T testing the immune system

Amid the flurry of grant writing and experimentation, statistical analysis sometimes gets less attention than it requires. Here, we describe fully the considerations that should go into the employment of the statistical two-sample t test.

Active-control trials with binary data: a comparison of methods for testing superiority or non-inferiority using the odds ratio

This paper considers methods for testing for superiority or non-inferiority in active-control trials with binary data, when the relative treatment effect is expressed as an odds ratio. Three asymptotic tests for the log-odds ratio based on the unconditional binary likelihood are presented, namely the likelihood ratio, Wald and score tests. All three tests can be implemented straightforwardly in standard statistical software packages, as can the corresponding confidence intervals. Simulations indicate that the three alternatives are similar in terms of the Type I error, with values close to the nominal level. However, when the non-inferiority margin becomes large, the score test slightly exceeds the nominal level. In general, the highest power is obtained from the score test, although all three tests are similar and the observed differences in power are not of practical importance. Copyright (C) 2007 John Wiley & Sons, Ltd.

Ranald Macdonald and statistical inference

Ranald Roderick Macdonald (1945-2007) was an important contributor to mathematical psychology in the UK, as a referee and action editor for British Journal of Mathematical and Statistical Psychology and as a participant and organizer at the British Psychological Society's Mathematics, statistics and computing section meetings. This appreciation argues that his most important contribution was to the foundations of significance testing, where his concern about what information was relevant in interpreting the results of significance tests led him to be a persuasive advocate for the 'Weak Fisherian' form of hypothesis testing.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

Testing for significance of phase synchronisation dynamics in the EEG

A number of tests exist to check for statistical significance of phase synchronisation within the Electroencephalogram (EEG); however, the majority suffer from a lack of generality and applicability. They may also fail to account for temporal dynamics in the phase synchronisation, regarding synchronisation as a constant state instead of a dynamical process. Therefore, a novel test is developed for identifying the statistical significance of phase synchronisation based upon a combination of work characterising temporal dynamics of multivariate time-series and Markov modelling. We show how this method is better able to assess the significance of phase synchronisation than a range of commonly used significance tests. We also show how the method may be applied to identify and classify significantly different phase synchronisation dynamics in both univariate and multivariate datasets.

The statistical downscaling model-decision centric (SDSM-DC): conceptual basis and applications

Regional climate downscaling has arrived at an important juncture. Some in the research community favour continued refinement and evaluation of downscaling techniques within a broader framework of uncertainty characterisation and reduction. Others are calling for smarter use of downscaling tools, accepting that conventional, scenario-led strategies for adaptation planning have limited utility in practice. This paper sets out the rationale and new functionality of the Decision Centric (DC) version of the Statistical DownScaling Model (SDSM-DC). This tool enables synthesis of plausible daily weather series, exotic variables (such as tidal surge), and climate change scenarios guided, not determined, by climate model output. Two worked examples are presented. The first shows how SDSM-DC can be used to reconstruct and in-fill missing records based on calibrated predictor-predictand relationships. Daily temperature and precipitation series from sites in Africa, Asia and North America are deliberately degraded to show that SDSM-DC can reconstitute lost data. The second demonstrates the application of the new scenario generator for stress testing a specific adaptation decision. SDSM-DC is used to generate daily precipitation scenarios to simulate winter flooding in the Boyne catchment, Ireland. This sensitivity analysis reveals the conditions under which existing precautionary allowances for climate change might be insufficient. We conclude by discussing the wider implications of the proposed approach and research opportunities presented by the new tool.

Hypotheses testing for structural calibration model

The main objective of this paper is to discuss maximum likelihood inference for the comparative structural calibration model (Barnett, in Biometrics 25:129-142, 1969), which is frequently used in the problem of assessing the relative calibrations and relative accuracies of a set of p instruments, each designed to measure the same characteristic on a common group of n experimental units. We consider asymptotic tests to answer the outlined questions. The methodology is applied to a real data set and a small simulation study is presented.

Improved testing inference in mixed linear models

Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Often, the number of observations is small, and it is thus important to use inference strategies that incorporate small sample corrections. In this paper, we develop modified versions of the likelihood ratio test for fixed effects inference in mixed linear models. In particular, we derive a Bartlett correction to such a test, and also to a test obtained from a modified profile likelihood function. Our results generalize those in [Zucker, D.M., Lieberman, O., Manor, O., 2000. Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood. Journal of the Royal Statistical Society B, 62,827-838] by allowing the parameter of interest to be vector-valued. Additionally, our Bartlett corrections allow for random effects nonlinear covariance matrix structure. We report simulation results which show that the proposed tests display superior finite sample behavior relative to the standard likelihood ratio test. An application is also presented and discussed. (C) 2008 Elsevier B.V. All rights reserved.

Testing hypotheses in the Birnbaum-Saunders distribution under type-II censored samples

The two-parameter Birnbaum-Saunders distribution has been used successfully to model fatigue failure times. Although censoring is typical in reliability and survival studies, little work has been published on the analysis of censored data for this distribution. In this paper, we address the issue of performing testing inference on the two parameters of the Birnbaum-Saunders distribution under type-II right censored samples. The likelihood ratio statistic and a recently proposed statistic, the gradient statistic, provide a convenient framework for statistical inference in such a case, since they do not require to obtain, estimate or invert an information matrix, which is an advantage in problems involving censored data. An extensive Monte Carlo simulation study is carried out in order to investigate and compare the finite sample performance of the likelihood ratio and the gradient tests. Our numerical results show evidence that the gradient test should be preferred. Further, we also consider the generalized Birnbaum-Saunders distribution under type-II right censored samples and present some Monte Carlo simulations for testing the parameters in this class of models using the likelihood ratio and gradient tests. Three empirical applications are presented. (C) 2011 Elsevier B.V. All rights reserved.

Benchmarking new statistical techniques in ration-based modelling of corporate collapse

Up until 1979, Multiple Discriminant Analysis (MDA) was the primary multivariate methodological approaches to ratio-based modelling of corporate collapse. However, as new statistical tools became available, researchers started testing them with the primary objective of deriving models that would at least do as good a job as MDA, but that rely on fewer assumptions. Regardless of which methodological approach was chosen, most were compared to MDA. This paper analyses 84 studies on ratio based modelling of corporate collapse over the period 1968 to 2004. The results indicate that when MDA was not the primary methodology it was the benchmark of choice for comparison; thereby, demonstrating its importance as a foundation multivariate methodological approach in signalling corporate collapse.

Testing convergence of Fiji's tourism markets

The convergence hypothesis for tourism markets is based on the tenet that when tourism markets are converging the difference between total international visitor arrivals to a country and international visitor arrivals from a particular country will be stationary. We argue that if this is true, then convergence can also be tested through examining whether total visitor arrivals and visitor arrivals from a particular market are cointegrated. We test the convergence hypothesis by examining visitor arrivals to Fiji from eight tourist source markets, using both unit root and cointegration tests. We find strong statistical evidence that Fiji's tourism markets converge.

The successful school: a genuine trend or a statistical artifice?

Schools are increasingly being expected to make improvements based on data about students' learning outcomes. Such an expectation implies that principals, teachers and key personnel within systems can read and act upon the data available. There is evidence, however, that many people have poor understanding of statistical information, and that many factors inside and outside the school have an effect on students' outcomes. This study considers one primary school's data from statewide testing programs. Trends across time are considered as a basis for making judgments about the school's performance in improving students' learning outcomes in literacy and numeracy.

Testing the immunocompetence handicap hypothesis : a review of the evidence

The immunocompetence handicap hypothesis was formulated 12 years ago in an attempt to offer a proximate mechanism by which female choice of males could be explained by endocrine control of honest signalling. The hypothesis suggested that testosterone has a dual effect in males of controlling the development of sexual signals while causing immunosuppression. Our purpose in this review is to examine the empirical evidence to date that has attempted to test the hypothesis, and to conduct a meta-analysis on two of the assumptions of the hypothesis, that testosterone reduces immunocompetence and increases parasitism, to ascertain any statistical trend in the data. There is some evidence to suggest that testosterone is responsible for the magnitude of trait expression or development of sexual traits, but this is by no means conclusive. The results of many studies attempting to find evidence for the supposed immunosuppressive qualities of testosterone are difficult to interpret since they are observational rather than experimental. Of the experimental studies, the data obtained are ambiguous, and this is reflected in the result of the meta-analysis. Overall, the meta-analysis found a significant suppressive effect of testosterone on immunity, in support of the hypothesis, but this effect disappeared when we controlled for multiple studies on the same species. There was no effect of testosterone on direct measures of immunity, but it did increase ectoparasite abundance in several studies, in particular in reptiles. A funnel analysis indicated that the results were robust to a publication bias. Alternative substances that interact with testosterone, such as glucocorticoids, may be important. Ultimately, a greater understanding is required of the complex relationships that exist both within and between the endocrine and immune systems and their consequences for mate choice decision making.

Realized volatility and correlation in grain futures markets: testing for spillover effects

Fluctuations in commodity prices are a major concern to many market participants. This paper uses realized volatility methods to calculate daily volatility and correlation estimates for three grain futures prices (corn, soybean, and wheat). The realized volatility estimates exhibit properties consistent with the stylized facts observed in earlier studies. According to daily realized correlations and regression coefficients, the spot returns from the three grain futures are positively related. The realized estimates are then used to evaluate the degree of volatility transmission across grain futures prices. The impulse response analysis is conducted by fitting the vector autoregressive model to realized volatility and correlation estimates, using the bootstrap method for statistical inference. The results indicate that rich dynamic interactions exist among the volatilities and correlations across the grain futures markets.

Reliability of isokinetic strength and aerobic power testing for patients with chronic heart failure

PURPOSE: The objective of this study was to assess the reliability of testing skeletal muscle strength and peak aerobic power in a clinical population of patients with chronic heart failure (CHF).

METHODS: Thirty-three patients with CHF (New York Heart Association (NYHA) Functional Class 2.3 ± 0.5; left ventricular ejection fraction 27% ± 7%; age 65 ± 9 years; 28:5 male-female ratio) underwent two identical series of tests (T1 and T2), 1 week apart, for strength and endurance of the muscle groups responsible for knee extension/flexion and elbow extension/flexion. The patients also underwent two graded exercise tests on a bicycle ergometer to measure peak oxygen consumption (VO_2peak). Three months later, 18 of the patients underwent a third test (T3) for each of the measures. Means were compared using MANOVA with repeated measures for strength and endurance, and ANOVA with repeated measures for VO_2peak.

RESULTS: Combining data for all four movement patterns, the expression of strength increased from T1 to T2 by 12% ± 25% (P < .001; intraclass correlation coefficient [ICC] = 0.89). Correspondingly, endurance increased by 13% ± 23% (P = .004; ICC = 0.87). Peak oxygen consumption was not significantly different (16.2 ± 0.8 and 16.1 ± 0.8 mL·kg^-1·min^-1 for T1 and T2, respectively;P = .686; ICC = 0.91). There were no significant differences between T2 and T3 for strength (2% ± 17%;P = .736; ICC = 0.92) or muscle endurance (-1% ± 15%;P = .812; ICC = 0.96), but VO_2peak decreased from 16.7 ± 1.2 to 14.9 ± 0.9 mL·kg^-1·min^-1 (-10% ± 18%;P = .021; ICC = 0.89).

CONCLUSIONS: These data suggest that in a population of patients with CHF, a familiarization trial for skeletal muscle strength testing is necessary. Although familiarization is not required for assessing oxygen consumption as a single measurement, VO_2peak declined markedly in the 3-month period for which these patients were followed. Internal consistency within patients was high for the second and third strength trials and the first and second tests of VO_2peak.