Sharp simultaneous confidence intervals for the means of selected populations with application to microarray data analysis

Summary Simultaneous inference for a large number, N, of parameters is a challenge. In some situations, such as microarray experiments, researchers are only interested in making inference for the K parameters corresponding to the K most extreme estimates. Hence it seems important to construct simultaneous confidence intervals for these K parameters. The naïve simultaneous confidence intervals for the K means (applied directly without taking into account the selection) have low coverage probabilities. We take an empirical Bayes approach (or an approach based on the random effect model) to construct simultaneous confidence intervals with good coverage probabilities. For N= 10,000 and K= 100, typical for microarray data, our confidence intervals could be 77% shorter than the naïve K‐dimensional simultaneous intervals.     

Conditionally unbiased and near unbiased estimation of the selected treatment mean for multistage drop‐the‐losers trials

The two‐stage drop‐the‐loser design provides a framework for selecting the most promising of K experimental treatments in stage one, in order to test it against a control in a confirmatory analysis at stage two. The multistage drop‐the‐losers design is both a natural extension of the original two‐stage design, and a special case of the more general framework of Stallard & Friede ( 2008 ) (Stat. Med. 27 , 6209–6227). It may be a useful strategy if deselecting all but the best performing treatment after one interim analysis is thought to pose an unacceptable risk of dropping the truly best treatment. However, estimation has yet to be considered for this design. Building on the work of Cohen & Sackrowitz ( 1989 ) (Stat. Prob. Lett. 8 , 273–278), we derive unbiased and near‐unbiased estimates in the multistage setting. Complications caused by the multistage selection process are shown to hinder a simple identification of the multistage uniform minimum variance conditionally unbiased estimate (UMVCUE); two separate but related estimators are therefore proposed, each containing some of the UMVCUEs theoretical characteristics. For a specific example of a three‐stage drop‐the‐losers trial, we compare their performance against several alternative estimators in terms of bias, mean squared error, confidence interval width and coverage.     

Test‐compatible confidence intervals for adaptive two‐stage single‐arm designs with binary endpoint

Inference after two‐stage single‐arm designs with binary endpoint is challenging due to the nonunique ordering of the sampling space in multistage designs. We illustrate the problem of specifying test‐compatible confidence intervals for designs with nonconstant second‐stage sample size and present two approaches that guarantee confidence intervals consistent with the test decision. Firstly, we extend the well‐known Clopper–Pearson approach of inverting a family of two‐sided hypothesis tests from the group‐sequential case to designs with fully adaptive sample size. Test compatibility is achieved by using a sample space ordering that is derived from a test‐compatible estimator. The resulting confidence intervals tend to be conservative but assure the nominal coverage probability. In order to assess the possibility of further improving these confidence intervals, we pursue a direct optimization approach minimizing the mean width of the confidence intervals. While the latter approach produces more stable coverage probabilities, it is also slightly anti‐conservative and yields only negligible improvements in mean width. We conclude that the Clopper–Pearson‐type confidence intervals based on a test‐compatible estimator are the best choice if the nominal coverage probability is not to be undershot and compatibility of test decision and confidence interval is to be preserved.     

Estimating index of population trend by re-sampling techniques (jackknife and bootstrap) and its application to the life table study of rice leaf roller, Cnaphalocrocis medinalis (Lepidoptera: Pyralidae)

Taking a published natural population life table of rice leaf roller, Cnaphalocrocis medinalis (Lepidoptera: Pyralidae), as an example, we estimated the population trend index, I, via re‐sampling methods (jackknife and bootstrap), determined its statistical properties and illustrated the application of these methods in determining the control effectiveness of bio‐agents and chemical insecticides. Depending on the simulation outputs, the smoothed distribution pattern of the estimates of I by delete‐1 jackknife is visually distinguishable from the normal density, but the smoothed pattern produced by delete‐d jackknife, and logarithm‐transformed smoothed patterns produced by both empirical and parametric bootstraps, matched well the corresponding normal density. Thus, the estimates of I produced by delete‐1 jackknife were not used to determine the suppressive effect of wasps and insecticides. The 95% percent confidence intervals or the narrowest 95 percentiles and Z‐test criterion were employed to compare the effectiveness of Trichogramma japonicum Ashmead and insecticides (powder, 1.5% mevinphos + 3% alpha‐hexachloro cyclohexane) against the rice leaf roller based on the estimates of I produced by delete‐d jackknife and bootstrap techniques. At α= 0.05 level, there were statistical differences between wasp treatment and control, and between wasp and insecticide treatments, if the normality is ensured, or by the narrowest 95 percentiles. However, there is still no difference between insecticide treatment and control. By Z‐test criterion, wasp treatment is better than control and insecticide treatment with P‐value < 0.01. Insecticide treatment is similar to control with P‐value > 0.2 indicating that 95% confidence intervals procedure is more conservative. Although similar conclusions may be drawn by re‐sampling techniques, such as the delta method, about the suppressive effect of trichogramma and insecticides, the normality of the estimates can be checked and guaranteed, and the correlation among sequential life stages of rice leaf roller is also considered in the estimation. Judged by the P‐values from Z‐test, the delta method is more conservative.     

Asymptotical Tests on the Equivalence,Substantial Difference and Non‐inferiority Problems with Two Proportions

Let d = p₂ ? p₁ be the difference between two binomial proportions obtained from two independent trials. For parameter d, three pairs of hypothesis may be of interest: H₁: d ≤ δ vs. K₁: d > δ; H₂: d ? (δ₁, δ₂) vs. K₂: d ∈ (δ₁, δ₂); and H₃: d ∈ [δ₁, δ₂] vs. K₃: d ? [δ₁, δ₂], where H_i is the null hypothesis and K_i is the alternative hypothesis. These tests are useful in clinical trials, pharmacological and vaccine studies and in statistics generally. The three problems may be investigated by exact unconditional tests when the sample sizes are moderate. Otherwise, one should use approximate (or asymptotical) tests generally based on a Z‐statistics like those suggested in the paper. The article defines a new procedure for testing H₂ or H₃, demonstrates that this is more powerful than tests based on confidence intervals (the classic TOST – two one sided tests – test), defines two corrections for continuity which reduce the liberality of the three tests, and selects the one that behaves better. The programs for executing the unconditional exact and asymptotic tests described in the paper can be loaded at http://www.ugr.es/~bioest/software.htm. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Association of IFN‐γ polymorphisms with ankylosing spondylitis risk

The case‐control study was designed to investigate the genetic effects of interferon‐gamma (IFN‐γ) rs2069727 and rs1861494 polymorphisms on ankylosing spondylitis (AS) susceptibility in a Chinese Han population. Blood samples were collected from 108 AS patients and 110 healthy controls. IFN‐γ polymorphisms were genotyped by polymerase chain reaction‐restriction fragment length polymorphism (PCR‐RFLP). Hardy‐Weinberg equilibrium (HWE) test was performed in control group. Odds ratios (OR) with 95% confidence intervals (95% CI) were calculated using chi‐square test to evaluate the association between AS susceptibility and IFN‐γ polymorphisms, and the results were adjusted by logistic regressive analysis. The frequency of rs2069727 CC genotype was much higher in cases than that in controls, suggested its significant association with increased AS risk (adjusted OR = 5.899, 95% CI = 1.563‐22.261; P = .009). In addition, C allele also showed close association with increased risk of AS (adjusted OR = 2.052, 95% CI = 1.286‐1.704, P  = 0 .003). While the genotype and allele frequencies of IFN‐γ rs1861494 polymorphism were not significantly different between patients and controls (P  > 0.05 for all), IFN‐γ rs2069727 polymorphism is significantly associated with increased AS risk in a Chinese Han Population.     

ICAM‐1 and MKL‐1 polymorphisms impose considerable impacts on coronary heart disease occurrence

This study was aimed to explore the correlation of intercellular adhesion molecule‐1 (ICAM‐1) K469E and megakaryoblastic leukaemia factor‐1 (MKL‐1) ?184C/T polymorphisms with the susceptibility to coronary heart disease (CHD) in the Chinese Han population. 100 CHD patients and 91 healthy people that had no blood connection with each other were enrolled in this case‐control study. ICAM‐1 and MKL‐1 polymorphisms were genotyped by polymerase chain reaction‐restriction fragment length polymorphism (PCR‐RFLP) approach. Multiple logistic regression was used to analyse the correlation between polymorphisms of ICAM‐1 and MKL‐1 and CHD susceptibility. Differences of genotype and allele frequencies of the two SNPs between case and control groups were analysed by chi‐square test. Odds ratios (ORs) and 95% confidence intervals (CIs) were indicated relative susceptibility of CHD. The distributions of ICAM‐1 and MKL‐1 polymorphisms in each group conformed to Hardy‐Weinberg equilibrium (HWE). After adjusting for traditional risk factors, the TT genotype frequency of MKL‐1 ?184C/T polymorphism was found significantly higher in case group than in control group (P < .05). Meanwhile, T allele frequency increased in case group compared with control group, and the differences had statistical significance (P = .04, OR = 2.34, 95% CI = 1.34‐5.26). Logistic regression analysis in this study proved that smoking, hypertension, diabetes and triglyceride (TG) were all risk factors for CHD ICAM‐1 K469E polymorphism has no association with the onset of CHD. But MKL‐1 ?184C/T polymorphism is associated with the risk of CHD and T allele might be a susceptibility factor for CHD.     

TESTING FOR PHYLOGENETIC SIGNAL IN BIOLOGICAL TRAITS: THE UBIQUITY OF CROSS‐PRODUCT STATISTICS

To evaluate rates of evolution, to establish tests of correlation between two traits, or to investigate to what degree the phylogeny of a species assemblage is predictive of a trait value so‐called tests for phylogenetic signal are used. Being based on different approaches, these tests are generally thought to possess quite different statistical performances. In this article, we show that the Blomberg et al. K and K*, the Abouheif index, the Moran's I, and the Mantel correlation are all based on a cross‐product statistic, and are thus all related to each other when they are associated to a permutation test of phylogenetic signal. What changes is only the way phylogenetic and trait similarities (or dissimilarities) among the tips of a phylogeny are computed. The definitions of the phylogenetic and trait‐based (dis)similarities among tips thus determines the performance of the tests. We shortly discuss the biological and statistical consequences (in terms of power and type I error of the tests) of the observed relatedness among the statistics that allow tests for phylogenetic signal. Blomberg et al. K* statistic appears as one on the most efficient approaches to test for phylogenetic signal. When branch lengths are not available or not accurate, Abouheif's C_mean statistic is a powerful alternative to K*.     

Pooled analysis of clinical outcome for EGFR TKI‐treated patients with EGFR mutation‐positive NSCLC

Patients with non‐small‐cell lung cancer (NSCLC) appear to gain particular benefit from treatment with epidermal growth factor receptor (EGFR) tyrosine‐kinase inhibitors (TKI) if their disease tests positive for EGFR activating mutations. Recently, several large, controlled, phase III studies have been published in NSCLC patients with EGFR mutation‐positive tumours. Given the increased patient dataset now available, a comprehensive literature search for EGFR TKIs or chemotherapy in EGFR mutation‐positive NSCLC was undertaken to update the results of a previously published pooled analysis. Pooling eligible progression‐free survival (PFS) data from 27 erlotinib studies (n = 731), 54 gefitinib studies (n = 1802) and 20 chemotherapy studies (n = 984) provided median PFS values for each treatment. The pooled median PFS was: 12.4 months (95% accuracy intervals [AI] 11.6–13.4) for erlotinib‐treated patients; 9.4 months (95% AI 9.0–9.8) for gefitinib‐treated patients; and 5.6 months (95% AI 5.3–6.0) for chemotherapy. Both erlotinib and gefitinib resulted in significantly longer PFS than chemotherapy (permutation testing; P = 0.000 and P = 0.000, respectively). Data on more recent TKIs (afatinib, dacomitinib and icotinib) were insufficient at this time‐point to carry out a pooled PFS analysis on these compounds. The results of this updated pooled analysis suggest a substantial clear PFS benefit of treating patients with EGFR mutation‐positive NSCLC with erlotinib or gefitinib compared with chemotherapy.     

Effective antimicrobial activity of Cbf‐K16 and Cbf‐A7A13 against NDM‐1‐carrying Escherichia coli by DNA binding after penetrating the cytoplasmic membrane in vitro

New Delhi metallo‐beta‐lactamase‐1(NDM‐1)‐carrying isolates, which are resistant to most clinical used antibiotics except for tigecycline and colistin, have been found worldwide. Cathelicidin‐BF (BF‐30) is found in the venom of the snake Bungarus fasciatus and exhibits broad antimicrobial activity. Cbf‐K₁₆ and Cbf‐A₇A₁₃ were obtained by mutating Lys¹⁶, Ala⁷, and Ala¹³ of BF‐30, respectively. To investigate their antimicrobial activities against NDM‐1 carrying bacteria, recombinant Escherichia coli BL21 (DE3)‐NDM‐1 with high NDM‐1 activity was constructed by inserting the Klebsiella pneumoniae NDM‐1 gene (GenBank accession no. HQ328085) into a pET28a vector and transforming it into E. coli BL21 (DE3). The peptides showed effective antimicrobial activities against NDM‐1‐carrying E. coli, and the minimum inhibitory concentrations of Cbf‐K₁₆ and Cbf‐A₇A₁₃ were only 4 and 8 µg/ml, whereas those of minimum bactericidal concentrations were 8 and 16 µg/ml, respectively. A time course experiment showed that colony forming unit counts rapidly decreased, and bacteria were thoroughly eliminated within 3 and 6 h by the Cbf‐K₁₆ and Cbf‐A₇A₁₃ treatments, respectively. The peptides penetrated the bacterial cell membrane and enabled β‐galactosidase leakage, and caused the cytoplasmic membrane to become permeable, and finally bound to the DNA. The genomic DNA of E. coli was completely unable to migrate on an agarose gel after Cbf‐K₁₆ treatment (8 µg/ml). These data demonstrated that Cbf‐K₁₆ and Cbf‐A₇A₁₃ possess effective antimicrobial activity against drug‐resistant strains, including NDM‐1 carrying E. coli BL21 (DE3)‐NDM‐1, by binding to DNA after penetrating the cytoplasmic membrane in vitro, which may have potential therapeutic value for the treatment of NDM‐1‐carrying bacterial infections. Copyright © 2013 European Peptide Society and John Wiley & Sons, Ltd.     

Alternative Confidence Regions for Bonferroni‐Based Closed‐Testing Procedures that are not Alpha‐Exhaustive

This article complements the results in Guilbaud (Biometrical Journal 2008; 50 :678–692). Simultaneous confidence regions were derived in that article that correspond to any given multiple testing procedure (MTP) in a fairly large class of consonant closed‐testing procedures based on marginal p‐values and weighted Bonferroni tests for intersection hypotheses. This class includes Holm's MTP, the fixed‐sequence MTP, gatekeeping MTPs, fallback MTPs, multi‐stage fallback MTPs, and recently proposed MTPs specified through a graphical representation and associated rejection algorithm. More general confidence regions are proposed in this article. These regions are such that for certain underlying MTPs which are not alpha‐exhaustive, they lead to confidence assertions that may be sharper than rejection assertions for some rejected null hypotheses H when not all Hs are rejected, which is not the case with the previously proposed regions. In fact, various alternative confidence regions may be available for such an underlying MTP. These results are shown through an extension of the previous direct arguments (without invoking the partitioning principle), and under the same general setup; so for instance, estimated quantities and marginal confidence regions are not restricted to be of any particular kinds/dimensions. The relation with corresponding confidence regions of Strassburger and Bretz (Statistics in Medicine 2008; 27 :4914–4927) is described. The results are illustrated with fallback and parallel‐gatekeeping MTPs.     

lac‐1 and lag‐1 with ras‐1 affect aging and the biological clock in Neurospora crassa

Using an automated cell counting technique developed previously (Case et al., Ecology and Evolution 2014; 4: 3494), we explore the lifespan effects of lac‐1, a ceramide synthase gene paralogous to lag‐1 in Neurospora crassa in conjunction with the band bd (ras‐1) gene. We find that the replicative lifespan of a lac‐1^KO bd double mutants is short, about one race tube cycle, and this double mutant lacks a strong ~21‐hr clock cycle as shown by race tube and fluorometer analysis of fluorescent strains including lac‐1^KO. This short replicative lifespan phenotype is contrasted with a very long estimated chronological lifespan for lac‐1^KO bd double mutants from 247 to 462 days based on our regression analyses on log viability, and for the single mutant lac‐1^KO, 161 days. Both of these estimated lifespans are much higher than that of previously studied WT and bd single mutant strains. In a lac‐1 rescue and induction experiment, the expression of lac‐1⁺ as driven by a quinic acid‐dependent promoter actually decreases the median chronological lifespan of cells down to only 7 days, much lower than the 34‐day median lifespan found in control bd conidia also grown on quinic acid media, which we interpret as an effect of balancing selection acting on ceramide levels based on previous findings from the literature. Prior work has shown phytoceramides can act as a signal for apoptosis in stressed N. crassa cells. To test this hypothesis of balancing selection on phytoceramide levels, we examine the viability of WT, lag‐1^KO bd, and lac‐1^KO bd strains following the dual stresses of heat and glycolysis inhibition, along with phytoceramide treatments of different dosages. We find that the phytoceramide dosage–response curve is altered in the lag‐1^KO bd mutant, but not in the lac‐1^KO bd mutant. We conclude that phytoceramide production is responsible for the previously reported longevity effects in the lag‐1^KO bd mutant, but a different ceramide may be responsible for the longevity effect observed in the lac‐1^KO bd mutant.     

The Nonparametric Behrens‐Fisher Problem: Asymptotic Theory and a Small‐Sample Approximation

A generalization of the Behrens‐Fisher problem for two samples is examined in a nonparametric model. It is not assumed that the underlying distribution functions are continuous so that data with arbitrary ties can be handled. A rank test is considered where the asymptotic variance is estimated consistently by using the ranks over all observations as well as the ranks within each sample. The consistency of the estimator is derived in the appendix. For small samples (n₁, n₂ ≥ 10), a simple approximation by a central t‐distribution is suggested where the degrees of freedom are taken from the Satterthwaite‐Smith‐Welch approximation in the parametric Behrens‐Fisher problem. It is demonstrated by means of a simulation study that the Wilcoxon‐Mann‐Whitney‐test may be conservative or liberal depending on the ratio of the sample sizes and the variances of the underlying distribution functions. For the suggested approximation, however, it turns out that the nominal level is maintained rather accurately. The suggested nonparametric procedure is applied to a data set from a clinical trial. Moreover, a confidence interval for the nonparametric treatment effect is given.     

The role of plasma membrane H+‐ATPase in jasmonate‐induced ion fluxes and stomatal closure in Arabidopsis thaliana

Methyl jasmonate (MeJA) elicits stomatal closure in many plant species. Stomatal closure is accompanied by large ion fluxes across the plasma membrane (PM). Here, we recorded the transmembrane ion fluxes of H⁺, Ca²⁺ and K⁺ in guard cells of wild‐type (Col‐0) Arabidopsis, the CORONATINE INSENSITIVE1 (COI1) mutant coi1‐1 and the PM H⁺‐ATPase mutants aha1‐6 and aha1‐7, using a non‐invasive micro‐test technique. We showed that MeJA induced transmembrane H⁺ efflux, Ca²⁺ influx and K⁺ efflux across the PM of Col‐0 guard cells. However, this ion transport was abolished in coi1‐1 guard cells, suggesting that MeJA‐induced transmembrane ion flux requires COI1. Furthermore, the H⁺ efflux and Ca²⁺ influx in Col‐0 guard cells was impaired by vanadate pre‐treatment or PM H⁺‐ATPase mutation, suggesting that the rapid H⁺ efflux mediated by PM H⁺‐ATPases could function upstream of the Ca²⁺ flux. After the rapid H⁺ efflux, the Col‐0 guard cells had a longer oscillation period than before MeJA treatment, indicating that the activity of the PM H⁺‐ATPase was reduced. Finally, the elevation of cytosolic Ca²⁺ concentration and the depolarized PM drive the efflux of K⁺ from the cell, resulting in loss of turgor and closure of the stomata.     

Merosesquiterpenoids and Ten‐Membered Macrolides from a Soft Coral‐Derived Lophiostoma sp. Fungus

One new merosesquiterpenoid, craterellin D ( 1 ), along with one known analog, craterellin A ( 2 ), and five known ten‐membered macrolides, 3 – 7 , were isolated from a soft coral‐derived Lophiostoma sp. fungus. The absolute configuration of 1 was established based on biogenetic consideration with the co‐isolated analog 2 , whose configuration was determined by modified Mosher's method and single‐crystal X‐ray diffraction analysis using CuK_α radiation. The absolute configuration of 3 was determined by X‐ray diffraction analysis using CuK_α radiation. Compounds 2 and 3 showed antibacterial activities against Bacillus cereus with a MIC value of 3.12 μM .     

Effects of amyloid peptides on A‐type K+ currents of Drosophila larval cholinergic neurons

Accumulation of amyloid (Aβ) peptides has been suggested to be the primary event in Alzheimer's disease. In neurons, K⁺ channels regulate a number of processes, including setting the resting potential, keeping action potentials short, timing interspike intervals, synaptic plasticity, and cell death. In particular, A‐type K⁺ channels have been implicated in the onset of LTP in mammalian neurons, which is thought to underlie learning and memory. A number of studies have shown that Aβ peptides alter the properties of K⁺ currents in mammalian neurons. We set out to determine the effects of Aβ peptides on the neuronal A‐type K⁺ channels of Drosophila. Treatment of cells for 18 h with 1 μM Aβ1‐42 altered the kinetics of the A‐type K⁺ current, shifting steady‐state inactivation to more depolarized potentials and increasing the rate of recovery from inactivation. It also caused a decrease in neuronal viability. Thus it seems that alteration in the properties of the A‐type K⁺ current is a prelude to the amyloid‐induced death of neurons. This alteration in the properties of the A‐type K⁺ current may provide a basis for the early memory impairment that was observed prior to neurodegeneration in a recent study of a transgenic Drosophila melanogaster line over‐expressing the human Aβ1‐42 peptide. © 2006 Wiley Periodicals, Inc. J Neurobiol, 2006     

Bayesian model aggregation for ensemble‐based estimates of protein pKa values

This article investigates an ensemble‐based technique called Bayesian Model Averaging (BMA) to improve the performance of protein amino acid pK_a predictions. Structure‐based pK_a calculations play an important role in the mechanistic interpretation of protein structure and are also used to determine a wide range of protein properties. A diverse set of methods currently exist for pK_a prediction, ranging from empirical statistical models to ab initio quantum mechanical approaches. However, each of these methods are based on a set of conceptual assumptions that can effect a model's accuracy and generalizability for pK_a prediction in complicated biomolecular systems. We use BMA to combine eleven diverse prediction methods that each estimate pK_a values of amino acids in staphylococcal nuclease. These methods are based on work conducted for the pK_a Cooperative and the pK_a measurements are based on experimental work conducted by the García‐Moreno lab. Our cross‐validation study demonstrates that the aggregated estimate obtained from BMA outperforms all individual prediction methods with improvements ranging from 45 to 73% over other method classes. This study also compares BMA's predictive performance to other ensemble‐based techniques and demonstrates that BMA can outperform these approaches with improvements ranging from 27 to 60%. This work illustrates a new possible mechanism for improving the accuracy of pK_a prediction and lays the foundation for future work on aggregate models that balance computational cost with prediction accuracy. Proteins 2014; 82:354–363. © 2013 Wiley Periodicals, Inc.     

A simple covarion‐based approach to analyse nucleotide substitution rates

Using the ratio of nonsynonymous to synonymous nucleotide substitution rates (K_a/K_s) is a common approach for detecting positive selection. However, calculation of this ratio over a whole gene combines amino acid sites that may be under positive selection with those that are highly conserved. We introduce a new covarion‐based method to sample only the sites potentially under selective pressure. Using ancestral sequence reconstruction over a phylogenetic tree coupled with calculation of K_a/K_s ratios, positive selection is better detected by this simple covarion‐based approach than it is using a whole gene analysis or a windowing analysis. This is demonstrated on a synthetic dataset and is tested on primate leptin, which indicates a previously undetected round of positive selection in the branch leading to Gorilla gorilla.     

Permutation‐based inference for the AUC: A unified approach for continuous and discontinuous data

We investigate rank‐based studentized permutation methods for the nonparametric Behrens–Fisher problem, that is, inference methods for the area under the ROC curve. We hereby prove that the studentized permutation distribution of the Brunner‐Munzel rank statistic is asymptotically standard normal, even under the alternative. Thus, incidentally providing the hitherto missing theoretical foundation for the Neubert and Brunner studentized permutation test. In particular, we do not only show its consistency, but also that confidence intervals for the underlying treatment effects can be computed by inverting this permutation test. In addition, we derive permutation‐based range‐preserving confidence intervals. Extensive simulation studies show that the permutation‐based confidence intervals appear to maintain the preassigned coverage probability quite accurately (even for rather small sample sizes). For a convenient application of the proposed methods, a freely available software package for the statistical software R has been developed. A real data example illustrates the application.