A Robust Method for Large‐Scale Multiple Hypotheses Testing

When drawing large‐scale simultaneous inference, such as in genomics and imaging problems, multiplicity adjustments should be made, since, otherwise, one would be faced with an inflated type I error. Numerous methods are available to estimate the proportion of true null hypotheses π₀, among a large number of hypotheses tested. Many methods implicitly assume that the π₀ is large, that is, close to 1. However, in practice, mid‐range π₀ values are frequently encountered and many of the widely used methods tend to produce highly variable or biased estimates of π₀. As a remedy in such situations, we propose a hierarchical Bayesian model that produces an estimator of π₀ that exhibits considerably less bias and is more stable. Simulation studies seem indicative of good method performance even when low‐to‐moderate correlation exists among test statistics. Method performance is assessed in simulated settings and its practical usefulness is illustrated in an application to a type II diabetes study.     

Rejoinder

Article http://dx.doi.org/10.1002/bimj.4710360113 Letter to the editor http://dx.doi.org/10.1002/bimj.200810429     

Marginally specified generalized linear mixed models: a robust approach

Longitudinal data modeling is complicated by the necessity to deal appropriately with the correlation between observations made on the same individual. Building on an earlier nonrobust version proposed by Heagerty (1999, Biometrics 55, 688-698), our robust marginally specified generalized linear mixed model (ROBMS-GLMM) provides an effective method for dealing with such data. This model is one of the first to allow both population-averaged and individual-specific inference. As well, it adopts the flexibility and interpretability of generalized linear mixed models for introducing dependence but builds a regression structure for the marginal mean, allowing valid application with time-dependent (exogenous) and time-independent covariates. These new estimators are obtained as solutions of a robustified likelihood equation involving Huber's least favorable distribution and a collection of weights. Huber's least favorable distribution produces estimates that are resistant to certain deviations from the random effects distributional assumptions. Innovative weighting strategies enable the ROBMS-GLMM to perform well when faced with outlying observations both in the response and covariates. We illustrate the methodology with an analysis of a prospective longitudinal study of laryngoscopic endotracheal intubation, a skill that numerous health-care professionals are expected to acquire. The principal goal of our research is to achieve robust inference in longitudinal analyses.     

Variable selection for marginal longitudinal generalized linear models

Variable selection is an essential part of any statistical analysis and yet has been somewhat neglected in the context of longitudinal data analysis. In this article, we propose a generalized version of Mallows's C(p) (GC(p)) suitable for use with both parametric and nonparametric models. GC(p) provides an estimate of a measure of model's adequacy for prediction. We examine its performance with popular marginal longitudinal models (fitted using GEE) and contrast results with what is typically done in practice: variable selection based on Wald-type or score-type tests. An application to real data further demonstrates the merits of our approach while at the same time emphasizing some important robust features inherent to GC(p).     

Comparison of maximum statistics for hypothesis testing when a nuisance parameter is present only under the alternative

In many practical problems, a hypothesis testing involves a nuisance parameter which appears only under the alternative hypothesis. Davies (1977, Biometrika 64, 247-254) proposed the maximum of the score statistics over the whole range of the nuisance parameter as a test statistic for this type of hypothesis testing. Freidlin, Podgor, and Gastwirth (1999, Biometrics 55, 883-886) studied two other simpler maximum test statistics, the maximum of the score statistics at two extreme points of the nuisance parameter, and the maximum of the score statistics at three points of the nuisance parameter including the two extreme points. In this article, we compare the powers of these three maximum-type statistics in the context of three genetic problems.     

Robust Tests for Candidate‐Gene Association Using Case‐Parents Trios with a Multi‐Allelic Marker

In case‐parents trios design, the association between a multi‐allelic candidate‐gene and a disease can be detected by using maximum of score tests (max‐score) when the mode of inheritance is known. We apply the maximum of the max‐score statistics and the maximum of likelihood ratio statistics when the genetic model is unknown and examine their robust properties compared to max‐score statistics. The simulation results demonstrate that the two maximum robust tests are more efficacious and robust across all genetic models compared with the three max‐score tests. Moreover, in most situations, the maximum of the max‐score tests seems to be more powerful than the maximum of the likelihood ratio tests. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Systems Biology-an interdisciplinary approach

System-level approaches in biology are not new but foundations of “Systems Biology” are achieved only now at the beginning of the 21st century [Kitano, H., 2001. Foundations of Systems Biology. MIT Press, Cambridge, MA]. The renewed interest for a system-level approach is linked to the progress in collecting experimental data and to the limits of the “reductionist” approach. System-level understanding of native biological and pathological systems is needed to provide potential therapeutic targets. Examples of interdisciplinary approach in Systems Biology are described in U.S., Japan and Europe. Robustness in biology, metabolic engineering and idiotypic networks are discussed in the framework of Systems Biology.     

Evolutionary dynamics and highly optimized tolerance

We develop a numerical model of a lattice community based on Highly Optimized Tolerance (HOT), which relates the evolution of complexity to robustness tradeoffs in an uncertain environment. With the model, we explore scenarios for evolution and extinction which are abstractions of processes which are commonly discussed in biological and ecological case studies. These include the effects of different habitats on the phenotypic traits of the organisms, the effects of different mutation rates on adaptation, fitness, and diversity, and competition between generalists and specialists. The model exhibits a wide variety of microevolutionary and macroevolutionary phenomena which can arise in organisms which are subject to random mutation, and selection based on fitness evaluated in a specific environment. Generalists arise in uniform habitats, where different disturbances occur with equal frequency, while specialists arise when the relative frequency of different disturbances is skewed. Fast mutators are seen to play a primary role in adaptation, while slow mutators preserve well-adapted configurations. When uniform and skewed habitats are coupled through migration of the organisms, we observe a primitive form of punctuated equilibrium. Rare events in the skewed habitat lead to extinction of the specialists, whereupon generalists invade from the uniform habitat, adapt to their new surroundings, ultimately leading their progeny to become vulnerable to extinction in a subsequent rare disturbance.     

Calculating biological behaviors of epigenetic states in the phage λ life cycle

The biology and behavior of bacteriophage regulation have been the focus of classical investigations of molecular control of gene expression. Both qualitative and quantitative aspects of this behavior have been systematically characterized experimentally. Complete understanding of the robustness and stability of the genetic circuitry for the lysis-lysogeny switch remains an unsolved puzzle. It is an excellent test case for our understanding of biological behavior of an integrated network based on its physical, chemical, DNA, protein, and functional properties. We have used a new approach to non-linear dynamics to formulate a new mathematical model, performed a theoretical study on the phage life cycle, and solved the crucial part of this puzzle. We find a good quantitative agreement between the theoretical calculation and published experimental observations in the protein number levels, the lysis frequency in the lysogen culture, and the lysogenization frequency for mutants of O_R. We also predict the desired robustness for the genetic switch. We believe that this is the first successful example in the quantitative calculation of robustness and stability of the phage regulatory network, one of the simplest and most well-studied regulatory systems.     

On the Behaviour of Fligner-Wolfe-Trend Test “Control versus k Treatments” with Application in Toxicology

The behaviour of Fligner-Wolfe-trend test “control versus k treatments” was characterized by simulation. Sample size estimation took place via non-central t-distribution. Some results on asymptotic efficiency were shown and compared with simulation results for small sample sizes. A test version for umbrella alternatives was given and characterized by simulation.