primary causal factor of synostosis in this rabbit model.     

A comparative review of statistical methods for discovering differentially expressed genes in replicated microarray experiments

MOTIVATION: A common task in analyzing microarray data is to determine which genes are differentially expressed across two kinds of tissue samples or samples obtained under two experimental conditions. Recently several statistical methods have been proposed to accomplish this goal when there are replicated samples under each condition. However, it may not be clear how these methods compare with each other. Our main goal here is to compare three methods, the t-test, a regression modeling approach (Thomas et al., Genome Res., 11, 1227-1236, 2001) and a mixture model approach (Pan et al., http://www.biostat.umn.edu/cgi-bin/rrs?print+2001,2001a,b) with particular attention to their different modeling assumptions. RESULTS: It is pointed out that all the three methods are based on using the two-sample t-statistic or its minor variation, but they differ in how to associate a statistical significance level to the corresponding statistic, leading to possibly large difference in the resulting significance levels and the numbers of genes detected. In particular, we give an explicit formula for the test statistic used in the regression approach. Using the leukemia data of Golub et al. (Science, 285, 531-537, 1999), we illustrate these points. We also briefly compare the results with those of several other methods, including the empirical Bayesian method of Efron et al. (J. Am. Stat. Assoc., to appear, 2001) and the Significance Analysis of Microarray (SAM) method of Tusher et al. (PROC: Natl Acad. Sci. USA, 98, 5116-5121, 2001).     

Nonparametric identification of the minimum effective dose

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.     

Significance Levels of Randomization Trend Tests in the Event of Rare Occurrences

In the statistical evaluation of data from a dose-response experiment, it is frequently of interest to test for dose-related trend: an increasing trend in response with increasing dose. The randomization trend test, a generalization of Fisher's exact test, has been recommended for animal tumorigenicity testing when the numbers of tumor occurrences are small. This paper examines the type I error of the randomization trend test, and the Cochran-Armitage and Mantel-Haenszel tests. Simulation results show that when the tumor incidence rates are less than 10%, the randomization test is conservative; the test becomes very conservative when the incidence rate is less than 5%. The Cochran-Armitage and Mantel-Haenszel tests are slightly anti-conservative (liberal) when the incidence rates are larger than 3%. Further, we propose a less conservatived method of calculating the p-value of the randomization trend test by excluding some permutations whose probabilities of occurrence are greater than the probability of the the observed outcome.     

Gender governs the relationship between exercise intensity and growth hormone release in young adults.

We previously reported that in young adult males growth hormone (GH) release is related to exercise intensity in a linear dose-response manner (Pritzlaff et al. J Appl Physiol 87: 498-504, 1999). To investigate the effects of gender and exercise intensity on GH release, eight women (24.3 +/- 1.3 yr, 171 +/- 3.2 cm height, 63.6 +/- 8.7 kg weight) were each tested on six randomly ordered occasions [1 control condition (C), 5 exercise conditions (Ex)]. Serum GH concentrations were measured in samples obtained at 10-min intervals between 0700 and 0900 (baseline) and 0900 and 1300 (Ex + recovery or C). Integrated GH concentrations (IGHC) were calculated by trapezoidal reconstruction. During Ex, subjects exercised for 30 min (0900-0930) at one of the following intensities [normalized to the lactate threshold (LT)]: 25 and 75% of the difference between LT and rest, at LT, and at 25 and 75% of the difference between LT and peak O2 uptake. No differences were observed among conditions for baseline IGHC. To determine whether total (Ex + recovery) IGHC changed with increasing exercise intensity, slopes associated with individual linear regression models were subjected to a Wilcoxon signed-rank test. To test for gender differences, data in women were compared with the previously published data in men. A Wilcoxon ranked-sums two-tailed test was used to analyze the slopes and intercepts from the regression models. Total IGHC increased linearly with increasing exercise intensity. The slope and intercept values for the relationship between total IGHC and exercise intensity were greater in women than in men. Deconvolution analysis (0700-1300 h) revealed that, regardless of gender, increasing exercise intensity resulted in a linear increase in the mass of GH secreted per pulse and summed GH production rate, with no changes in GH secretory pulse frequency or apparent half-life of elimination. Exercise reduced the half-duration of GH secretory burst in men but not in women. Gender comparisons revealed that women had greater basal (nonpulsatile) GH secretion across all conditions, more frequent GH secretory pulses, a greater GH secretory pulse amplitude, a greater production rate, and a trend for a greater mass of GH secreted per pulse than men. We conclude that, in young adults, the GH secretory response to exercise is related to exercise intensity in a linear dose-response pattern. For each incremental increase in exercise intensity, the fractional stimulation of GH secretion is greater in women than in men.     

Testing superiority and non-inferiority hypotheses in active controlled clinical trials

Switching between testing for superiority and non-inferiority has been an important statistical issue in the design and analysis of active controlled clinical trial. In practice, it is often conducted with a two-stage testing procedure. It has been assumed that there is no type I error rate adjustment required when either switching to test for non-inferiority once the data fail to support the superiority claim or switching to test for superiority once the null hypothesis of non-inferiority is rejected with a pre-specified non-inferiority margin in a generalized historical control approach. However, when using a cross-trial comparison approach for non-inferiority testing, controlling the type I error rate sometimes becomes an issue with the conventional two-stage procedure. We propose to adopt a single-stage simultaneous testing concept as proposed by Ng (2003) to test both non-inferiority and superiority hypotheses simultaneously. The proposed procedure is based on Fieller's confidence interval procedure as proposed by Hauschke et al. (1999).