Simultaneous inference of a binary composite endpoint and its components.

Binary composite endpoints offer some advantages as a way to succinctly combine evidence from a number of related binary endpoints recorded in the same clinical trial into a single outcome. However, as some concerns about the clinical relevance as well as the interpretation of such composite endpoints have been raised, it is recommended to evaluate the composite endpoint jointly with the involved components. We propose an approach for carrying out simultaneous inference based on separate model fits for each endpoint, yet controlling the familywise type I error rate asymptotically. The key idea is to stack parameter estimates from the different fits and derive their joint asymptotic distribution. Simulations show that the proposed approach comes closer to nominal levels and has comparable or higher power as compared to existing approaches, even for moderate sample sizes (around 100-200 observations). The method is compared to the gatekeeping approach and results are provided in the Supplementary Material. In two data examples we show how the procedure may be adapted to handle local significance levels specified through a priori given weights.

A critical appraisal of analyzing nasal provocation test results in allergen immunotherapy trials.

BACKGROUND: The statistical analysis of nasal provocation tests is very complex. We compared the conventional analysis with the maximally selected test statistics and the hierarchical ordered logistic model. METHODS: We re-analyzed data from a trial with 112 patients suffering from grass pollen allergy. The patients had been randomized to receive either intralymphatic immunotherapy (ILIT) or subcutaneous immunotherapy (SCIT). RESULTS: The conventional analysis indicated that the logarithmized ratio between the pre- and the post-treatment threshold concentration was significantly lower for ILIT than for SCIT. The maximally selected test statistics was used to test different threshold symptom scores that would imply positive clinical symptoms at the given allergen concentration. A threshold score of 3 maximised the difference in improvement between the ILIT and the SCIT groups. The hierarchical ordered logistic model does not take threshold allergen concentrations as the basis for analysis, but the single scores measured at each concentration. This approach simultaneously considers the treatment effect (ILIT versus SCIT), the time effect (pre- versus post-treatment), and the dose effect (different allergen concentrations). The hierarchical ordered logistic model revealed that the clinical improvement was greater after ILIT than after SCIT. CONCLUSION: As the choice of method can affect the outcome, guidelines for analysis are highly needed.

Simultaneous confidence intervals on multivariate non-inferiority.

We discuss the analysis of non-inferiority trials based on a multi-armed design with multiple correlated endpoints. We consider five different scenarios: (1) global non-inferiority; (2) non-inferiority for subsets of comparisons; (3) global non-inferiority for a treatment group; (4) global non-inferiority for an endpoint; and (5) local non-inferiority. We describe and compare related approaches, which are based on the union-intersection and intersection-union test principles - alone and in combination. Because non-inferiority thresholds for many differently scaled endpoints are rarely available in practice, the approaches described focus on the estimation of simultaneous confidence limits and their post hoc interpretation on non-inferiority. We discuss and demonstrate pros and cons by means of a real data example.

The psychiatric vulnerability gene CACNA1C and its sex-specific relationship with personality traits, resilience factors and depressive symptoms in the general population.

Genome-wide association studies have reported an association between the A-allele of rs1006737 within CACNA1C and affective disorders and schizophrenia. The aim of the present study was to investigate the relationship between rs1006737 and established and potential endophenotypes for these disorders in a population-based cohort of 3793 subjects, using an analytical method designed to assess a previously reported sex-specific effect of CACNA1C. The investigated endophenotypes included personality traits and resilience factors. At 10-year follow-up, subjects were screened for depressive symptoms. All subjects were genotyped for rs1006737. The direction of the effect and mode of inheritance of rs1006737 differed between the sexes. In men, the A-allele was associated with higher emotional lability and lower resilience, that is, lower sense of coherence (P=0.021), lower perceived social support (P=0.018), lower dispositional optimism (P=0.032) and more depressive symptoms at follow-up (P=0.007). In women, the A-allele was associated with lower emotional lability and stronger resilience, that is, higher sense of coherence (P=0.00028), higher perceived social support (P=0.010), lower neuroticism (P=0.022) and fewer depressive symptoms at follow-up (P=0.035). After conservative Bonferroni correction for 32 tests, results only remained significant for sense of coherence in women (P=0.009). These results suggest that CACNA1C is involved in the genetic architecture of endophenotypes for affective disorders and schizophrenia, and that it shows a distinct sex-specific effect. Comprehensive phenotype characterization in case-control samples and the general population, as well as an adequate modeling of sex-specific genetic effects, may be warranted to elucidate the pathogenetic mechanisms conferred by robustly identified susceptibility genes.

Analytical method transfer: improving interpretability with ratio-based statistical approaches.

After assay validation in an originating laboratory, an analytical method needs to be transferred to one or several production laboratories, because measured outcomes among the laboratories must agree. To state agreement, the locations (e.g. means) must be equivalent and the production laboratory must be non-inferior to the originating one concerning scales (e.g. standard deviations). Here, parametric and non-parametric approaches based on marginal confidence intervals for the ratio of locations and the ratio of scales are presented. These intervals are appropriate for a matched pairs design without repeated measurements. Results of simulation studies investigating the power and the control of the type I error are shown and limits of the approaches are discussed. In addition, a Bland-Altman plot with tolerance intervals is proposed. As illustrated in the example proportional differences greatly improve the interpretation of the results compared to absolute differences.

An alternative to animal testing in the quality control of erythropoietin.

A physico-chemical method has been developed as an alternative to the current bioassay in normocythaemic mice for estimating the biological activity of erythropoietin batches. Capillary zone electrophoresis was used for quantification of the isoforms and their substructures were further elucidated by N-glycan mapping techniques. The analytical study was carried out on a total of 40 batches of epoetin beta which were selected to cover an adequate range of precisely established potency values. The relationship between the biological and chemical parameters was evaluated statistically in order to identify suitable covariates for the prediction of the biological activity. Out of several alternatives, a prediction model which is based on the percentages of isoforms per batch and the degree of sialidation was selected and tested. This model is comparable in terms of accuracy to the established in vivo bioassay, but is far superior in terms of precision. Further advantages of the method are improved animal welfare and savings in time and effort. The question whether the prediction model already meets the requirements for replacing the bioassay according to the ICH guideline Q6B is discussed.

Parametric and non-parametric prediction intervals based phase II control charts for repeated bioassay data.

Quality control for repeated bioassay runs can be performed by phase II control charts, well-known from industrial quality control. The value of interest is the potency, of which a single value per run is available. Parametric and non-parametric prediction intervals are described to estimate quality control intervals for future re-test runs. Violations against the normal distribution occur in real data frequently, particularly outliers. The non-parametric prediction intervals are limited to not too small sample sizes in both the historical and future sampling phases. Therefore, robust prediction intervals based on winsorization are proposed. R-functions for all prediction intervals are provided.

Joint one-sided and two-sided simultaneous confidence intervals.

For the analysis of multiarmed clinical trials often a set consisting of a mixture of one- and two-sided tests can be preferred over a set of common two-sided hypotheses settings. Here we show the straightforward application of existing multiple comparison procedures for the difference and ratio of normally distributed means to complex trial designs, involving one and two test directions. The proposed contrast tests provide a more flexible framework than the existing methods at nearly similar power. An application is illustrated for an example with multiple treatment doses and two active controls; statistical software codes are included for R and SAS System.

Effects of cultivation of genetically modified Bt maize on epigeic arthropods (Araneae; Carabidae).

A field study was conducted in Germany to determine the possible effects of transgenic maize cultivation on nontarget epigeic predator organisms. During the growing period of 2001-2003, the activity abundances of spiders and carabid beetles were recorded and compared in three treatments: (1) Bt-maize (Mon 810) expressing the Cry1ab protein from Bacillus thuringiensis (Berliner), (2) an isogenic variety, and (3) the isogenic variety treated with insecticide. All three treatments were replicated in eight plots. The results were evaluated using three different methods. The activity abundances of single species were statistically analyzed by confidence interval methods. In addition, the phenological behaviors of the spider and carabid beetle species were determined, and multivariate statistical evaluation of the community by principal component analysis was conducted. Significantly different activity abundances in Bt plots compared with isogenic control plots were observed both for spiders and carabid beetles during 2001. However, in 2002 and 2003, no changes in community structure were detectable in any of the treatments. The change in the first year may have been caused by the influence of a massive cornborer infestation and accompanying large changes in microclimatic factors.

How to deal with multiple treatment or dose groups in randomized clinical trials?

Multiplicity adjustment in general is currently a controversial topic. This review focuses on the proof of efficacy in randomized clinical trials. The ICH guidelines mandate control of the familywise error rate. Confidence intervals are clinically more appropriate than P-values or yes/no decisions. Therefore, simultaneous confidence intervals are proposed for several designs and aims in clinical trials. The computation of simultaneous confidence intervals for the difference or the ratio is demonstrated by means of real data examples using the R-packages multcomp and mratios. A special problem is the evaluation of dose-finding trials with and without the assumption that the effects increase with increasing doses. Simultaneous intervals are presented not only for one-way layouts and normal distributed endpoints, but also for higher way layouts, generalized linear models, and mixed models. Under importance ordering, the conditional testing of all hypotheses at level alpha will be shown using the intersection-union test principle. Other multiplicity issues (i.e. multiple endpoints, multiple analyses, and subgroup analyses) are discussed.

Simultaneous confidence intervals for ratios with applications to the comparison of several treatments with a control.

OBJECTIVES: In this article, we illustrate and compare exact simultaneous confidence sets with various approximate simultaneous confidence intervals for multiple ratios as applied to many-to-one comparisons. Quite different datasets are analyzed to clarify the points. METHODS: The methods are based on existing probability inequalities (e.g., Bonferroni, Slepian and Sidak), estimation of nuisance parameters and re-sampling techniques. Exact simultaneous confidence sets based on the multivariate t-distribution are constructed and compared with approximate simultaneous confidence intervals. RESULTS: It is found that the coverage probabilities associated with the various methods of constructing simultaneous confidence intervals (for ratios) in manyto-one comparisons depend on the ratios of the coefficient of variation for the mean of the control group to the coefficient of variation for the mean of the treatments. If the ratios of the coefficients of variations are less than one, the Bonferroni corrected Fieller confidence intervals have almost the same coverage probability as the exact simultaneous confidence sets. Otherwise, the use of Bonferroni intervals leads to conservative results. CONCLUSIONS: When the ratio of the coefficient of variation for the mean of the control group to the coefficient of variation for the mean of the treatments are greater than one (e.g., in balanced designs with increasing effects), the Bonferroni simultaneous confidence intervals are too conservative. Therefore, we recommend not using Bonferroni for this kind of data. On the other hand, the plug-in method maintains the intended confidence coefficient quite satisfactorily; therefore, it can serve as the best alternative in any case.

Testing dose-response relationships with a priori unknown, possibly nonmonotone shapes.

Usually, a monotone dose-response dependence can be assumed for the simultaneous comparison of increasing levels of a certain drug. However, sometimes a reversal of the dose-response curve is likely to occur at the higher doses. We investigate such violations of the monotonicity assumption. Adequate alternatives are discussed and the "protected trend alternative" is introduced. Together with the umbrella patterns described in the literature, we introduce new testing approaches for both alternatives. P-values/quantiles and power values/sample sizes are made numerically available and hence are readily computed. A short power study and the analysis of a data set from the literature demonstrate the improved behavior of the new methods.

Identifying the maximum safe dose: a multiple testing approach.

Identifying the maximum safe dose (MAXSD) is an objective of both randomized clinical dose-finding studies for the safety endpoint and toxicological studies. MAXSD is defined as the highest experimental dose with no significant increased safety effect relative to the placebo or control group. In safety assessment, the primary control of the false-negative error rate is more important than that of the false-positive rate. Therefore, we propose a multiple testing procedure for equivalence in the many-to-one design with a priori ordered contrasts (shifted control vs. dose), where the acceptable risk delta is defined in advance. Tests for shifted and ratio hypotheses are presented and discussed.

Report and summary of the major conclusions from statistics in genotoxicity testing working group from the International Workshop on Genotoxicity Test Procedures (IWGTP), March 1999.

A working group of five statisticians experienced in the use of statistical methods in mutagenicity reviewed aspects of the statistical analysis of genotoxicity test procedures. Issues discussed included methods for integrating biological importance and statistical significance, the relationship of the experimental unit to the experimental design, and the impact of new developments in statistics and computing. Three major recommendations were made relating to the need for: (1) the effective use of statistical advice in designing interlaboratory and intralaboratory investigations; (2) the development of appropriate experimental designs for new assays; and (3) education and training in the use of statistical methodology in mutagenicity testing. Environ. Mol. Mutagen. 35:260-263, 2000 Published 2000 Wiley-Liss, Inc.

Lifelong administration of high doses of ibandronate increases bone mass and maintains bone quality of lumbar vertebrae in rats.

As part of a long-term safety study the bisphosphonate ibandronate was investigated for its effects on bone quality in lumbar vertebrae in rats. Bone area, bone density and mechanical properties were assessed by peripheral quantitative computed tomography (pQCT), dual-energy X-ray absorptiometry (DXA) and compression tests. Female and male groups of Wistar rats received either vehicle or 3, 7 or 15 mg/kg per day of ibandronate over 104 weeks orally by gavage. Compared with the control group, bone mineral density, compressive strength and stiffness were significantly higher in ibandronate-treated animals, whereas no changes occurred in strain or modulus of elasticity. The increase in vertebral body stress was significant in some of the ibandronate-treated groups. The changes in mechanical properties appear to be due mainly to an increase in bone mass. A highly significant correlation was found between bone mineral density measured either by DXA (r = 0.86) or pQCT (r = 0.85) and maximal strength in vertebral bodies (p < 0.0001 each). In conclusion, we demonstrated that lifelong administration of doses of ibandronate far in excess of any therapeutically intended dose not only increases bone mass and apparent density, but also maintains or even slightly improves bone quality. Bone mineral density measured either by pQCT or DXA can be used as a predictor for ultimate strength in rat lumbar vertebral bodies after treatment with ibandronate.