A Global Sensitivity Test for Evaluating Statistical Hypotheses with Nonidentifiable Models

Summary We consider the problem of evaluating a statistical hypothesis when some model characteristics are nonidentifiable from observed data. Such a scenario is common in meta‐analysis for assessing publication bias and in longitudinal studies for evaluating a covariate effect when dropouts are likely to be nonignorable. One possible approach to this problem is to fix a minimal set of sensitivity parameters conditional upon which hypothesized parameters are identifiable. Here, we extend this idea and show how to evaluate the hypothesis of interest using an infimum statistic over the whole support of the sensitivity parameter. We characterize the limiting distribution of the statistic as a process in the sensitivity parameter, which involves a careful theoretical analysis of its behavior under model misspecification. In practice, we suggest a nonparametric bootstrap procedure to implement this infimum test as well as to construct confidence bands for simultaneous pointwise tests across all values of the sensitivity parameter, adjusting for multiple testing. The methodology's practical utility is illustrated in an analysis of a longitudinal psychiatric study.     

Fractal dimension of electroencephalographic time series and underlying brain processes

 Fractal dimension has been proposed as a useful measure for the characterization of electrophysiological time series. This paper investigates what the pointwise dimension of electroencephalographic (EEG) time series can reveal about underlying neuronal generators. The following theoretical assumptions concerning brain function were made (i) within the cortex, strongly coupled neural assemblies exist which oscillate at certain frequencies when they are active, (ii) several such assemblies can oscillate at a time, and (iii) activity flow between assemblies is minimal. If these assumptions are made, cortical activity can be considered as the weighted sum of a finite number of oscillations (plus noise). It is shown that the correlation dimension of finite time series generated by multiple oscillators increases monotonically with the number of oscillators. Furthermore, it is shown that a reliable estimate of the pointwise dimension of the raw EEG signal can be calculated from a time series as short as a few seconds. These results indicate that (i) The pointwise dimension of the EEG allows conclusions regarding the number of independently oscillating networks in the cortex, and (ii) a reliable estimate of the pointwise dimension of the EEG is possible on the basis of short raw signals. Received: 1 September 1994/Accepted in revised form: 16 May 1995     

Improving regions of deviation gait symmetry analysis with pointwise T tests

The regions of deviation method has been proposed as a technique for identifying regions of the gait cycle where joint motion deviates from normal (Shorter et al., 2008). The original statistical analysis distinguished only peak values during stance and swing. In the current article, we extend the approach by examining deviations from normal throughout the entire gait cycle using pointwise t tests. These methods were demonstrated on hind-limb joint angles of 21 Labrador Retrievers without and with cranial cruciate ligament disease. Results were compared with peak difference analysis previously performed on these subjects. All points in the gait cycle where symmetry deviations were significantly affected by cranial cruciate ligament disease (via pointwise t tests) were defined as regions of deviation from symmetry. Discriminant function analysis was used to consider single subjects and validate that these regions were truly areas of difference between groups. Regions of deviation encompassed previously determined significant peak differences, while extending analysis to additional areas of asymmetry. Discriminant function analysis suggested that the region of deviation method is a viable approach for distinguishing motion pattern differences. This enhanced method may help researchers better understand the mechanisms behind lameness and compensation.     

Heterogeneity in multiple transmission pathways: modelling the spread of cholera and other waterborne disease in networks with a common water source

Many factors influencing disease transmission vary throughout and across populations. For diseases spread through multiple transmission pathways, sources of variation may affect each transmission pathway differently. In this paper we consider a disease that can be spread via direct and indirect transmission, such as the waterborne disease cholera. Specifically, we consider a system of multiple patches with direct transmission occurring entirely within patch and indirect transmission via a single shared water source. We investigate the effect of heterogeneity in dual transmission pathways on the spread of the disease. We first present a 2-patch model for which we examine the effect of variation in each pathway separately and propose a measure of heterogeneity that incorporates both transmission mechanisms and is predictive of R₀. We also explore how heterogeneity affects the final outbreak size and the efficacy of intervention measures. We conclude by extending several results to a more general n-patch setting.     

A semiparametric response surface model for assessing drug interaction

Summary .   When multiple drugs are administered simultaneously, investigators are often interested in assessing whether the drug combinations are synergistic, additive, or antagonistic. Existing response surface models are not adequate to capture the complex patterns of drug interactions. We propose a two-component semiparametric response surface model with a parametric function to describe the additive effect of a combination dose and a nonparametric function to capture the departure from the additive effect. The nonparametric function is estimated using the technique developed in thin plate splines, and the pointwise bootstrap confidence interval for this function is constructed. The proposed semiparametric model offers an effective way of formulating the additive effect while allowing the flexibility of modeling a departure from additivity. Example and simulations are given to illustrate that the proposed model provides an excellent estimation for different patterns of interactions between two drugs.     

Genomewide linkage scan for opioid dependence and related traits

Risk of opioid dependence is genetically influenced. We recruited a sample of 393 small nuclear families (including 250 full-sib and 46 half-sib pairs), each with at least one individual with opioid dependence. Subjects underwent a detailed evaluation of substance dependence-related traits. As planned a priori to reduce heterogeneity, we used cluster analytic methods to identify opioid dependence-related symptom clusters, which were shown to be heritable. We then completed a genomewide linkage scan (with 409 markers) for the opioid-dependence diagnosis and for the two cluster-defined phenotypes represented by >250 families: the heavy-opioid-use cluster and the non-opioid-use cluster. Further exploratory analyses were completed for the other cluster-defined phenotypes. The statistically strongest results were seen with the cluster-defined traits. For the heavy-opioid-use cluster, we observed a LOD score of 3.06 on chromosome 17 (empirical pointwise P = .0002) for European American (EA) and African American (AA) subjects combined, and, for the non-opioid-use cluster, we observed a LOD score of 3.46 elsewhere on chromosome 17 (empirical pointwise P = .00002, uncorrected for multiple traits studied) for EA subjects only. We also identified a possible linkage (LOD score 2.43) of opioid dependence with chromosome 2 markers for the AA subjects. These results are an initial step in identifying genes for opioid dependence on the basis of a genomewide investigation (i.e., a study not conditioned on prior physiological candidate-gene hypotheses).     

Pointwise Hölder exponents of a model for skin laser Doppler flowmetry signals based on six nonlinear coupled oscillators with linear and parametric couplings: Comparison with experimental data from young healthy subjects

We study pointwise Hölder exponents of experimental and numerically simulated skin laser Doppler flowmetry (LDF) data that give a peripheral view of the cardiovascular system. The experimental signals are recorded in the forearm of young healthy subjects. The numerically simulated LDF data are computed from a model containing six nonlinear coupled oscillators reflecting six almost periodic rhythmic activities present in experimental LDF signals. Simulated LDF signals are for the first time generated with both linear and parametric couplings in order to represent cardiovascular system behaviors. Moreover, we propose the use of a parametric generalised quadratic variation (GQV) based estimation method for the estimation of the pointwise Hölder exponents. The latter identify possible multifractal characteristics of data. The GQV method is first tested on a white noise measure and then applied on the LDF data. The results of our signal processing analysis show that experimental LDF signals recorded in the forearm are weakly multifractal for young healthy subjects at rest. Furthermore, our findings show that the simulated data have a complexity similar to the one of signal recorded in young healthy subjects. However, their pointwise Hölder exponents have differences that we explain. This paper provides useful information to go deeper into the modeling of LDF data, which could bring enlightenment for a better understanding of the peripheral cardiovascular system.     

Energy landscape of k-point mutants of an RNA molecule

MOTIVATION: A k-point mutant of a given RNA sequence s = s(1), ..., s(n) is an RNA sequence s' = s'(1),..., s'(n) obtained by mutating exactly k-positions in s; i.e. Hamming distance between s and s' equals k. To understand the effect of pointwise mutation in RNA, we consider the distribution of energies of all secondary structures of k-point mutants of a given RNA sequence. RESULTS: Here we describe a novel algorithm to compute the mean and standard deviation of energies of all secondary structures of k-point mutants of a given RNA sequence. We then focus on the tail of the energy distribution and compute, using the algorithm AMSAG, the k-superoptimal structure; i.e. the secondary structure of a < or =k-point mutant having least free energy over all secondary structures of all k'-point mutants of a given RNA sequence, for k' < or = k. Evidence is presented that the k-superoptimal secondary structure is often closer, as measured by base pair distance and two additional distance measures, to the secondary structure derived by comparative sequence analysis than that derived by the Zuker minimum free energy structure of the original (wild type or unmutated) RNA.     

Multiple states in river and lake ecosystems

Nonlinear models of ecosystem dynamics that incorporate positive feedbacks and multiple, internally reinforced states have considerable explanatory power. However, linear models may be adequate, particularly if ecosystem behaviour is primarily controlled by external processes. In lake ecosystems, internal (mainly biotic) processes are thought to have major impacts on system behaviour, whereas in rivers, external (mainly physical) factors have traditionally been emphasized. We consider the hypothesis that models that exhibit multiple states are useful for understanding the behaviour of lake ecosystems, but not as useful for understanding stream ecosystems. Some of the best-known examples of multiple states come from lake ecosystems. We review some of these examples, and we also describe examples of multiple states in rivers. We conclude that the hypothesis is an oversimplification; the importance of physical forcing in rivers does not eliminate the possibility of internal feedbacks that create multiple states, although in rivers these feedbacks are likely to include physical as well as biotic processes. Nonlinear behaviour in aquatic ecosystems may be more common than current theory indicates.     

Two- and three-locus tests for linkage analysis using recombinant inbred lines

We consider fixed recombinant inbred lines (RILs) derived either by selfing or by full-sib mating; when applicable, we also consider intermated recombinant inbreds (IRIs). First, we show that the usual estimate of recombination fraction based on RIL data is biased, and we provide an estimate where the major part of that bias is removed. Second, we derive simple formulas to compute the frequencies of genotypes at three loci in RILs. We describe the nonindependence of multiple recombinations arising in RIL recombination data even though there may be no interference in each meiosis. Finally, we give formulas for interference tests, gene mapping, or QTL detection in RIL populations.     

Neural coding for the retrieval of multiple memory patterns

We investigate the retrieval dynamics in a feature-based semantic memory model, in which the features are coded by neurons of the Hindmarsh–Rose type in the chaotic regime. We consider the retrieval process as consisting of the synchronized firing activity of the neurons coding for the same memory pattern. The retrieval dynamics is investigated for multiple patterns, with particular attention to the case of overlapping memories. In this case, we hypothesize a dynamical nontransitive mechanism based on synchronization, that allows for a shared feature to participate in multiple memory representations. The problem of the choice of a cognitive plausible time-scale for the retrieval analysis is investigated by analyzing the information that can be inferred from finite-time analyses. Different types of indicators are proposed in order to evaluate the temporal dynamics of the neurons engaged in the retrieval process. We interpret the simulation results as suggestive of a role for chaotic dynamics in allowing for flexible composition of elementary meaningful units in memory representations.     

Malaria, danger, and risk perceptions among the Yao in rural Malawi

Findings from a study designed to discover how local understanding of malaria among Yao in Malawi relate to pregnancy risk definitions reveal that malaria in pregnancy is not perceived as a major risk. Using extended ethnographic field research and multiple methods, we argue a shift from narrow single-disease approaches to malaria during pregnancy is required and document women's concerns about exposure to multiple vulnerabilities during pregnancy, including witchcraft, extramarital affairs, and multiple dangerous illnesses. Four dimensions are implicated in Yao perceptions of risk: perceived adverse consequences in pregnancy; ease of treatment and cure; transmission and agency to control; and type of risk (social-medical). We discuss implications and consider malaria program features needed to address the complexity of perceived vulnerabilities and living conditions in resource-poor settings.     

Pattern formation in generalized Turing systems

Turing's model of pattern formation has been extensively studied analytically and numerically, and there is recent experimental evidence that it may apply in certain chemical systems. The model is based on the assumption that all reacting species obey the same type of boundary condition pointwise on the boundary. We call these scalar boundary conditions. Here we study mixed or nonscalar boundary conditions, under which different species satisfy different boundary conditions at any point on the boundary, and show that qualitatively new phenomena arise in this case. For example, we show that there may be multiple solutions at arbitrarily small lengths under mixed boundary conditions, whereas the solution is unique under homogeneous scalar boundary conditions. Moreover, even when the same solution exists under scalar and mixed boundary conditions, its stability may be different in the two cases. We also show that mixed boundary conditions can reduce the sensitivity of patterns to domain changes.Supported in part by NIH Grant # GM29123     

Composite temporal strategies in pathogen evolution: balancing invasion and persistence

There is ongoing interest in the conditions that favor the evolution of acute, highly transmissible infections in contrast to chronic ones. Earlier studies typically consider the evolution of a trait that is constant over the lifetime of an infection. However, for many pathogens, such traits can vary over this course. Here, we address the evolution of temporal patterns in limited host population sizes, where a trade-off between invasion and persistence can arise. This is of particular relevance to questions on the evolution of acuteness and chronicity. We ask whether population dynamics of transmission at the between-host level could lead pathogen adaptation to favor temporal strategies during the course of infection. To do this, we consider an infection to be composed of multiple stages, allowing each of these to evolve independently under a transmission–duration trade-off. We only consider selection taking place on the between-host level and examine the balance of invasion and persistence (i.e., maximizing replication vs. minimizing vulnerability to extinction), using several fitness-related measures. We find that a composite strategy that is ordered in time can confer higher fitness than any single, constant, strategy. We discuss the relevance of these results for the ordered expression of var genes in Plasmodium falciparum, as well as for infections that characteristically have several stages as in some bacterial pathogens.     

Bayesian Nonparametric Modeling for Comparison of Single-Neuron Firing Intensities

Summary .  We propose a fully inferential model-based approach to the problem of comparing the firing patterns of a neuron recorded under two distinct experimental conditions. The methodology is based on nonhomogeneous Poisson process models for the firing times of each condition with flexible nonparametric mixture prior models for the corresponding intensity functions. We demonstrate posterior inferences from a global analysis, which may be used to compare the two conditions over the entire experimental time window, as well as from a pointwise analysis at selected time points to detect local deviations of firing patterns from one condition to another. We apply our method on two neurons recorded from the primary motor cortex area of a monkey's brain while performing a sequence of reaching tasks.     

An application of beam theory to determine the stress and deformation of long bones

We present a generalized beam theory in which deformation and load are determined simultaneously, in order to analyze statically indeterminant problems involving long bones. We regard a long bone as a beam curved in three dimensions for which the cross-sectional properties vary continuously along its length. The theory is used to determine the force, moment, deflection and twist along the fifth metatarsal when it is subjected to both a pointwise and a distributed load.     

Protein secondary structure prediction using three neural networks and a segmental semi Markov model

Prediction of protein secondary structure is an important step towards elucidating its three dimensional structure and its function. This is a challenging problem in bioinformatics. Segmental semi Markov models (SSMMs) are one of the best studied methods in this field. However, incorporating evolutionary information to these methods is somewhat difficult. On the other hand, the systems of multiple neural networks (NNs) are powerful tools for multi-class pattern classification which can easily be applied to take these sorts of information into account.To overcome the weakness of SSMMs in prediction, in this work we consider a SSMM as a decision function on outputs of three NNs that uses multiple sequence alignment profiles. We consider four types of observations for outputs of a neural network. Then profile table related to each sequence is reduced to a sequence of four observations. In order to predict secondary structure of each amino acid we need to consider a decision function. We use an SSMM on outputs of three neural networks. The proposed SSMM has discriminative power and weights over different dependency models for outputs of neural networks. The results show that the accuracy of our model in predictions, particularly for strands, is considerably increased.     

Accommodating pathway information in expression quantitative trait locus analysis

The availability of high-throughput genotyping technologies and microarray assays has allowed researchers to consider pursuing investigations whose ultimate goal is the identification of genetic variations that influence levels of gene expression, e.g., "expression quantitative trait locus" or "eQTL" mapping studies. However, the large number of genes whose expression levels can be tested for association with genetic variations in such studies can create both statistical and biological interpretive problems. We consider the integrated analysis of eQTL mapping data that incorporates pathway, function, and disease process information. The goal of this analysis is to determine if compelling patterns emerge from the data that are consistent with the notion that perturbations in the molecular physiologic environment induced by genetic variations implicate the expression patterns of multiple genes via genetic network relationships or feedback mechanisms. We apply available genetic network and pathway analysis software, as well as a novel regression analysis technique, to carry out the proposed studies. We also consider extensions of the proposed strategies and areas of future research.     

Issues in the classification of multimodal communication signals

Communication involves complex behavior in multiple sensory channels, or "modalities." We provide an overview of multimodal communication and its costs and benefits, place examples of signals and displays from an array of taxa, sensory systems, and functions into our signal classification system, and consider issues surrounding the categorization of multimodal signals. The broadest level of classification is between signals with redundant and nonredundant components, with finer distinctions in each category. We recommend that researchers gather information on responses to each component of a multimodal signal as well as the response to the signal as a whole. We discuss the choice of categories, whether to categorize signals on the basis of the signal or the response, and how to classify signals if data are missing. The choice of behavioral assay may influence the outcome, as may the context of the communicative event. We also consider similarities and differences between multimodal and unimodal composite signals and signals that are sequentially, rather than simultaneously, multimodal.