Simultaneous Inference Using Multiple Marginal Models.

This tutorial describes single-step low-dimensional simultaneous inference with a focus on the availability of adjusted p values and compatible confidence intervals for more than just the usual mean value comparisons. The basic idea is, first, to use the influence of correlation on the quantile of the multivariate t-distribution: the higher the less conservative. In addition, second, the estimability of the correlation matrix using the multiple marginal models approach (mmm) using multiple models in the class of linear up to generalized linear mixed models. The underlying maxT-test using mmm is discussed by means of several real data scenarios using selected R packages. Surprisingly, different features are highlighted, among them: (i) analyzing different-scaled, correlated, multiple endpoints, (ii) analyzing multiple correlated binary endpoints, (iii) modeling dose as qualitative factor and/or quantitative covariate, (iv) joint consideration of several tuning parameters within the poly-k trend test, (v) joint testing of dose and time, (vi) considering several effect sizes, (vii) joint testing of subgroups and overall population in multiarm randomized clinical trials with correlated primary endpoints, (viii) multiple linear mixed effect models, (ix) generalized estimating equations, and (x) nonlinear regression models.

HSL1 and BAM1/2 impact epidermal cell development by sensing distinct signaling peptides.

The membrane receptor kinases HAESA and HSL2 recognize a family of IDA/IDL signaling peptides to control cell separation processes in different plant organs. The homologous HSL1 has been reported to regulate epidermal cell patterning by interacting with a different class of signaling peptides from the CLE family. Here we demonstrate that HSL1 binds IDA/IDL peptides with high, and CLE peptides with lower affinity, respectively. Ligand sensing capability and receptor activation of HSL1 require a SERK co-receptor kinase. Crystal structures with IDA/IDLs or with CLE9 reveal that HSL1-SERK1 complex recognizes the entire IDA/IDL signaling peptide, while only parts of CLE9 are bound to the receptor. In contrast, the receptor kinase BAM1 interacts with the entire CLE9 peptide with high affinity and specificity. Furthermore, the receptor tandem BAM1/BAM2 regulates epidermal cell division homeostasis. Consequently, HSL1-IDLs and BAM1/BAM2-CLEs independently regulate cell patterning in the leaf epidermal tissue.

The Tukey trend test: Multiplicity adjustment using multiple marginal models.

In dose-response analysis, it is a challenge to choose appropriate linear or curvilinear shapes when considering multiple, differently scaled endpoints. It has been proposed to fit several marginal regression models that try sets of different transformations of the dose levels as explanatory variables for each endpoint. However, the multiple testing problem underlying this approach, involving correlated parameter estimates for the dose effect between and within endpoints, could only be adjusted heuristically. An asymptotic correction for multiple testing can be derived from the score functions of the marginal regression models. Based on a multivariate t-distribution, the correction provides a one-step adjustment of p-values that accounts for the correlation between estimates from different marginal models. The advantages of the proposed methodology are demonstrated through three example datasets, involving generalized linear models with differently scaled endpoints, differing covariates, and a mixed effect model and through simulation results. The methodology is implemented in an R package.

Using historical control data in bioassays for regulatory toxicology.

Historical control data (HCD) consist of pooled control group responses from bioassays. These data must be collected and are often used or reported in regulatory toxicology studies for multiple purposes: as quality assurance for the test system, to help identify toxicological effects and their effect-size relevance and to address the statistical multiple comparison problem. The current manuscript reviews the various classical and potential new approaches for using HCD. Issues in current practice are identified and recommendations for improved use and discussion are provided. Furthermore, stakeholders are invited to discuss whether it is necessary to consider uncertainty when using HCD formally and statistically in toxicological discussions and whether binary inclusion/exclusion criteria for HCD should be revised to a tiered information contribution to assessments. Overall, the critical value of HCD in toxicological bioassays is highlighted when used in a weight-of-evidence assessment.

Inositol pyrophosphates promote the interaction of SPX domains with the coiled-coil motif of PHR transcription factors to regulate plant phosphate homeostasis.

Phosphorus is an essential nutrient taken up by organisms in the form of inorganic phosphate (Pi). Eukaryotes have evolved sophisticated Pi sensing and signaling cascades, enabling them to stably maintain cellular Pi concentrations. Pi homeostasis is regulated by inositol pyrophosphate signaling molecules (PP-InsPs), which are sensed by SPX domain-containing proteins. In plants, PP-InsP-bound SPX receptors inactivate Myb coiled-coil (MYB-CC) Pi starvation response transcription factors (PHRs) by an unknown mechanism. Here we report that a InsP8-SPX complex targets the plant-unique CC domain of PHRs. Crystal structures of the CC domain reveal an unusual four-stranded anti-parallel arrangement. Interface mutations in the CC domain yield monomeric PHR1, which is no longer able to bind DNA with high affinity. Mutation of conserved basic residues located at the surface of the CC domain disrupt interaction with the SPX receptor in vitro and in planta, resulting in constitutive Pi starvation responses. Together, our findings suggest that InsP8 regulates plant Pi homeostasis by controlling the oligomeric state and hence the promoter binding capability of PHRs via their SPX receptors.

Use compatibility intervals in regulatory toxicology.

Recently it was recommended to avoid significance tests, in particular dichotomization into significant/non-significant on the basis of a p-value and a fixed 5% significance level (i.e. false positive rate). As an alternative, the interpretation of a suitable effect size and its compatibility interval is recommended, i.e. confidence intervals whose compatibility with the data, the assumptions, and the models is shown. This concept is used for the evaluation of assays in regulatory toxicology with special emphasis on the proof of hazard and proof of safety. Three case studies for multiple endpoints, multiple models and the consideration of historical controls illustrate the applicability of this concept. The corresponding software code for the open-source R project for statistical computing (www.r-project.org) is provided.

Alternatives to statistical decision trees in regulatory (eco-)toxicological bioassays.

The goal of (eco-) toxicological testing is to experimentally establish a dose or concentration-response and to identify a threshold with a biologically relevant and probably non-random deviation from "normal". Statistical tests aid this process. Most statistical tests have distributional assumptions that need to be satisfied for reliable performance. Therefore, most statistical analyses used in (eco-)toxicological bioassays use subsequent pre- or assumption-tests to identify the most appropriate main test, so-called statistical decision trees. There are however several deficiencies with the approach, based on study design, type of tests used and subsequent statistical testing in general. When multiple comparisons are used to identify a non-random change against negative control, we propose to use robust testing, which can be generically applied without the need of decision trees. Visualization techniques and reference ranges also offer advantages over the current pre-testing approaches. We aim to promulgate the concepts in the (eco-) toxicological community and initiate a discussion for regulatory acceptance.

Two bifunctional inositol pyrophosphate kinases/phosphatases control plant phosphate homeostasis.

Many eukaryotic proteins regulating phosphate (Pi) homeostasis contain SPX domains that are receptors for inositol pyrophosphates (PP-InsP), suggesting that PP-InsPs may regulate Pi homeostasis. Here we report that deletion of two diphosphoinositol pentakisphosphate kinases VIH1/2 impairs plant growth and leads to constitutive Pi starvation responses. Deletion of phosphate starvation response transcription factors partially rescues vih1 vih2 mutant phenotypes, placing diphosphoinositol pentakisphosphate kinases in plant Pi signal transduction cascades. VIH1/2 are bifunctional enzymes able to generate and break-down PP-InsPs. Mutations in the kinase active site lead to increased Pi levels and constitutive Pi starvation responses. ATP levels change significantly in different Pi growth conditions. ATP-Mg2+ concentrations shift the relative kinase and phosphatase activities of diphosphoinositol pentakisphosphate kinases in vitro. Pi inhibits the phosphatase activity of the enzyme. Thus, VIH1 and VIH2 relay changes in cellular ATP and Pi concentrations to changes in PP-InsP levels, allowing plants to maintain sufficient Pi levels.

Concerted expression of a cell cycle regulator and a metabolic enzyme from a bicistronic transcript in plants.

Eukaryotic mRNAs frequently contain upstream open reading frames (uORFs), encoding small peptides that may control translation of the main ORF (mORF). Here, we report the characterization of a distinct bicistronic transcript in Arabidopsis. We analysed loss-of-function phenotypes of the inorganic polyphosphatase TRIPHOSPHATE TUNNEL METALLOENZYME 3 (AtTTM3), and found that catalytically inactive versions of the enzyme could fully complement embryo and growth-related phenotypes. We could rationalize these puzzling findings by characterizing a uORF in the AtTTM3 locus encoding CELL DIVISION CYCLE PROTEIN 26 (CDC26), an orthologue of the cell cycle regulator. We demonstrate that AtCDC26 is part of the plant anaphase promoting complex/cyclosome (APC/C), regulates accumulation of APC/C target proteins and controls cell division, growth and embryo development. AtCDC26 and AtTTM3 are translated from a single transcript conserved across the plant lineage. While there is no apparent biochemical connection between the two gene products, AtTTM3 coordinates AtCDC26 translation by recruiting the transcript into polysomes. Our work highlights that uORFs may encode functional proteins in plant genomes.

Publisher Correction: The SERK3 elongated allele defines a role for BIR ectodomains in brassinosteroid signalling.

In the version of this Letter originally published, there were errors in the x axis labels of Figs 1, 2 and 4: in Fig. 1b, the label Col-0 should not have been included on the axis; in Fig. 2b BIR should have read BIR2, and DN221 should have read D122N; in Fig. 4f, pSEK3 should have read pSERK3. These figures have now been amended in all versions of the Letter.

The SERK3 elongated allele defines a role for BIR ectodomains in brassinosteroid signalling.

The leucine-rich repeat receptor kinase (LRR-RK) BRASSINOSTEROID INSENSITIVE 1 (BRI1) requires a shape-complementary SOMATIC EMBRYOGENESIS RECEPTOR KINASE (SERK) co-receptor for brassinosteroid sensing and receptor activation1. Interface mutations that weaken the interaction between receptor and co-receptor in vitro reduce brassinosteroid signalling responses2. The SERK3 elongated (elg) allele3-5 maps to the complex interface and shows enhanced brassinosteroid signalling, but surprisingly no tighter binding to the BRI1 ectodomain in vitro. Here, we report that rather than promoting the interaction with BRI1, the elg mutation disrupts the ability of the co-receptor to interact with the ectodomains of BRI1-ASSOCIATED-KINASE1 INTERACTING KINASE (BIR) receptor pseudokinases, negative regulators of LRR-RK signalling6. A conserved lateral surface patch in BIR LRR domains is required for targeting SERK co-receptors and the elg allele maps to the core of the complex interface in a 1.25 Å BIR3-SERK1 structure. Collectively, our structural, quantitative biochemical and genetic analyses suggest that brassinosteroid signalling complex formation is negatively regulated by BIR receptor ectodomains.

Mechanistic basis for the activation of plant membrane receptor kinases by SERK-family coreceptors.

Plant-unique membrane receptor kinases with leucine-rich repeat ectodomains (LRR-RKs) can sense small molecule, peptide, and protein ligands. Many LRR-RKs require SERK-family coreceptor kinases for high-affinity ligand binding and receptor activation. How one coreceptor can contribute to the specific binding of distinct ligands and activation of different LRR-RKs is poorly understood. Here we quantitatively analyze the contribution of SERK3 to ligand binding and activation of the brassinosteroid receptor BRI1 and the peptide hormone receptor HAESA. We show that while the isolated receptors sense their respective ligands with drastically different binding affinities, the SERK3 ectodomain binds the ligand-associated receptors with very similar binding kinetics. We identify residues in the SERK3 N-terminal capping domain, which allow for selective steroid and peptide hormone recognition. In contrast, residues in the SERK3 LRR core form a second, constitutive receptor-coreceptor interface. Genetic analyses of protein chimera between BRI1 and SERK3 define that signaling-competent complexes are formed by receptor-coreceptor heteromerization in planta. A functional BRI1-HAESA chimera suggests that the receptor activation mechanism is conserved among different LRR-RKs, and that their signaling specificity is encoded in the kinase domain of the receptor. Our work pinpoints the relative contributions of receptor, ligand, and coreceptor to the formation and activation of SERK-dependent LRR-RK signaling complexes regulating plant growth and development.

Simultaneous small-sample comparisons in longitudinal or multi-endpoint trials using multiple marginal models.

Simultaneous inference in longitudinal, repeated-measures, and multi-endpoint designs can be onerous, especially when trying to find a reasonable joint model from which the interesting effects and covariances are estimated. A novel statistical approach known as multiple marginal models greatly simplifies the modelling process: the core idea is to "marginalise" the problem and fit multiple small models to different portions of the data, and then estimate the overall covariance matrix in a subsequent, separate step. Using these estimates guarantees strong control of the family-wise error rate, however only asymptotically. In this paper, we show how to make the approach also applicable to small-sample data problems. Specifically, we discuss the computation of adjusted P values and simultaneous confidence bounds for comparisons of randomised treatment groups as well as for levels of a nonrandomised factor such as multiple endpoints, repeated measures, or a series of points in time or space. We illustrate the practical use of the method with a data example.

Multi-arm trials with multiple primary endpoints and missing values.

We present an extension of multiple contrast tests for multiple endpoints to the case of missing values. The endpoints are assumed to be normally distributed and correlated and to have equal covariance matrices for the different treatments. Different multivariate t distributions will be applied, differing in endpoint-specific degrees of freedom. In contrast to competing methods, the familywise error type I is maintained in the strong sense in an admissible range, and the problem of different marginal errors type I is avoided. The information of all observations is exploited, thereby enabling a gain in power compared with a complete case analysis.

Identification of the minimum effective dose for normally distributed data using a Bayesian variable selection approach.

The identification of the minimum effective dose is of high importance in the drug development process. In early stage screening experiments, establishing the minimum effective dose can be translated into a model selection based on information criteria. The presented alternative, Bayesian variable selection approach, allows for selection of the minimum effective dose, while taking into account model uncertainty. The performance of Bayesian variable selection is compared with the generalized order restricted information criterion on two dose-response experiments and through the simulations study. Which method has performed better depends on the complexity of the underlying model and the effect size relative to noise.

A General Framework for the Evaluation of Genetic Association Studies Using Multiple Marginal Models.

OBJECTIVE: In this study, we present a simultaneous inference procedure as a unified analysis framework for genetic association studies. METHODS: The method is based on the formulation of multiple marginal models that reflect different modes of inheritance. The basic advantage of this methodology is that no explicit formulation of the correlation between the test statistics is required. Moreover, the genotype scores are considered as a quantitative explanatory variable, i.e., regression models are used. RESULTS: The proposed approach covers a wide variety of endpoints (binary, count, quantitative, and time-to-event data). In addition, multiple endpoints of different types can be assessed simultaneously. This allows the detection of pleiotropic effects while taking the mode of inheritance into account. Moreover, multiple loci can be assessed simultaneously. CONCLUSION: The flexibility of the proposed approach is demonstrated while analyzing a variety of data examples.

Mechanistic insight into a peptide hormone signaling complex mediating floral organ abscission.

Plants constantly renew during their life cycle and thus require to shed senescent and damaged organs. Floral abscission is controlled by the leucine-rich repeat receptor kinase (LRR-RK) HAESA and the peptide hormone IDA. It is unknown how expression of IDA in the abscission zone leads to HAESA activation. Here we show that IDA is sensed directly by the HAESA ectodomain. Crystal structures of HAESA in complex with IDA reveal a hormone binding pocket that accommodates an active dodecamer peptide. A central hydroxyproline residue anchors IDA to the receptor. The HAESA co-receptor SERK1, a positive regulator of the floral abscission pathway, allows for high-affinity sensing of the peptide hormone by binding to an Arg-His-Asn motif in IDA. This sequence pattern is conserved among diverse plant peptides, suggesting that plant peptide hormone receptors may share a common ligand binding mode and activation mechanism.

Boxplots for grouped and clustered data in toxicology.

The vast majority of toxicological papers summarize experimental data as bar charts of means with error bars. While these graphics are easy to generate, they often obscure essential features of the data, such as outliers or subgroups of individuals reacting differently to a treatment. In particular, raw values are of prime importance in toxicology; therefore, we argue they should not be hidden in messy supplementary tables but rather unveiled in neat graphics in the results section. We propose jittered boxplots as a very compact yet comprehensive and intuitively accessible way of visualizing grouped and clustered data from toxicological studies together with individual raw values and indications of statistical significance. A web application to create these plots is available online.

Statistical approaches for the determination of cut points in anti-drug antibody bioassays.

Cut points in immunogenicity assays are used to classify future specimens into anti-drug antibody (ADA) positive or negative. To determine a cut point during pre-study validation, drug-naive specimens are often analyzed on multiple microtiter plates taking sources of future variability into account, such as runs, days, analysts, gender, drug-spiked and the biological variability of un-spiked specimens themselves. Five phenomena may complicate the statistical cut point estimation: i) drug-naive specimens may contain already ADA-positives or lead to signals that erroneously appear to be ADA-positive, ii) mean differences between plates may remain after normalization of observations by negative control means, iii) experimental designs may contain several factors in a crossed or hierarchical structure, iv) low sample sizes in such complex designs lead to low power for pre-tests on distribution, outliers and variance structure, and v) the choice between normal and log-normal distribution has a serious impact on the cut point. We discuss statistical approaches to account for these complex data: i) mixture models, which can be used to analyze sets of specimens containing an unknown, possibly larger proportion of ADA-positive specimens, ii) random effects models, followed by the estimation of prediction intervals, which provide cut points while accounting for several factors, and iii) diagnostic plots, which allow the post hoc assessment of model assumptions. All methods discussed are available in the corresponding R add-on package mixADA.

Statistical methods and software for validation studies on new in vitro toxicity assays.

When a new in vitro assay method is introduced, it should be validated against the best available knowledge or a reference standard assay. For assays resulting in a simple binary outcome, the data can be displayed as a 2×2 table. Based on the estimated sensitivity and specificity, and the assumed prevalence of true positives in the population of interest, the positive and negative predictive values of the new assay can be calculated. We briefly discuss the experimental design of validation experiments and previously published methods for computing confidence intervals for predictive values. The application of the methods is illustrated for two toxicological examples, by using tools available in the free software, namely, R: confidence intervals for predictive values are computed for a validation study of an in vitro test battery, and sample size calculation is illustrated for an acute toxicity assay. The R code necessary to reproduce the results is given.