Regression analysis of spatial data.

Many of the most interesting questions ecologists ask lead to analyses of spatial data. Yet, perhaps confused by the large number of statistical models and fitting methods available, many ecologists seem to believe this is best left to specialists. Here, we describe the issues that need consideration when analysing spatial data and illustrate these using simulation studies. Our comparative analysis involves using methods including generalized least squares, spatial filters, wavelet revised models, conditional autoregressive models and generalized additive mixed models to estimate regression coefficients from synthetic but realistic data sets, including some which violate standard regression assumptions. We assess the performance of each method using two measures and using statistical error rates for model selection. Methods that performed well included generalized least squares family of models and a Bayesian implementation of the conditional auto-regressive model. Ordinary least squares also performed adequately in the absence of model selection, but had poorly controlled Type I error rates and so did not show the improvements in performance under model selection when using the above methods. Removing large-scale spatial trends in the response led to poor performance. These are empirical results; hence extrapolation of these findings to other situations should be performed cautiously. Nevertheless, our simulation-based approach provides much stronger evidence for comparative analysis than assessments based on single or small numbers of data sets, and should be considered a necessary foundation for statements of this type in future.

Random assignment of intervention points in two phase single-case designs: data-division-specific distributions

The present study explores the statistical properties of a randomization test based on the random assignment of the intervention point in a two-phase (AB) single-case design. The focus is on randomization distributions constructed with the values of the test statistic for all possible random assignments and used to obtain p-values. The shape of those distributions is investigated for each specific data division defined by the moment in which the intervention is introduced. Another aim of the study consisted in testing the detection of inexistent effects (i.e., production of false alarms) in autocorrelated data series, in which the assumption of exchangeability between observations may be untenable. In this way, it was possible to compare nominal and empirical Type I error rates in order to obtain evidence on the statistical validity of the randomization test for each individual data division. The results suggest that when either of the two phases has considerably less measurement times, Type I errors may be too probable and, hence, the decision making process to be carried out by applied researchers may be jeopardized.

An efficient algorithm to perform multiple testing in epistasis screening

Background: Research in epistasis or gene-gene interaction detection for human complex traits has grown over the last few years. It has been marked by promising methodological developments, improved translation efforts of statistical epistasis to biological epistasis and attempts to integrate different omics information sources into the epistasis screening to enhance power. The quest for gene-gene interactions poses severe multiple-testing problems. In this context, the maxT algorithm is one technique to control the false-positive rate. However, the memory needed by this algorithm rises linearly with the amount of hypothesis tests. Gene-gene interaction studies will require a memory proportional to the squared number of SNPs. A genome-wide epistasis search would therefore require terabytes of memory. Hence, cache problems are likely to occur, increasing the computation time. In this work we present a new version of maxT, requiring an amount of memory independent from the number of genetic effects to be investigated. This algorithm was implemented in C++ in our epistasis screening software MBMDR-3.0.3. We evaluate the new implementation in terms of memory efficiency and speed using simulated data. The software is illustrated on real-life data for Crohn’s disease. Results: In the case of a binary (affected/unaffected) trait, the parallel workflow of MBMDR-3.0.3 analyzes all gene-gene interactions with a dataset of 100,000 SNPs typed on 1000 individuals within 4 days and 9 hours, using 999 permutations of the trait to assess statistical significance, on a cluster composed of 10 blades, containing each four Quad-Core AMD Opteron(tm) Processor 2352 2.1 GHz. In the case of a continuous trait, a similar run takes 9 days. Our program found 14 SNP-SNP interactions with a multiple-testing corrected p-value of less than 0.05 on real-life Crohn’s disease (CD) data. Conclusions: Our software is the first implementation of the MB-MDR methodology able to solve large-scale SNP-SNP interactions problems within a few days, without using much memory, while adequately controlling the type I error rates. A new implementation to reach genome-wide epistasis screening is under construction. In the context of Crohn’s disease, MBMDR-3.0.3 could identify epistasis involving regions that are well known in the field and could be explained from a biological point of view. This demonstrates the power of our software to find relevant phenotype-genotype higher-order associations.

Randomized comparison of biodegradable polymer sirolimus-eluting stents versus durable polymer everolimus-eluting stents for percutaneous coronary revascularization: Rationale and design of the BIOSCIENCE trial.

BACKGROUND: Biodegradable polymers for release of antiproliferative drugs from metallic drug-eluting stents aim to improve long-term vascular healing and efficacy. We designed a large scale clinical trial to compare a novel thin strut, cobalt-chromium drug-eluting stent with silicon carbide-coating releasing sirolimus from a biodegradable polymer (O-SES, Orsiro; Biotronik, Bülach, Switzerland) with the durable polymer-based Xience Prime/Xpedition everolimus-eluting stent (EES) (Xience Prime/Xpedition stent, Abbott Vascular, IL) in an all-comers patient population. DESIGN: The multicenter BIOSCIENCE trial (NCT01443104) randomly assigned 2,119 patients to treatment with biodegradable polymer sirolimus-eluting stents (SES) or durable polymer EES at 9 sites in Switzerland. Patients with chronic stable coronary artery disease or acute coronary syndromes, including non-ST-elevation and ST-elevation myocardial infarction, were eligible for the trial if they had at least 1 lesion with a diameter stenosis >50% appropriate for coronary stent implantation. The primary end point target lesion failure (TLF) is a composite of cardiac death, target vessel myocardial infarction, and clinically driven target lesion revascularization within 12 months. Assuming a TLF rate of 8% at 12 months in both treatment arms and accepting 3.5% as a margin for noninferiority, inclusion of 2,060 patients would provide more than 80% power to detect noninferiority of the biodegradable polymer SES compared with the durable polymer EES at a 1-sided type I error of 0.05. Clinical follow-up will be continued through 5 years. CONCLUSION: The BIOSCIENCE trial will determine whether the biodegradable polymer SES is noninferior to the durable polymer EES with respect to TLF.

Data-division-specific robustness and power of randomization tests for ABAB designs

This study deals with the statistical properties of a randomization test applied to an ABAB design in cases where the desirable random assignment of the points of change in phase is not possible. In order to obtain information about each possible data division we carried out a conditional Monte Carlo simulation with 100,000 samples for each systematically chosen triplet. Robustness and power are studied under several experimental conditions: different autocorrelation levels and different effect sizes, as well as different phase lengths determined by the points of change. Type I error rates were distorted by the presence of autocorrelation for the majority of data divisions. Satisfactory Type II error rates were obtained only for large treatment effects. The relationship between the lengths of the four phases appeared to be an important factor for the robustness and the power of the randomization test.

Regression-based techniques for statistical decision making in single-case designs

The present study evaluates the performance of four methods for estimating regression coefficients used to make statistical decisions regarding intervention effectiveness in single-case designs. Ordinary least squares estimation is compared to two correction techniques dealing with general trend and one eliminating autocorrelation whenever it is present. Type I error rates and statistical power are studied for experimental conditions defined by the presence or absence of treatment effect (change in level or in slope), general trend, and serial dependence. The results show that empirical Type I error rates do not approximate the nominal ones in presence of autocorrelation or general trend when ordinary and generalized least squares are applied. The techniques controlling trend show lower false alarm rates, but prove to be insufficiently sensitive to existing treatment effects. Consequently, the use of the statistical significance of the regression coefficients for detecting treatment effects is not recommended for short data series.

Fast and Rigorous Computation of Gene and Pathway Scores from SNP-Based Summary Statistics.

Integrating single nucleotide polymorphism (SNP) p-values from genome-wide association studies (GWAS) across genes and pathways is a strategy to improve statistical power and gain biological insight. Here, we present Pascal (Pathway scoring algorithm), a powerful tool for computing gene and pathway scores from SNP-phenotype association summary statistics. For gene score computation, we implemented analytic and efficient numerical solutions to calculate test statistics. We examined in particular the sum and the maximum of chi-squared statistics, which measure the strongest and the average association signals per gene, respectively. For pathway scoring, we use a modified Fisher method, which offers not only significant power improvement over more traditional enrichment strategies, but also eliminates the problem of arbitrary threshold selection inherent in any binary membership based pathway enrichment approach. We demonstrate the marked increase in power by analyzing summary statistics from dozens of large meta-studies for various traits. Our extensive testing indicates that our method not only excels in rigorous type I error control, but also results in more biologically meaningful discoveries.

Redundancy gain : manifestations, causes and predictions

Les temps de réponse dans une tache de reconnaissance d’objets visuels diminuent de façon significative lorsque les cibles peuvent être distinguées à partir de deux attributs redondants. Le gain de redondance pour deux attributs est un résultat commun dans la littérature, mais un gain causé par trois attributs redondants n’a été observé que lorsque ces trois attributs venaient de trois modalités différentes (tactile, auditive et visuelle). La présente étude démontre que le gain de redondance pour trois attributs de la même modalité est effectivement possible. Elle inclut aussi une investigation plus détaillée des caractéristiques du gain de redondance. Celles-ci incluent, outre la diminution des temps de réponse, une diminution des temps de réponses minimaux particulièrement et une augmentation de la symétrie de la distribution des temps de réponse. Cette étude présente des indices que ni les modèles de course, ni les modèles de coactivation ne sont en mesure d’expliquer l’ensemble des caractéristiques du gain de redondance. Dans ce contexte, nous introduisons une nouvelle méthode pour évaluer le triple gain de redondance basée sur la performance des cibles doublement redondantes. Le modèle de cascade est présenté afin d’expliquer les résultats de cette étude. Ce modèle comporte plusieurs voies de traitement qui sont déclenchées par une cascade d’activations avant de satisfaire un seul critère de décision. Il offre une approche homogène aux recherches antérieures sur le gain de redondance. L’analyse des caractéristiques des distributions de temps de réponse, soit leur moyenne, leur symétrie, leur décalage ou leur étendue, est un outil essentiel pour cette étude. Il était important de trouver un test statistique capable de refléter les différences au niveau de toutes ces caractéristiques. Nous abordons la problématique d’analyser les temps de réponse sans perte d’information, ainsi que l’insuffisance des méthodes d’analyse communes dans ce contexte, comme grouper les temps de réponses de plusieurs participants (e. g. Vincentizing). Les tests de distributions, le plus connu étant le test de Kolmogorov- Smirnoff, constituent une meilleure alternative pour comparer des distributions, celles des temps de réponse en particulier. Un test encore inconnu en psychologie est introduit : le test d’Anderson-Darling à deux échantillons. Les deux tests sont comparés, et puis nous présentons des indices concluants démontrant la puissance du test d’Anderson-Darling : en comparant des distributions qui varient seulement au niveau de (1) leur décalage, (2) leur étendue, (3) leur symétrie, ou (4) leurs extrémités, nous pouvons affirmer que le test d’Anderson-Darling reconnait mieux les différences. De plus, le test d’Anderson-Darling a un taux d’erreur de type I qui correspond exactement à l’alpha tandis que le test de Kolmogorov-Smirnoff est trop conservateur. En conséquence, le test d’Anderson-Darling nécessite moins de données pour atteindre une puissance statistique suffisante.

An adaptive approach to implementing bivariate group sequential clinical trial designs

In clinical trials, situations often arise where more than one response from each patient is of interest; and it is required that any decision to stop the study be based upon some or all of these measures simultaneously. Theory for the design of sequential experiments with simultaneous bivariate responses is described by Jennison and Turnbull (Jennison, C., Turnbull, B. W. (1993). Group sequential tests for bivariate response: interim analyses of clinical trials with both efficacy and safety endpoints. Biometrics 49:741-752) and Cook and Farewell (Cook, R. J., Farewell, V. T. (1994). Guidelines for monitoring efficacy and toxicity responses in clinical trials. Biometrics 50:1146-1152) in the context of one efficacy and one safety response. These expositions are in terms of normally distributed data with known covariance. The methods proposed require specification of the correlation, ρ between test statistics monitored as part of the sequential test. It can be difficult to quantify ρ and previous authors have suggested simply taking the lowest plausible value, as this will guarantee power. This paper begins with an illustration of the effect that inappropriate specification of ρ can have on the preservation of trial error rates. It is shown that both the type I error and the power can be adversely affected. As a possible solution to this problem, formulas are provided for the calculation of correlation from data collected as part of the trial. An adaptive approach is proposed and evaluated that makes use of these formulas and an example is provided to illustrate the method. Attention is restricted to the bivariate case for ease of computation, although the formulas derived are applicable in the general multivariate case.

Incorporating data received after a sequential trial has stopped into the final analysis: implementation and comparison of methods

In a sequential clinical trial, accrual of data on patients often continues after the stopping criterion for the study has been met. This is termed “overrunning.” Overrunning occurs mainly when the primary response from each patient is measured after some extended observation period. The objective of this article is to compare two methods of allowing for overrunning. In particular, simulation studies are reported that assess the two procedures in terms of how well they maintain the intended type I error rate. The effect on power resulting from the incorporation of “overrunning data” using the two procedures is evaluated.

An adaptive group sequential design for phase II/III clinical trials that select a single treatment from several

There is increasing interest in combining Phases II and III of clinical development into a single trial in which one of a small number of competing experimental treatments is ultimately selected and where a valid comparison is made between this treatment and the control treatment. Such a trial usually proceeds in stages, with the least promising experimental treatments dropped as soon as possible. In this paper we present a highly flexible design that uses adaptive group sequential methodology to monitor an order statistic. By using this approach, it is possible to design a trial which can have any number of stages, begins with any number of experimental treatments, and permits any number of these to continue at any stage. The test statistic used is based upon efficient scores, so the method can be easily applied to binary, ordinal, failure time, or normally distributed outcomes. The method is illustrated with an example, and simulations are conducted to investigate its type I error rate and power under a range of scenarios.

A practical comparison of group-sequential and adaptive designs

Sequential methods provide a formal framework by which clinical trial data can be monitored as they accumulate. The results from interim analyses can be used either to modify the design of the remainder of the trial or to stop the trial as soon as sufficient evidence of either the presence or absence of a treatment effect is available. The circumstances under which the trial will be stopped with a claim of superiority for the experimental treatment, must, however, be determined in advance so as to control the overall type I error rate. One approach to calculating the stopping rule is the group-sequential method. A relatively recent alternative to group-sequential approaches is the adaptive design method. This latter approach provides considerable flexibility in changes to the design of a clinical trial at an interim point. However, a criticism is that the method by which evidence from different parts of the trial is combined means that a final comparison of treatments is not based on a sufficient statistic for the treatment difference, suggesting that the method may lack power. The aim of this paper is to compare two adaptive design approaches with the group-sequential approach. We first compare the form of the stopping boundaries obtained using the different methods. We then focus on a comparison of the power of the different trials when they are designed so as to be as similar as possible. We conclude that all methods acceptably control type I error rate and power when the sample size is modified based on a variance estimate, provided no interim analysis is so small that the asymptotic properties of the test statistic no longer hold. In the latter case, the group-sequential approach is to be preferred. Provided that asymptotic assumptions hold, the adaptive design approaches control the type I error rate even if the sample size is adjusted on the basis of an estimate of the treatment effect, showing that the adaptive designs allow more modifications than the group-sequential method.

Sequentially testing for a gene-drug interaction in a genomewide analysis

Assaying a large number of genetic markers from patients in clinical trials is now possible in order to tailor drugs with respect to efficacy. The statistical methodology for analysing such massive data sets is challenging. The most popular type of statistical analysis is to use a univariate test for each genetic marker, once all the data from a clinical study have been collected. This paper presents a sequential method for conducting an omnibus test for detecting gene-drug interactions across the genome, thus allowing informed decisions at the earliest opportunity and overcoming the multiple testing problems from conducting many univariate tests. We first propose an omnibus test for a fixed sample size. This test is based on combining F-statistics that test for an interaction between treatment and the individual single nucleotide polymorphism (SNP). As SNPs tend to be correlated, we use permutations to calculate a global p-value. We extend our omnibus test to the sequential case. In order to control the type I error rate, we propose a sequential method that uses permutations to obtain the stopping boundaries. The results of a simulation study show that the sequential permutation method is more powerful than alternative sequential methods that control the type I error rate, such as the inverse-normal method. The proposed method is flexible as we do not need to assume a mode of inheritance and can also adjust for confounding factors. An application to real clinical data illustrates that the method is computationally feasible for a large number of SNPs. Copyright (c) 2007 John Wiley & Sons, Ltd.

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.

Detecting the node-density artifact in phylogeny reconstruction

The node-density effect is an artifact of phylogeny reconstruction that can cause branch lengths to be underestimated in areas of the tree with fewer taxa. Webster, Payne, and Pagel (2003, Science 301:478) introduced a statistical procedure (the "delta" test) to detect this artifact, and here we report the results of computer simulations that examine the test's performance. In a sample of 50,000 random data sets, we find that the delta test detects the artifact in 94.4% of cases in which it is present. When the artifact is not present (n = 10,000 simulated data sets) the test showed a type I error rate of approximately 1.69%, incorrectly reporting the artifact in 169 data sets. Three measures of tree shape or "balance" failed to predict the size of the node-density effect. This may reflect the relative homogeneity of our randomly generated topologies, but emphasizes that nearly any topology can suffer from the artifact, the effect not being confined only to highly unevenly sampled or otherwise imbalanced trees. The ability to screen phylogenies for the node-density artifact is important for phylogenetic inference and for researchers using phylogenetic trees to infer evolutionary processes, including their use in molecular clock dating. [Delta test; molecular clock; molecular evolution; node-density effect; phylogenetic reconstruction; speciation; simulation.]