Comparison of profile-likelihood-based confidence intervals with other rank-based methods for the two-sample problem in ordered categorical data.

For ordered categorical data from randomized clinical trials, the relative effect, the probability that observations in one group tend to be larger, has been considered appropriate for a measure of an effect size. Although the Wilcoxon-Mann-Whitney test is widely used to compare two groups, the null hypothesis is not just the relative effect of 50%, but the identical distribution between groups. The null hypothesis of the Brunner-Munzel test, another rank-based method used for arbitrary types of data, is just the relative effect of 50%. In this study, we compared actual type I error rates (or 1 - coverage probability) of the profile-likelihood-based confidence intervals for the relative effect and other rank-based methods in simulation studies at the relative effect of 50%. The profile-likelihood method, as with the Brunner- Munzel test, does not require any assumptions on distributions. Actual type I error rates of the profile-likelihood method and the Brunner-Munzel test were close to the nominal level in large or medium samples, even under unequal distributions. Those of the Wilcoxon-Mann-Whitney test largely differed from the nominal level under unequal distributions, especially under unequal sample sizes. In small samples, the actual type I error rates of Brunner-Munzel test were slightly larger than the nominal level and those of the profile-likelihood method were even larger. We provide a paradoxical numerical example: only the Wilcoxon-Mann-Whitney test was significant under equal sample sizes, but by changing only the allocation ratio, it was not significant but the profile-likelihood method and the Brunner-Munzel test were significant. This phenomenon might reflect the nature of the Wilcoxon-Mann-Whitney test in the simulation study, that is, the actual type I error rates become over and under the nominal level depending on the allocation ratio.

Group sequential methods for the Mann-Whitney parameter.

Late phase clinical trials are occasionally planned with one or more interim analyses to allow for early termination or adaptation of the study. While extensive theory has been developed for the analysis of ordered categorical data in terms of the Wilcoxon-Mann-Whitney test, there has been comparatively little discussion in the group sequential literature on how to provide repeated confidence intervals and simple power formulas to ease sample size determination. Dealing more broadly with the nonparametric Behrens-Fisher problem, we focus on the comparison of two parallel treatment arms and show that the Wilcoxon-Mann-Whitney test, the Brunner-Munzel test, as well as a test procedure based on the log win odds, a modification of the win ratio, asymptotically follow the canonical joint distribution. In addition to developing power formulas based on these results, simulations confirm the adequacy of the proposed methods for a range of scenarios. Lastly, we apply our methodology to the FREEDOMS clinical trial (ClinicalTrials.gov Identifier: NCT00289978) in patients with relapse-remitting multiple sclerosis.

Testing for equality of distributions using the concept of (niche) overlap.

In this paper, we propose a new non-parametric test for equality of distributions. The test is based on the recently introduced measure of (niche) overlap and its rank-based estimator. As the estimator makes only one basic assumption on the underlying distribution, namely continuity, the test is universal applicable in contrast to many tests that are restricted to only specific scenarios. By construction, the new test is capable of detecting differences in location and scale. It thus complements the large class of rank-based tests that are constructed based on the non-parametric relative effect. In simulations this new test procedure obtained higher power and lower type I error compared to two common tests in several settings. The new procedure shows overall good performance. Together with its simplicity, this test can be used broadly. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s00362-021-01239-y.

Ranking procedures for repeated measures designs with missing data: Estimation, testing and asymptotic theory.

We develop purely nonparametric methods for the analysis of repeated measures designs with missing values. Hypotheses are formulated in terms of purely nonparametric treatment effects. In particular, data can have different shapes even under the null hypothesis and therefore, a solution to the nonparametric Behrens-Fisher problem in repeated measures designs will be presented. Moreover, global testing and multiple contrast test procedures as well as simultaneous confidence intervals for the treatment effects of interest will be developed. All methods can be applied for the analysis of metric, discrete, ordinal, and even binary data in a unified way. Extensive simulation studies indicate a satisfactory control of the nominal type-I error rate, even for small sample sizes and a high amount of missing data (up to 30%). We apply the newly developed methodology to a real data set, demonstrating its application and interpretation.

Evidence-based urology: importance of relative vs absolute effect.

In order to effectively apply research evidence - in particular the results of clinical trials - to daily patient care, clinicians need to understand the magnitude of treatment benefits and harms, and the ways authors may express that magnitude. Authors may express outcomes using either relative or absolute measures, or both together. Relative measures make the magnitude of treatment effect appear much greater than absolute. Absolute effects are, however, more important to patients than relative effects. Here, using examples from the urological literature, we discuss the concepts of relative and absolute measures. PATIENT SUMMARY: When presenting the results of a trial, different ways of describing the same risk can influence the way patients and their doctors perceive the results. Reports can choose relative or absolute measures - or report both. Absolute measures are more informative in understanding the risk of an outcome patients face when not treated, and how treatment improves that risk.

Goldilocks Rounding: Achieving Balance Between Accuracy and Parsimony in the Reporting of Relative Effect Estimates.

Researchers often report a measure to several decimal places more than what is sensible or realistic. Rounding involves replacing a number with a value of lesser accuracy while minimizing the practical loss of validity. This practice is generally acceptable to simplify data presentation and to facilitate the communication and comparison of research results. Rounding also may reduce spurious accuracy when the extraneous digits are not justified by the exactness of the recording instrument or data collection procedure. However, substituting a more explicit or simpler representation for an original measure may not be practicable or acceptable if an adequate degree of accuracy is not retained. The error introduced by rounding exact numbers may result in misleading conclusions and the interpretation of study findings. For example, rounding the upper confidence interval for a relative effect estimate of 0.996 to 2 decimal places may obscure the statistical significance of the result. When presenting the findings of a study, authors need to be careful that they do not report numbers that contain too few significant digits. Equally important, they should avoid providing more significant figures than are warranted to convey the underlying meaning of the result.

On evidence cycles in network meta-analysis.

As an extension of pairwise meta-analysis of two treatments, network meta-analysis has recently attracted many researchers in evidence-based medicine because it simultaneously synthesizes both direct and indirect evidence from multiple treatments and thus facilitates better decision making. The Bayesian hierarchical model is a popular method to implement network meta-analysis, and it is generally considered more powerful than conventional pairwise meta-analysis, leading to more precise effect estimates with narrower credible intervals. However, the improvement of effect estimates produced by Bayesian network meta-analysis has never been studied theoretically. This article shows that such improvement depends highly on evidence cycles in the treatment network. When all treatment comparisons are assumed to have different heterogeneity variances, a network meta-analysis produces posterior distributions identical to separate pairwise meta-analyses for treatment comparisons that are not contained in any evidence cycles. However, this equivalence does not hold under the commonly-used assumption of a common heterogeneity variance for all comparisons. Simulations and a case study are used to illustrate the equivalence of the Bayesian network and pairwise meta-analyses in certain networks.

Concentration dependence of human and mouse aryl hydrocarbon receptor responsiveness to polychlorinated biphenyl exposures: Implications for aroclor mixtures.

1. Aryl hydrocarbon receptor (AhR) ligands, including 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) and polychlorinated biphenyls (PCBs), are endocrine disrupting chemicals associated with nonalcoholic fatty liver disease. This study documents the species-specific differences between mouse (high affinity mAhR) and human AhR (hAhR) activation by PCB congeners and Aroclor mixtures. 2. AhR activation by TCDD or PCBs 77, 81, 114, 114, 126, and 169 was measured using luciferase reporter constructs transfected into either Hepa1c1c7 mouse or HepG2 human liver cell lines. The EC50 values were lower in Hepa1c1c7 cells than HepG2 cells for all compounds tested except PCB 81. The results for TCDD and PCB 126 were validated in primary human and mouse hepatocytes by measuring CYP1A1 gene transcript levels. 3. Because humans are exposed to PCB mixtures, several mixtures (Aroclors 1254; 1260; and 1260 + 0.1% PCB126 each at 10 µg/ml) were then tested. Neither Aroclor 1254 nor Aroclor 1260 increased luciferase activity by the transfected AhR reporter construct. The Aroclor 1260 + 0.1% PCB 126 mixture induced mAhR-mediated transactivation, but not hAhR activation in cell lines. 4. In summary, significant concentration-dependent differences exist between human and mouse AhR activation by PCBs. Relative effect potencies differed, in some cases, from published toxic equivalency factors.

Optimal sample size planning for the Wilcoxon-Mann-Whitney test.

There are many different proposed procedures for sample size planning for the Wilcoxon-Mann-Whitney test at given type-I and type-II error rates α and ß, respectively. Most methods assume very specific models or types of data to simplify calculations (eg, ordered categorical or metric data, location shift alternatives, etc). We present a unified approach that covers metric data with and without ties, count data, ordered categorical data, and even dichotomous data. For that, we calculate the unknown theoretical quantities such as the variances under the null and relevant alternative hypothesis by considering the following "synthetic data" approach. We evaluate data whose empirical distribution functions match the theoretical distribution functions involved in the computations of the unknown theoretical quantities. Then, well-known relations for the ranks of the data are used for the calculations. In addition to computing the necessary sample size N for a fixed allocation proportion t = n1 /N, where n1 is the sample size in the first group and N = n1 + n2 is the total sample size, we provide an interval for the optimal allocation rate t, which minimizes the total sample size N. It turns out that, for certain distributions, a balanced design is optimal. We give a characterization of such distributions. Furthermore, we show that the optimal choice of t depends on the ratio of the two variances, which determine the variance of the Wilcoxon-Mann-Whitney statistic under the alternative. This is different from an optimal sample size allocation in case of the normal distribution model.

Evaluation of the phototoxicity of unsubstituted and alkylated polycyclic aromatic hydrocarbons to mysid shrimp (Americamysis bahia): Validation of predictive models.

Crude oils are composed of an assortment of hydrocarbons, some of which are polycyclic aromatic hydrocarbons (PAHs). Polycyclic aromatic hydrocarbons are of particular interest due to their narcotic and potential phototoxic effects. Several studies have examined the phototoxicity of individual PAHs and fresh and weathered crude oils, and several models have been developed to predict PAH toxicity. Fingerprint analyses of oils have shown that PAHs in crude oils are predominantly alkylated. However, current models for estimating PAH phototoxicity assume toxic equivalence between unsubstituted (i.e., parent) and alkyl-substituted compounds. This approach may be incorrect if substantial differences in toxic potency exist between unsubstituted and substituted PAHs. The objective of the present study was to examine the narcotic and photo-enhanced toxicity of commercially available unsubstituted and alkylated PAHs to mysid shrimp (Americamysis bahia). Data were used to validate predictive models of phototoxicity based on the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap approach and to develop relative effect potencies. Results demonstrated that photo-enhanced toxicity increased with increasing methylation and that phototoxic PAH potencies vary significantly among unsubstituted compounds. Overall, predictive models based on the HOMO-LUMO gap were relatively accurate in predicting phototoxicity for unsubstituted PAHs but are limited to qualitative assessments. Environ Toxicol Chem 2017;36:2043-2049. © 2017 SETAC.

Relative effect potency estimates of dioxin-like activity for dioxins, furans, and dioxin-like PCBs in adults based on cytochrome P450 1A1 and 1B1 gene expression in blood.

BACKGROUND: In the risk assessment of PCDDs, PCDFs, and dioxin-like (DL) PCBs, regulatory authorities support the use of the toxic equivalency factor (TEF)-scheme derived from a heterogeneous data set of the relative effect potency (REPs) estimates. OBJECTIVES: We sought to determine REPs for dioxin-like compounds (DLCs) using expression of cytochrome P450 (CYP) 1A1 and 1B1 mRNA in human peripheral blood mononuclear cells representing two different pathways. METHODS: We used a sex and age adjusted regression-based approach comparing the strength of association between each DLC and the cytochrome P450 (CYP) 1A1 and 1B1 mRNA expression in 320 adults residing in an organochlorine-polluted area of eastern Slovakia. RESULTS: We calculated REPs based on CYP1A1 expression for 4 PCDDs, 8 PCDFs, and 1 PCB congener, and based on CYP1B1 expression for 5 PCDFs and 11 PCB congeners. REPs from CYP1A1 correlated with REPs previously derived from thyroid volume (ρ=0.85; p<0.001) and serum FT4 (ρ=0.77; p=0.009). The 13 log REPs from CYP1A1 correlated with log WHO-TEFs (r=0.63; p=0.015) and 11 log PCB REPs with PCB consensus toxicity factors (CTFs) for compounds with WHO-TEFs (r=0.80; p=0.003). The complete set of derived 56 log REPs correlated with the log CTFs (r=0.77; p=0.001) and log WHO-TEFs (r=0.81; p<0.001). CONCLUSIONS: REPs calculated from thyroid and cytochrome P450 endpoints realistically reflect human exposure scenarios because they are based on human chronic and low-dose exposures. While the CYP 1A1 seems more suitable for toxicity evaluation of PCDD/Fs, the CYP 1B1 is more apt for PCDFs and PCBs and reflects different pathways.

The fingerprints of dioxin-like bromocarbazoles and chlorocarbazoles in selected forest soils in Germany.

The occurrence of bromocarbazoles and chlorocarbazoles was studied in 86 forest soil samples from different regions in Germany. Carbazole, 3-chlorocarbazole, 3-bromocarbazole and 3,6-dibromocarbazole were qualitatively detected in the humic layer of 59 soil samples with bromocarbazoles reported here for the first time in soil. Furthermore, the halogenated carbazoles, PCDD/Fs and PCBs were detected in the humic and mineral soil horizons (0-5 cm and 5-10 cm) of a subset of 11 soil samples subjected to quantitative analysis. Concentrations ranged from 0.6 to 267.6 ng/g (carbazole); 0.2-7.2 ng/g (3-bromocarbazole); 0.0-9.1 ng/g (3-chlorocarbazole); 0.2-19.8 ng/g (3,6-dibromocarbazole); 0.4-67.6 ng/g (3,6-dichlorocarbazole); 0.0-0.7 ng/g (PCDDs); 0.0-0.3 ng/g (PCDFs) and 0.0-33.7 ng/g (PCBs). Concentrations decreased with depth and correlated positively to total organic carbon (TOC). When it was based on TOC%, an increase in concentration with depth was observed in most soil samples. With respect to dioxin-like toxicity, 3-bromocarbazole, 3-chlorocarbazole, 3,6-dibromocarbazole and 3,6-dichlorocarbazoles caused induction of CYP1A1-dependent EROD activity in HII4E rat hepatoma cell line. Their relative effect potency after 72 h exposure ranged from 0.00005 to 0.00013 and was directly related to the degree of halogenation with 2,3,7,8-tetrachlorodibenzo-p-dioxin as reference. Furthermore, their contribution to overall soil dioxin-like toxicity was not significant in comparison to PCDD/Fs and PCBs though the sum toxic equivalency was limited to three halogenated carbazole congeners. Bromocarbazoles and chlorocarbazoles are emerging dioxin-like toxic environmental contaminants with potential for wide distribution occurring simultaneously with PCDD/Fs and PCBs.

Pure non-dioxin-like PCB congeners suppress induction of AhR-dependent endpoints in rat liver cells.

The relative potencies of non-ortho-substituted coplanar polychlorinated biphenyl (PCB) congeners to activate the aryl hydrocarbon receptor (AhR) and to cause the AhR-dependent toxic events are essential for their risk assessment. Since some studies suggested that abundant non-dioxin-like PCB congeners (NDL-PCBs) may alter the AhR activation by PCB mixtures and possibly cause non-additive effects, we evaluated potential suppressive effects of NDL-PCBs on AhR activation, using a series of 24 highly purified NDL-PCBs. We investigated their impact on the model AhR agonist-induced luciferase reporter gene expression in rat hepatoma cells and on induction of CYP1A1/1B1 mRNAs and deregulation of AhR-dependent cell proliferation in rat liver epithelial cells. PCBs 128, 138, and 170 significantly suppressed AhR activation (with IC50 values from 1.4 to 5.6 µM), followed by PCBs 28, 47, 52, and 180; additionally, PCBs 122, 153, and 168 showed low but still significant potency to reduce luciferase activity. Detection of CYP1A1 mRNA levels in liver epithelial cells largely confirmed these results for the most abundant NDL-PCBs, whereas the other AhR-dependent events (CYP1B1 mRNA expression, induction of cell proliferation in confluent cells) were less sensitive to NDL-PCBs, thus indicating a more complex regulation of these endpoints. The present data suggest that some NDL-PCBs could modulate overall dioxin-like effects in complex mixtures.

Inference for Surrogate Endpoint Validation in the Binary Case.

Surrogate endpoint validation for a binary surrogate endpoint and a binary true endpoint is investigated using the criteria of proportion explained (PE) and the relative effect (RE). The concepts of generalized confidence intervals and fiducial intervals are used for computing confidence intervals for PE and RE. The numerical results indicate that the proposed confidence intervals are satisfactory in terms of coverage probability, whereas the intervals based on Fieller's theorem and the delta method fall short in this regard. Our methodology can also be applied to interval estimation problems in a causal inference-based approach to surrogate endpoint validation.

Statistical Validation of Surrogate Endpoints: Another Look at the Prentice Criterion and Other Criteria.

For the statistical validation of surrogate endpoints, an alternative formulation is proposed for testing Prentice's fourth criterion, under a bivariate normal model. In such a setup, the criterion involves inference concerning an appropriate regression parameter, and the criterion holds if the regression parameter is zero. Testing such a null hypothesis has been criticized in the literature since it can only be used to reject a poor surrogate, and not to validate a good surrogate. In order to circumvent this, an equivalence hypothesis is formulated for the regression parameter, namely the hypothesis that the parameter is equivalent to zero. Such an equivalence hypothesis is formulated as an alternative hypothesis, so that the surrogate endpoint is statistically validated when the null hypothesis is rejected. Confidence intervals for the regression parameter and tests for the equivalence hypothesis are proposed using bootstrap methods and small sample asymptotics, and their performances are numerically evaluated and recommendations are made. The choice of the equivalence margin is a regulatory issue that needs to be addressed. The proposed equivalence testing formulation is also adopted for other parameters that have been proposed in the literature on surrogate endpoint validation, namely, the relative effect and proportion explained.

Conazole fungicides inhibit Leydig cell testosterone secretion and androgen receptor activation in vitro.

Conazole fungicides are widely used in agriculture despite their suspected endocrine disrupting properties. In this study, the potential (anti-)androgenic effects of ten conazoles were assessed and mutually compared with existing data. Effects of cyproconazole (CYPRO), fluconazole (FLUC), flusilazole (FLUS), hexaconazole (HEXA), myconazole (MYC), penconazole (PEN), prochloraz (PRO), tebuconazole (TEBU), triadimefon (TRIA), and triticonazole (TRIT) were examined using murine Leydig (MA-10) cells and human T47D-ARE cells stably transfected with an androgen responsive element and a firefly luciferase reporter gene. Six conazoles caused a decrease in basal testosterone (T) secretion by MA-10 cells varying from 61% up to 12% compared to vehicle-treated control. T secretion was concentration-dependently inhibited after exposure of MA-10 cells to several concentrations of FLUS (IC50 = 12.4 µM) or TEBU (IC50 = 2.4 µM) in combination with LH. The expression of steroidogenic and cholesterol biosynthesis genes was not changed by conazole exposure. Also, there were no changes in reactive oxygen species (ROS) formation that could explain the altered T secretion after exposure to conazoles. Nine conazoles decreased T-induced AR activation (IC50s ranging from 10.7 to 71.5 µM) and effect potencies (REPs) were calculated relative to the known AR antagonist flutamide (FLUT). FLUC had no effect on AR activation by T. FLUS was the most potent (REP = 3.61) and MYC the least potent (REP = 0.03) AR antagonist. All other conazoles had a comparable REP from 0.12 to 0.38. Our results show distinct in vitro anti-androgenic effects of several conazole fungicides arising from two mechanisms: inhibition of T secretion and AR antagonism, suggesting potential testicular toxic effects. These effects warrant further mechanistic investigation and clearly show the need for accurate exposure data in order to perform proper (human) risk assessment of this class of compounds.