Statistical analysis of functional response experiments

The aim of this paper is to highlight the benefits of a full data analysis of a functional response data set, compared to the usual one‐pass regression analysis. In a biological control setting where the choice of organism is often based on comparative studies of the functional responses, it is imperative to have both reliable estimates and a feeling of the degree of confidence one is willing to put on the figures. We analyzed a data set involving the freshwater predator Notonecta glauca (Hemiptera) preying on Asellus aquaticus during 24 h. The specific aim of the analysis was to test whether the functional response is of type II or type III. The different stages of a complete analysis are (1) a preliminary inspection of the data, (2) model building, (3) a model check and (4) a combination of the results with independent information. We argue that the analysis is best done with the predation rate as response and define a test for the location of its maximum. The existence of a maximum is typical for type III functional response. We explain why the binomial distribution is a natural error distribution, and how to implement the regression analysis within the family of generalized linear models using two competing link functions, the logit and the reciprocal. There is marked overdispersion which increases with increasing prey numbers. We use prior weights to take account of it. Using all available data, a type III functional response is warranted with the reciprocal link, but not with the logit link Model checks using Pearson residuals and regression diagnostics based on point deletions show that three points have a particularly strong influence on the parameter estimates. If these are deleted, the functional response type III is then warranted for both link functions. The complete analysis enables us to determine the various degrees of uncertainty and to draw biological conclusions with corresponding confidence. We are convinced that the data set shows a type III functional response, but we are less sure about which link function to choose. Furthermore, the marked overdispersion at high density, the regression diagnostics, as well as independent information on a change in the behaviour of the prey at high density, indicate that the experimental conditions may have changed as a function of the prey density.     

Quantitative analysis of ligand-receptor interactions in physiological experiments

In isolated smooth muscles of the sea cucumber, the rat intestine, vas deferens and portal vein, and in chick embryonic amnion, contractile responses of smooth muscles to transmitters and their agonists were described with two equations: p = (Pm.A(n))/(EC50n + A(n)) [7] or p = [(Pm1.An1)/(EC50(1)n1 + An1)] + [(Pm2.An2)/(EC50(2)n2 + An2)] [8]. The findings reveal a possibility of ligand-receptor interaction according to several models: a single receptor pool with n = 1 or n not equal to 1; two receptor pools in the same effector system with n1 = n2 or n1 not equal to n2.     

Statistical analysis of insect preference in two-choice experiments

Many studies of insect behavior in relation to chemicals from different plants require the use of statistical tests for determining whether attraction, repulsion, or neutrality is significant. In this paper, we propose a simple and efficient nonparametric statistical procedure for testing hypotheses about insect preference in two-choice experiments with individual insects. Three criteria are provided in order to detect the following alternatives to neutrality: (i) general attraction (or repulsion) in a sample population, (ii) strong variability of the individual responses, and (iii) slight but similar behavioral effects. Illustrations are given from two-choice experiments concerning the European corn borer (Ostrinia nubilalisHbn.) female's oviposition behavior.     

Statistical methods in finite element analysis

Finite element analysis (FEA) is a commonly used tool within many areas of engineering and can provide useful information in structural analysis of mechanical systems. However, most analyses within the field of biomechanics usually take no account either of the wide variation in material properties and geometry that may occur in natural tissues or manufacturing imperfections in synthetic materials. This paper discusses two different methods of incorporating uncertainty in FE models. The first, Taguchi's robust parameter design, uses orthogonal matrices to determine how to vary the parameters in a series of FE models, and provides information on the sensitivity of a model to input parameters. The second, probabilistic analysis, enables the distribution of a response variable to be determined from the distributions of the input variables. The methods are demonstrated using a simple example of an FE model of a beam that is assigned material properties and geometry over a range similar to an orthopaedic fixation plate. In addition to showing how each method may be used on its own, we also show how computational effort may be minimised by first identifying the most important input variables before determining the effects of imprecision.     

Statistical bioinformatic methods in microbial genome analysis

It is probable that, increasingly, genome investigations are going to be based on statistical formalization. This review summarizes the state of art and potentiality of using statistics in microbial genome analysis. First, I focus on recent advances in functional genomics, such as finding genes and operons, identifying gene conversion events, detecting DNA replication origins and analysing regulatory sites. Then I describe how to use phylogenetic methods in genome analysis and methods for genome-wide scanning for positively selected amino acids. I conclude with speculations on the future course of genome statistical modeling.     

Statistical methodology for the analysis of dye-switch microarray experiments

Background  

In individually dye-balanced microarray designs, each biological sample is hybridized on two different slides, once with Cy3 and once with Cy5. While this strategy ensures an automatic correction of the gene-specific labelling bias, it also induces dependencies between log-ratio measurements that must be taken into account in the statistical analysis.     

Statistical analysis of survival data from radiation countermeasure experiments

We present an introduction to, and examples of, Cox proportional hazards regression in the context of animal lethality studies of potential radioprotective agents. This established method is seldom used to analyze survival data collected in such studies, but is appropriate in many instances. Presenting a hypothetical radiation study that examines the efficacy of a potential radioprotectant both in the absence and presence of a potential modifier, we detail how to implement and interpret results from a Cox proportional hazards regression analysis used to analyze the survival data, and we provide relevant SAS? code. Cox proportional hazards regression analysis of survival data from lethal radiation experiments (1) considers the whole distribution of survival times rather than simply the commonly used proportions of animals that survived, (2) provides a unified analysis when multiple factors are present, and (3) can increase statistical power by combining information across different levels of a factor. Cox proportional hazards regression should be considered as a potential statistical method in the toolbox of radiation researchers.     

Statistical methods for estimating complexity from competition experiments between two populations

Often a screening or selection experiment targets a cell or tissue, which presents many possible molecular targets and identifies a correspondingly large number of ligands. We describe a statistical method to extract an estimate of the complexity or richness of the set of molecular targets from competition experiments between distinguishable ligands, including aptamers derived from combinatorial experiments (SELEX or phage display). In simulations, the non-parametric statistic provides a robust estimate of complexity from a 100 ×100 matrix of competition experiments, which is clearly feasible in high-throughput format. The statistic and method are potentially applicable to other ligand binding situations.     

Interactive control of physiological experiments

Physiological and biological experiments often require the imposition of repeated influences on an organ or organic system. Then the experimental protocol requires many repetitive functions with adjustable interval times and magnitudes, which are prepared or dictated by experimental results. To control such an experimental set-up interactively with a small computer we chose a more or less general approach. A special language syntax has been developed for: (i) experiment definition; (ii) experiment composition in advance; (iii) real-time control during the actual experiment; and (iv) registration of the actual protocol parameters. The interactive control was realized using the special language and an interpreter as one of the parallel processes for the experimental control.     

Statistical accuracy in fluorescence fluctuation experiments

The mathematical expression of the signal to noise ratio in fluorescence fluctuation experiments is derived for arbitrary sample profiles and for any mechanism of translational motion, and experimentally verified. The signal to noise ratio depends on the mean count rate per particle per dwell time, the mean number of particles per sample volume, time characteristics of the correlation function, sample profile characteristics, and the data collection time. Statistical accuracy of the third order moment of fluorescence intensity fluctuations is also studied. The optimum concentration for the third order moment analysis is about one particle per sample volume. Received: 13 February 1996 / Accepted: 20 September 1996     

Statistical methods for the analysis of two-arm non-inferiority trials with binary outcomes

The aim of this contribution is to give an overview of approaches to testing for non-inferiority of one out of two binomial distributions as compared to the other in settings involving independent samples (the paired samples case is not considered here but the major conclusions and recommendations can be shown to hold for both sampling schemes). In principle, there is an infinite number of different ways of defining (one-sided) equivalence in any multiparameter setting. In the binomial two-sample problem, the following three choices of a measure of dissimilarity between the underlying distributions are of major importance for real applications: the odds ratio (OR), the relative risk (RR), and the difference (DEL) of both binomial parameters. It is shown that for all three possibilities of formulating the hypotheses of a non-inferiority problem concerning two binomial proportions, reasonable testing procedures providing exact control over the type-I error risk are available. As a particularly useful and versatile way of handling mathematically nonnatural parametrizations like RR and DELTA, the approach through Bayesian posterior probabilities of hypotheses with respect to some non-informative reference prior has much to recommend it. In order to ensure that the corresponding testing procedure be valid in the classical, i.e. frequentist sense, it suffices to use straightforward computational techniques yielding suitably corrected nominal significance levels. In view of the availability of testing procedures with satisfactory properties for all parametrizations of main practical interest, the discussion of the pros and cons of these methods has to focus on the question of which of the underlying measures of dissimilarity should be preferred on grounds of logic and intuition. It is argued that the OR clearly merits to be given preference also with regard to this latter kind of criteria since the non-inferiority hypotheses defined in terms of the other parametric functions are bounded by lines which cross the boundaries of the parameter space. From this fact, we conclude that the exact Fisher type test for one-sided equivalence provides the most reasonable approach to the confirmatory analysis of non-inferiority trials involving two independent samples of binary data. The marked conservatism of the nonrandomized version of this test can largely be removed by using a suitably increased nominal significance level (depending, in addition to the target level, on the sample sizes and the equivalence margin), or by replacing it with a Bayesian test for non-inferiority with respect to the odds ratio.     

Statistical significance in comparative ethological experiments

This paper is concerned with the statistical analysis of data from comparative experiments in applied animal behaviour research. It is emphasized that the statistical analysis of experimental results should be in accordance with the design of the experiment. An example is given to illustrate this.     

Statistical challenges in the analysis of two-dimensional difference gel electrophoresis experiments using DeCyder

MOTIVATION: The DeCyder software (GE Healthcare) is the current state-of-the-art commercial product for the analysis of two-dimensional difference gel electrophoresis (2D DIGE) experiments. Analyses complementing DeCyder are suggested by incorporating recent advances from the microarray data analysis literature. A case study on the effect of smallpox vaccination is used to compare the results obtained from DeCyder with the results obtained by applying moderated t-tests adjusted for multiple comparisons to DeCyder output data that was additionally normalized. RESULTS: Application of the more stringent statistical tests applied to the normalized 2D DIGE data decreased the number of potentially differentially expressed proteins from the number obtained from DeCyder and increased the confidence in detecting differential expression in human clinical studies.