Modeling tumor onset and multiplicity using transition models with latent variables

We describe a method for modeling carcinogenicity from animal studies where the data consist of counts of the number of tumors present over time. The research is motivated by applications to transgenic rodent studies, which have emerged as an alternative to chronic bioassays for screening possible carcinogens. In transgenic mouse studies, the endpoint of interest is frequently skin papilloma, with weekly examinations determining how many papillomas each animal has at a particular point in time. It is assumed that each animal has two unobservable latent variables at each time point. The first indicates whether or not the tumors are in a multiplying state and the second is the potential number of additional tumors if the tumors are in a multiplying state. The product of these variables follows a zero-inflated Poisson distribution, and the EM algorithm can be used to maximize the observed-data pseudo-likelihood, based on the latent variables. A generalized estimating equations robust variance estimator adjusts for dependency among outcomes within individual animals. The method is applied to testing for a dose-related trend in both tumor incidence and multiplicity in carcinogenicity studies.     

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.     

Data Mining in the U.S. National Toxicology Program (NTP) Database Reveals a Potential Bias Regarding Liver Tumors in Rodents Irrespective of the Test Agent

Long-term studies in rodents are the benchmark method to assess carcinogenicity of single substances, mixtures, and multi-compounds. In such a study, mice and rats are exposed to a test agent at different dose levels for a period of two years and the incidence of neoplastic lesions is observed. However, this two-year study is also expensive, time-consuming, and burdensome to the experimental animals. Consequently, various alternatives have been proposed in the literature to assess carcinogenicity on basis of short-term studies. In this paper, we investigated if effects on the rodents’ liver weight in short-term studies can be exploited to predict the incidence of liver tumors in long-term studies. A set of 138 paired short- and long-term studies was compiled from the database of the U.S. National Toxicology Program (NTP), more precisely, from (long-term) two-year carcinogenicity studies and their preceding (short-term) dose finding studies. In this set, data mining methods revealed patterns that can predict the incidence of liver tumors with accuracies of over 80%. However, the results simultaneously indicated a potential bias regarding liver tumors in two-year NTP studies. The incidence of liver tumors does not only depend on the test agent but also on other confounding factors in the study design, e.g., species, sex, type of substance. We recommend considering this bias if the hazard or risk of a test agent is assessed on basis of a NTP carcinogenicity study.     

Age-adjusted exact trend tests in the event of rare occurrences

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.     

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.     

Incorporating observability thresholds of tumors into the two-stage carcinogenesis model

This paper discusses a general way of incorporating the growth kinetics of malignant tumors with the two-stage carcinogenesis model. The model is presented using time-homogeneous rate parameters. In that case, the differential equations comprising the model are straightforward to solve using standard numerical techniques and software. An extension of the method to time-dependent rate parameters is included in Appendix A. Allowing the rate parameters to be time-dependent does incur computational cost. An expression is given for the expected time without visible tumor, a generalization of the expected time to an observable tumor that includes the possibility of tumor regression. The model is illustrated using incidental liver tumor data in control rats from NTP rodent carcinogenicity studies, using linear birth-death kinetics of tumors combined with a non-absorbing detection limit. The approach is also shown to be potentially useful with tumor observability thresholds having more complicated features.     

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 the efficiency of age-adjusted tests in animal carcinogenicity experiments

Based on asymptotic relative efficiency calculations, Ryan (1985, Biometrics 41, 525-531) concludes that, in the analysis of animal carcinogenicity experiments, age-adjusted tests of tumor rates should be routinely preferred to simple proportions tests for both lethal and nonlethal tumors. We recalculate the asymptotic efficiencies of the simple proportions test relative to the log-rank test for the lethal tumor case. For a simplified model it is shown that the relative efficiency may be easily computed as a function of the crude tumor rate and the survival rate at the time of terminal sacrifice. More generally, we calculate by numerical quadrature the asymptotic relative efficiency for all models considered by Ryan and, using simulations, examine the relevance of asymptotic efficiencies to typical sample sizes. Contrary to the numerical results of Ryan, we find, for experiments with good survival and typical tumor rates, that the relative efficiencies are greater than 95%, usually about 99%. In the nonlethal tumor case, similar results follow from Ryan for tumor rates and survival rates typically encountered in practice. As it is often difficult to determine whether or not a tumor is lethal, we conclude for equal interim mortality rates, that the simple proportions test is usually adequate in evaluating animal carcinogenicity experiments.     

Semiparametric Bayes Multiple Testing: Applications to Tumor Data

Summary In National Toxicology Program (NTP) studies, investigators want to assess whether a test agent is carcinogenic overall and specific to certain tumor types, while estimating the dose‐response profiles. Because there are potentially correlations among the tumors, a joint inference is preferred to separate univariate analyses for each tumor type. In this regard, we propose a random effect logistic model with a matrix of coefficients representing log‐odds ratios for the adjacent dose groups for tumors at different sites. We propose appropriate nonparametric priors for these coefficients to characterize the correlations and to allow borrowing of information across different dose groups and tumor types. Global and local hypotheses can be easily evaluated by summarizing the output of a single Monte Carlo Markov chain (MCMC). Two multiple testing procedures are applied for testing local hypotheses based on the posterior probabilities of local alternatives. Simulation studies are conducted and an NTP tumor data set is analyzed illustrating the proposed approach.     

Trimmed Weighted Simes' Test for Two One‐Sided Hypotheses With Arbitrarily Correlated Test Statistics

The two‐sided Simes test is known to control the type I error rate with bivariate normal test statistics. For one‐sided hypotheses, control of the type I error rate requires that the correlation between the bivariate normal test statistics is non‐negative. In this article, we introduce a trimmed version of the one‐sided weighted Simes test for two hypotheses which rejects if (i) the one‐sided weighted Simes test rejects and (ii) both p‐values are below one minus the respective weighted Bonferroni adjusted level. We show that the trimmed version controls the type I error rate at nominal significance level α if (i) the common distribution of test statistics is point symmetric and (ii) the two‐sided weighted Simes test at level 2α controls the level. These assumptions apply, for instance, to bivariate normal test statistics with arbitrary correlation. In a simulation study, we compare the power of the trimmed weighted Simes test with the power of the weighted Bonferroni test and the untrimmed weighted Simes test. An additional result of this article ensures type I error rate control of the usual weighted Simes test under a weak version of the positive regression dependence condition for the case of two hypotheses. This condition is shown to apply to the two‐sided p‐values of one‐ or two‐sample t‐tests for bivariate normal endpoints with arbitrary correlation and to the corresponding one‐sided p‐values if the correlation is non‐negative. The Simes test for such types of bivariate t‐tests has not been considered before. According to our main result, the trimmed version of the weighted Simes test then also applies to the one‐sided bivariate t‐test with arbitrary correlation.     

Ankylosis of hock joints in group caged male B6C3F1 mice

Enlarged hock joints were observed during 1983 in B6C3F1 mice of chronic toxicity and carcinogenicity studies sponsored by the National Toxicology Program (NTP). Subsequently, approximately 9,500 B6C3F1 mice on 32 NTP chemical toxicity and carcinogenicity studies were evaluated for this condition by clinical examination. Group caged male B6C3F1 mice had thickening and reduced mobility of the hock joints at prevalences of 1.2% up to 6 months of age; 23% at 6 to 12 months of age; and 62% at 13 to 26 months of age. Group caged female B6C3F1 mice had a prevalence of 2% or less. Histologically, affected mice had periarticular exostoses on the bones of the hock joints, with formation of bony bridges around joints and deposition of new bone in joint spaces, resulting in partial or complete ankylosis. Individually caged male and female B6C3F1 mice were not affected. The cause of the ankylosis was not determined, but its occurrence in the NTP studies has been reduced by individual caging.     

Mechanistic considerations in small fish carcinogenicity testing

Historically, small fish species have proven useful both as environmental sentinels and as versatile test animals in toxicity and carcinogenicity bioassays. They can be bred in large numbers, have low maintenance and bioassay costs, and have a low background incidence of tumors. However, more mechanistic information is needed to help validate the information garnered from these models and to keep pace with other more fully developed animal models. This paper focuses on mechanistic considerations when using small fish models for carcinogenicity testing. Several small aquarium fish species have proven useful. The Japanese medaka is perhaps the best characterized small fish model for carcinogenicity testing; however, the zebrafish is emerging as an important model because it is well characterized genetically. Both route and methodology of exposure may affect the outcome of the study. Most studies have been conducted by introducing the test compound into the ambient water, but dietary exposures and embryo microinjection have also been used. Other considerations in study design include use of an initiating carcinogen, such as diethlynitrosamine, and differences in xenobiotic metabolism, such as the fact that fish CYP2B is refractory to phenobarbital induction. The small size of these models has perhaps limited some types of mechanistic studies, such as formation and repair of DNA adducts in response to carcinogen exposure. However, improved analytical methods are allowing greater resolution and should be applied to small fish species. Slide-based methods such as immunohistochemistry are an important adjunct to routine histopathology and should be included in study design. However, there is a need for development of more species-specific antibodies for fish research. There is also a need for more fish-specific data on cytokines, serum biochemistry, and oncogenes to strengthen the use of these important test models.     

Increased power of microarray analysis by use of an algorithm based on a multivariate procedure

MOTIVATION: The power of microarray analyses to detect differential gene expression strongly depends on the statistical and bioinformatical approaches used for data analysis. Moreover, the simultaneous testing of tens of thousands of genes for differential expression raises the 'multiple testing problem', increasing the probability of obtaining false positive test results. To achieve more reliable results, it is, therefore, necessary to apply adjustment procedures to restrict the family-wise type I error rate (FWE) or the false discovery rate. However, for the biologist the statistical power of such procedures often remains abstract, unless validated by an alternative experimental approach. RESULTS: In the present study, we discuss a multiplicity adjustment procedure applied to classical univariate as well as to recently proposed multivariate gene-expression scores. All procedures strictly control the FWE. We demonstrate that the use of multivariate scores leads to a more efficient identification of differentially expressed genes than the widely used MAS5 approach provided by the Affymetrix software tools (Affymetrix Microarray Suite 5 or GeneChip Operating Software). The practical importance of this finding is successfully validated using real time quantitative PCR and data from spike-in experiments. AVAILABILITY: The R-code of the statistical routines can be obtained from the corresponding author. CONTACT: Schuster@imise.uni-leipzig.de     

Classification according to chemical structure, mutagenicity to Salmonella and level of carcinogenicity of a further 42 chemicals tested for carcinogenicity by the U.S. National Toxicology Program

This paper is an extension and update of an earlier review published in this journal (Ashby and Tennant, 1988). A summary of the rodent carcinogenicity bioassay data on a further 42 chemicals tested by the U.S. National Toxicology Program (NTP) is presented. An evaluation of each chemical for structural alerts to DNA-reactivity is also provided, together with a summary of its mutagenicity to Salmonella. The 42 chemicals were numbered and evaluated as an extension of the earlier analysis of 222 NTP chemicals. The activity patterns and conclusions derived from the earlier study remain unchanged for the larger group of 264 chemicals. Based on the extended database of 264 NTP chemicals, the sensitivity of the Salmonella assay for rodent carcinogens is 58% and the specificity for the non-carcinogens is 73%. A total of 32 chemicals were defined as equivocal for carcinogenicity and, of these, 11 (34%) are mutagenic to Salmonella. An evaluation is made of instances where predictions of carcinogenicity, based on structural alerts, disagree with the Salmonella mutagenicity result (12% of the database). The majority of the disagreements are for structural alerts on non-mutagens, and that places these alerts as a sensitive primary screen with a specificity lower than that of the Salmonella assay. That analysis indicates some need for assays complementary to the Salmonella test when screening for potential genotoxic carcinogens. It also reveals that the correlation between structural alerts and mutagenicity to Salmonella is probably greater than 90%. Chemicals predicted to show Michael-type alkylating activity (i.e., CH2 = CHX; where X = an electron-withdrawing group, e.g. acrylamide) have been confirmed as a structural alert, and the halomethanes (624 are possible) have been classified as structurally-alerting. To this end an extended carcinogen-alert model structure is presented. Among the 138 NTP carcinogens now reviewed, 45 (33%) are non-mutagenic to Salmonella and possess a chemical structure that does not alert to DNA-reactivity. These carcinogens therefore either illustrate the need for complementary genetic screening tests to the Salmonella assay, or they represent the group of non-genotoxic carcinogens referred to most specifically by Weisburger and Williams (1981); the latter concept is favoured.     

Carcinogenicity test in B6C3F1 mice after parental and prenatal exposure to 50 Hz magnetic fields

Some epidemiological studies suggest association of childhood cancer with occupational exposure of the parents to magnetic fields. To test this relationship, 50 each of C57BL/6J female and C3H/HeJ male mice were exposed for 2 and 9 weeks, respectively, to 50 Hz sham (group A), 0.5 (group B), and 5 mT (group C) sinusoidal alternating magnetic fields. They were mated under the exposure for up to 2 weeks, and the exposure was continued until parturition. All the B6C3F1 offspring, without adjusting numbers of animals, were clinically observed without exposure to magnetic field for a nominal 78 weeks from 6-8 weeks of age after weaning and then euthanized for pathological examination according to a routine carcinogenicity test. 540 pups entered the test, and the survival rate was 96.7%. No F1 mouse died of tumoral diseases before a male in A group died of stomach cancer at 43 weeks of age. The first animal death in the exposed groups due to tumor occurred at 71 weeks of age. Eighteen animals died before necropsy at 84-86 weeks of age. No significant difference was detected in the final number of survivors and incidence of tumors between groups A and B, or A and C. Concerning reproduction total implants in group B were less than in group A and the difference was on the borderline of significance (P=.05). This difference was not reproduced in a later duplicate experiment.     

Standardized tumor rates for chronic bioassays

If crude experimental proportions of animals with tumors from chronic bioassays for carcinogenicity are used for low-dose extrapolation in a risk analysis, different dose-specific patterns of mortality due to competing risks can bias the results. In order to adjust tumor rates for differential mortality across dose groups, Farmer, Kodell, and Gaylor (1982, Risk Analysis 2, 27-34) recommended using nonparametric estimates of probability distributions of times to onset of tumors, with competing causes of death removed, when performing a risk analysis. This paper extends the approach of Farmer et al. by proposing a method for adjusting tumor rates to reflect lifetime or near-lifetime tumor incidences that would be obtained if all dose groups experienced the control mortality rate from causes other than the tumor of interest. Thus, natural mortality due to competing risks is explicitly included, rather than removed. The proposed standardized tumor rates are calculated as a summation of adjusted age-specific probabilities of dying with a tumor during the course of an animal bioassay for carcinogenicity plus the probability of being alive with a tumor at the terminal sacrifice.     

Correlations between 31P-NMR spectroscopy and tissue O2 tension measurements in a murine fibrosarcoma

Size-dependent changes in therapeutically relevant and interrelated metabolic parameters of a murine fibrosarcoma (FSaII) were investigated in vivo using conscious (unanesthetized) animals and tumor sizes less than or equal to 2% of body weight. Tumor pH and bioenergetics were evaluated by 31P nuclear magnetic resonance spectroscopy (31P-MRS), and tumor tissue oxygen tension (pO2) distribution was examined using O2-sensitive needle electrodes. During growth FSaII tumors showed a progressive loss of phosphocreatine (PCr) and nucleoside triphosphate (NTP) with increasing inorganic phosphate (Pi) and phosphomonoester (PME) signals. Ratios for PCr/Pi, PME/Pi, NTP/Pi, and phosphodiester/inorganic phosphate (PDE/Pi) as well as pH determined by 31P-NMR (pHNMR) and the mean tissue pO2 progressively declined as the tumors increased in size. The only relevant ratio increasing with tumor growth was PME/NTP. When the mean tissue pO2 value was plotted against pHNMR, NTP/Pi, PCr/Pi, PME/Pi, and PDE/Pi for tumor groups of similar mean volumes, a highly significant positive correlation was observed. There was a negative correlation between mean tumor tissue pO2 values and PME/NTP. From these results we concluded that 31P-MRS can detect changes in tumor bioenergetics brought about by changes in tumor oxygenation. Furthermore, the close correlation between oxygenation and energy status suggests that the microcirculation in FSaII tumors yields an O2-limited energy metabolism. Finally, a correlation between the proportion of pO2 readings between 0 and 2.5 mmHg and the radiobiologically hypoxic cell fraction in FSaII tumors was observed. The latter finding might be of particular importance for radiation therapy.     

Chemical structure, Salmonella mutagenicity and extent of carcinogenicity as indicators of genotoxic carcinogenesis among 222 chemicals tested in rodents by the U.S. NCI/NTP

A survey has been conducted of 222 chemicals evaluated for carcinogenicity in mice and rats by the United States NCI/NTP. The structure of each chemical has been assessed for potential electrophilic (DNA-reactive) sites, its mutagenicity to Salmonella recorded, and the level of its carcinogenicity to rodents tabulated. Correlations among these 3 parameters were then sought. A strong association exists among chemical structure (S/A), mutagenicity to Salmonella (Salm.) and the extent and sites of rodent tumorigenicity among the 222 compounds. Thus, a approximately 90% correlation exists between S/A and Salm. across the 115 carcinogens, the 24 equivocal carcinogens and the 83 non-carcinogens. This indicates the Salmonella assay to be a sensitive method of detecting intrinsic genotoxicity in a chemical. Concordance between S/A and Salm. have therefore been employed as an index of genotoxicity, and use of this index reveals two groups of carcinogens within the database, genotoxic and putatively non-genotoxic. These two broad groups are characterized by different overall carcinogenicity profiles. Thus, 16 tissues were subject to carcinogenesis only by genotoxins, chief among which were the stomach, Zymbal's glands, lung, subcutaneous tissue and circulatory system. Conclusions of carcinogenicity in these 16 tissues comprised 31% of the individual chemical/tissue reports of carcinogenicity. In contrast, both genotoxins and non-genotoxins were active in the remaining 13 tissues, chief among which was the mouse liver which accounted for 24% of all chemical/tissue reports of carcinogenicity. Further, the group of 70 carcinogens reported to be active in both species and/or in 2 or more tissues contained a higher proportion of Salmonella mutagens (70%) than observed for the group of 45 single-species/single-tissue carcinogens (39%). 30% of the 83 non-carcinogens were mutagenic to Salmonella. This confirms earlier observations that a significant proportion of in vitro genotoxins are non-carcinogenic, probably due to their non-absorption or preferential detoxification in vivo. Also, only 30% of the mouse liver-specific carcinogens were mutagenic to Salmonella. This is consistent with tumors being induced in this tissue (and to a lesser extent in other tissues of the mouse and rat) by mechanisms not dependent upon direct interaction of the test chemical with DNA. Detection of 103 of the 115 carcinogens could be achieved by use of only male rats and female mice.(ABSTRACT TRUNCATED AT 400 WORDS)     

Photoradiation therapy of cutaneous angiosarcomas in mice

Cutaneous angiosarcoma is a relatively rare but devastating malignant vascular tumor. It has a high incidence of recurrence following conventional therapeutic modalities applied either singly or in combination. The increased vascularity of cutaneous angiosarcomas, facilitating selective uptake and retention of a photosensitizing agent, such as hematoporphyrin derivative (HPD), suggests that these tumors would respond well to photoradiation therapy. To study the feasibility of this treatment modality, transplantable hemangiosarcomas were implanted in B6C3F1 female mice. Within 2.5 to 3.5 hours after intraperitoneal administration of HPD, fluorescence was recorded in the tumor as compared with surrounding normal skin. When these photosensitized tumors were exposed to 70 J/cm2 of laser energy from an argon-pumped dye laser at 630 nm, the tumors showed marked necrosis within 24 hours. In another series, the tumors were initially photosensitized with HPD for 3 hours and then treated with laser energy ranging from 0 to 96 J/cm2. A dual labeling procedure demonstrated a dose-related decrease in DNA synthesis rate in tumors that were exposed to 0 to 30 J/cm2 at 24 hours after treatment. Furthermore, tumor tissue exposed to laser energy in excess of 30 J/cm2 showed no significant cellular DNA synthesis. These data, supported by histologic evidence of tissue destruction, suggest that photoradiation therapy has a great potential as a therapeutic modality for cutaneous angiosarcomas.     

Testing for Treatment Effects on Subsets of Endpoints

Multiple endpoints are tested to assess an overall treatment effect and also to identify which endpoints or subsets of endpoints contributed to treatment differences. The conventional p‐value adjustment methods, such as single‐step, step‐up, or step‐down procedures, sequentially identify each significant individual endpoint. Closed test procedures can also detect individual endpoints that have effects via a step‐by‐step closed strategy. This paper proposes a global‐based statistic for testing an a priori number, say, r of the k endpoints, as opposed to the conventional approach of testing one (r = 1) endpoint. The proposed test statistic is an extension of the single‐step p‐value‐based statistic based on the distribution of the smallest p‐value. The test maintains strong control of the FamilyWise Error (FWE) rate under the null hypothesis of no difference in any (sub)set of r endpoints among all possible combinations of the k endpoints. After rejecting the null hypothesis, the individual endpoints in the sets that are rejected can be tested further, using a univariate test statistic in a second step, if desired. However, the second step test only weakly controls the FWE. The proposed method is illustrated by application to a psychosis data set.