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Results for “multiple testing”

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PubMed1983

Further results on a multiple-testing procedure for clinical trials.

O'Brien and Fleming (1979, Biometrics 35, 549-556) proposed a procedure for multiple testing in clinical trials for acute disease. We evaluated their procedure for chronic-disease models and found that it can be used without modification. Type I errors are unaltered and no loss of power is seen in comparison with single-sample procedures. However, average savings in sample size are less for the chronic-disease models than for the acute model. Finally, it is shown that for any specific disease model and fixed maximum number of inspections of the data, the percentage reduction in sample size can be readily predicted from the power.

Biometry↗

PubMed1987

Chemical detection of leukocytes in urine by means of a new multiple test strip.

The performance of the leukocyte test area of the new multiple urine test strip, Multistix-10-SG, was evaluated in both field trials and model experiments. The detection limit was found to be adequate for routine purposes. Unspecific reactions are rare and generally indicated by the results of the other test areas.

False Positive Reactions↗

PubMed1996

Adjusting for multiple testing when reporting research results: the Bonferroni vs Holm methods.

Public health researchers are sometimes required to make adjustments for multiple testing in reporting their results, which reduces the apparent significance of effects and thus reduces statistical power. The Bonferroni procedure is the most widely recommended way of doing this, but another procedure, that of Holm, is uniformly better. Researchers may have neglected Holm's procedure because it has been framed in terms of hypothesis test rejection rather than in terms of P values. An adjustment to P values based on Holm's method is presented in order to promote the method's use in public health research.

Animals↗

PubMed1984

Multiple testing of hypotheses in comparing two groups.

Researchers frequently encounter studies that compare two groups on many variables. We discourage the use of multiple tests of hypotheses on individual variables, an approach that ignores the correlation among the variables and increases the chance of a type I error. Instead of examining each variable separately, we recommend using multivariate procedures that integrate all measures on a person into a unified analysis of the differences between the two groups. We describe three multivariate procedures: Hotelling's T2, discriminant analysis, and logistic regression. We also discuss the use of Bonferroni's adjustment to preserve the overall chance of a type I error in conducting individual tests on each variable after doing the multivariate procedures. We review the underlying assumptions and relative merits and disadvantages of the three multivariate methods and recommend which method to use in various circumstances.

Analysis of Variance↗

PubMed2004

Multiple testing. Part II. Step-down procedures for control of the family-wise error rate.

The present article proposes two step-down multiple testing procedures for asymptotic control of the family-wise error rate (FWER): the first procedure is based on maxima of test statistics (step-down maxT), while the second relies on minima of unadjusted p-values (step-down minP). A key feature of our approach is the characterization and construction of a test statistics null distribution (rather than data generating null distribution) for deriving cut-offs for these test statistics (i.e., rejection regions) and the resulting adjusted p-values. For general null hypotheses, corresponding to submodels for the data generating distribution, we identify an asymptotic domination condition for a null distribution under which the step-down maxT and minP procedures asymptotically control the Type I error rate, for arbitrary data generating distributions, without the need for conditions such as subset pivotality. Inspired by this general characterization, we then propose as an explicit null distribution the asymptotic distribution of the vector of null value shifted and scaled test statistics. Step-down procedures based on consistent estimators of the null distribution are shown to also provide asymptotic control of the Type I error rate. A general bootstrap algorithm is supplied to conveniently obtain consistent estimators of the null distribution.

Journal Article↗

PubMed2004

Simple solution to a common statistical problem: interpreting multiple tests.

BACKGROUND: The misinterpretation of the results of multiple statistical tests is an error commonly made in scientific literature. When testing several outcome variables simultaneously, many researchers declare a statistically significant result for each test having a P value of <0.05, for example. This approach ignores the fact that, based on a probability result called the Bonferroni inequality, the risk of incorrectly declaring as significant > or =1 test result increases with the number of tests conducted. The implication of this practice is that many scientific results are presented as statistically significant when the underlying data do not adequately support such a claim (sometimes referred to as false-positive results). Although the sequentially rejective Bonferroni test is well known among statisticians, it is not used routinely in scientific literature. OBJECTIVE: The intent of this article was to increase the awareness and understanding of the sequentially rejective Bonferroni test, thereby expanding its use. METHODS: This article describes the statistical problem and demonstrates how the use of the sequentially rejective Bonferroni test ensures that incorrect declarations of statistical significance for > or =1 test result are bounded by 0.05, for example. CONCLUSION: The sequentially rejective Bonferroni test is an easily applied, versatile statistical tool that enables researchers to make simultaneous inferences from their data without risking an unacceptably high overall type I error rate.

Confidence Intervals↗

PubMed1985

[Problems of multiple tests and evaluations in drug research].

The well known inferential statistical procedures only take into account the test of a single hypothesis or the estimation of a single parameter. In practical drug research the scientist in most cases is interested in multiple tests of several hypotheses or a simultaneous estimation of several parameters. After introducing the principal problems of simultaneous statistical inference several statistical methods are discussed. These methods can be applied to a variety of problems in drug research.

Pharmacology↗

PubMed1984

HLA and disease: relative-risk regression methods and multiple testing considerations.

This paper discusses certain statistical issues arising in an analysis to relate HLA-B antigens to the incidence of graft-versus-host disease in a clinical study. The Cox regression method is used to develop a global test of the hypothesis of no association and to produce estimated relative-risk factors corresponding to the presence of each particular allele. Multiple-testing considerations are central to any attempt to identify pairs of alleles having significantly different relative-risk factors. A number of simultaneous-testing approaches are considered including cumulative P-value plotting and a direct simulation of the null distribution of the maximum pairwise ratio.

Anemia, Aplastic↗

PubMed2003

Importance sampling method of correction for multiple testing in affected sib-pair linkage analysis.

Using the Genetic Analysis Workshop 13 simulated data set, we compared the technique of importance sampling to several other methods designed to adjust p-values for multiple testing: the Bonferroni correction, the method proposed by Feingold et al., and naïve Monte Carlo simulation. We performed affected sib-pair linkage analysis for each of the 100 replicates for each of five binary traits and adjusted the derived p-values using each of the correction methods. The type I error rates for each correction method and the ability of each of the methods to detect loci known to influence trait values were compared. All of the methods considered were conservative with respect to type I error, especially the Bonferroni method. The ability of these methods to detect trait loci was also low. However, this may be partially due to a limitation inherent in our binary trait definitions.

Computer Simulation↗

PubMed1975

Single-channel autoanalyzer adpated for multiple tests without manifold changes.

A different approach to continuous-flow analysis is described, in which the initial reagent concentration is adjusted to fit a prefixed manifold while still providing optimum concentrations of the reactants in the mixing coils. A single-channel AutoAnalyzer so designed can perform multiple tests without the need to change manifolds. The system was assembled from a Technicon Sampler II and Pump II, a gilford 300 N spectrophotometer, and a Varian recorder. Results for calcium, uric acid, glucose, phosphorus, chloride, urea nitrogen, and carbon dioxide, analyzed on this instrument at a speed of 60 samples/h, compare favorably with those obtained with the AutoAnalyzer 12/60 and 6/60. The instrument is not restricted to certain methodologies and, in addition, can be used manually or for kinetic reactions.

Autoanalysis↗

PubMed2005

New concepts of multiple tests and their use for evaluating high-dimensional EEG data.

Recently, new concepts of type I error control in multiple comparisons have been proposed, in addition to FWE and FDR control. We introduce these criteria and investigate in simulations how the powers of corresponding test procedures for multiple endpoints depend on various quantities such as number and correlation of endpoints, percentage of false hypotheses, etc. We applied the different multiple tests to EEG coherence data. We compared the memory encoding of subsequently recalled and not recalled nouns. The results show that subsequently recalled nouns elicited significantly higher coherence than not recalled ones.

Acoustic Stimulation↗

PubMed1982

One-sample multiple testing procedure for phase II clinical trials.

Commonly, the central objective of Phase II clinical trials is the assessment of the antitumor 'therapeutic efficacy' of a specific treatment regimen. It is of interest to formulate test procedures which can be employed in these trials to decide whether or not this therapeutic efficacy warrants further investigation. For ethical reasons, these procedures should allow for early termination if initial results are extreme. In this paper, a one-sample multiple testing procedure is proposed which employs the standard single-stage test procedure at the last test, and which both allows for early termination and essentially preserves the size, power and simplicity of the single-stage procedure.

Clinical Trials as Topic↗

PubMed1989

A discussion on the conventional estimator of sensitivity and specificity in multiple tests.

Both the variation of positive responses (negative responses) among individuals and the internal correlation among responses for the same individual affect the precision of the estimate of sensitivity (specificity). To estimate the sensitivity (specificity) of a medical diagnostic test, this paper proposes a Bayesian approach with a simple Markov model to evaluate the performance of the conventional estimator under different situations. On the basis of the assumed model, we derive a general formula for the variance of the conventional estimator regarding multiple tests and present a quantitative discussion on the limitations of this estimator.

Analysis of Variance↗

PubMed2005

Hierarchical inverse Gaussian models and multiple testing: application to gene expression data.

Detecting differentially expressed genes in microarray experiments is a topic that has been well studied in the literature. Many hypothesis testing methods have been proposed that rely on strong distributional assumptions for the gene intensities. However, the shape of microarray data may vary substantially from one experiment to another, and model assumptions may be seriously violated in many cases. The literature on microarray data is mainly based on two distributions: the log-normal and the gamma distributions, that often appear to be effective when used in a Bayesian hierarchical framework. However, if a model that fits the data well in a global manner seems attractive, two points should be regarded with attention: the ability of the model to fit the tail of the observed distribution, and its robustness to a wrong specification of the model, in terms of error rates for the hypothesis tests. In order to focus on these aspects, we propose to use Bayesian models involving the inverse Gaussian distribution to describe gene expression data. We show that these models can be good competitors to the traditional Bayesian or random effect gamma or log-normal models in some situations. A multiple testing procedure is then proposed, based on an asymptotic property of the posterior probability of the one-sided alternative hypothesis. We show that the asymptotic property is well approximated for inverse Gaussian models, even when the number of observations available for each test is very small.

Journal Article↗

PubMed2000

Identifying the maximum safe dose: a multiple testing approach.

Identifying the maximum safe dose (MAXSD) is an objective of both randomized clinical dose-finding studies for the safety endpoint and toxicological studies. MAXSD is defined as the highest experimental dose with no significant increased safety effect relative to the placebo or control group. In safety assessment, the primary control of the false-negative error rate is more important than that of the false-positive rate. Therefore, we propose a multiple testing procedure for equivalence in the many-to-one design with a priori ordered contrasts (shifted control vs. dose), where the acceptable risk delta is defined in advance. Tests for shifted and ratio hypotheses are presented and discussed.

Animals↗

PubMedDate not supplied

Effects of maternal environment and postnatal multiple testing on adult rat offspring.

Two hundred thirty Wistar rats, obtained from undisturbed mothers and from mothers that were exposed to temporary isolation and/or laparotomy, were randomly exposed to three of the following specific behavioral test procedures: (1) conditioned avoidance response, (2) water T-maze, (3) open field, (4) activity wheel, (5) forelimb hanging, and (6) swimming. Performance of the offspring was examined during adulthood. Effects of previous testing on later testing performance and performance correlation between the two testing procedures were analyzed. The results indicate that (1) the maternal conditions manipulated in this study do not significantly affect behavior in the adult offspring (p greater than 0.05), and (2) performance of a previous task by the offspring does not significantly alter, and is not correlated with, the performance level on a second, unrelated task. Therefore, within these parameters, rats can be used for multiple testing procedures in a more practical and less costly means of behavioral investigation. These findings may be useful in the development and refinement of postnatal developmental toxicological screening procedures for agents that may be harmful to humans.

Animals↗

PubMed2006

Construction of null statistics in permutation-based multiple testing for multi-factorial microarray experiments.

MOTIVATION: The parametric F-test has been widely used in the analysis of factorial microarray experiments to assess treatment effects. However, the normality assumption is often untenable for microarray experiments with small replications. Therefore, permutation-based methods are called for help to assess the statistical significance. The distribution of the F-statistics across all the genes on the array can be regarded as a mixture distribution with a proportion of statistics generated from the null distribution of no differential gene expression whereas the other proportion of statistics generated from the alternative distribution of genes differentially expressed. This results in the fact that the permutation distribution of the F-statistics may not approximate well to the true null distribution of the F-statistics. Therefore, the construction of a proper null statistic to better approximate the null distribution of F-statistic is of great importance to the permutation-based multiple testing in microarray data analysis. RESULTS: In this paper, we extend the ideas of constructing null statistics based on pairwise differences to neglect the treatment effects from the two-sample comparison problem to the multifactorial balanced or unbalanced microarray experiments. A null statistic based on a subpartition method is proposed and its distribution is employed to approximate the null distribution of the F-statistic. The proposed null statistic is able to accommodate unbalance in the design and is also corrected for the undue correlation between its numerator and denominator. In the simulation studies and real biological data analysis, the number of true positives and the false discovery rate (FDR) of the proposed null statistic are compared with those of the permutated version of the F-statistic. It has been shown that our proposed method has a better control of the FDRs and a higher power than the standard permutation method to detect differentially expressed genes because of the better approximated tail probabilities.

Algorithms↗

PubMed2003

Comparison of methods for estimating the number of true null hypotheses in multiplicity testing.

When a large number of statistical tests is performed, the chance of false positive findings could increase considerably. The traditional approach is to control the probability of rejecting at least one true null hypothesis, the familywise error rate (FWE). To improve the power of detecting treatment differences, an alternative approach is to control the expected proportion of errors among the rejected hypotheses, the false discovery rate (FDR). When some of the hypotheses are not true, the error rate from either the FWE- or the FDR-controlling procedure is usually lower than the designed level. This paper compares five methods used to estimate the number of true null hypotheses over a large number of hypotheses. The estimated number of true null hypotheses is then used to improve the power of FWE- or FDR-controlling methods. Monte Carlo simulations are conducted to evaluate the performance of these methods. The lowest slope method, developed by Benjamini and Hochberg (2000) on the adaptive control of the FDR in multiple testing with independent statistics, and the mean of differences method appear to perform the best. These two methods control the FWE properly when the number of nontrue null hypotheses is small. A data set from a toxicogenomic microarray experiment is used for illustration.

Animals↗