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A note on one-sided tests with multiple endpoints.

Testing problems with multivariate one-sided alternative hypotheses are common in clinical trials with multiple endpoints. In the case of comparing two treatments, treatment 1 is often preferred if it is superior for at least one of the endpoints and not biologically inferior for the remaining endpoints. Bloch et al. (2001, Biometrics57, 1039-1047) propose an intersection-union test (IUT) for this testing problem, but their test does not utilize the appropriate multivariate one-sided test. In this note we modify their test by an alternative IUT that does utilize the appropriate one-sided test. Empirical and graphical evidence show that the proposed test is more appropriate for this testing problem.

Biometry↗

The Multiple Tasks Test: development and normal strategies.

Simultaneous challenge of posture and cognition ("dual tasks") may predict falls better than tests of isolated components of postural control. We describe a new balance test (the Multiple Tasks Test, MTT) which (1) is based upon simultaneous assessment of multiple (>2) postural components; (2) represents everyday situations; and (3) can be applied by clinicians. Relevant risk factors for falls and actual fall circumstances (identified from a prospective survey in Parkinson's disease) were used to design functional tests (or postural "components") that resembled everyday situations. We distinguished a "cognitive" component (answering serial questions) from largely "motor" components (standing up, sitting down, turning around, walking, avoiding obstacles, and touching the floor). Four additional components included carrying an empty or loaded tray, wearing shoes with slippery soles and reduced illumination. These components were combined to yield eight separate tasks of increasing complexity that were executed sequentially. The first and simplest task consisted of standing up, undisturbed walking, turning around and sitting down. For each of the next tasks, a new component was added to the earlier and otherwise identical task. All components within each task had to be performed simultaneously. Errors were defined as Hesitations (slowed performance) or Blocks (complete cessation), which were scored separately for execution of motor and cognitive components. Speed of performance was not stressed, but was measured for all tasks. The MTT was administered to 50 young healthy subjects (mean age 27.6 years) and 13 elderly subjects (mean age 62.0 years). To study learning effects, 20 different young subjects (mean age 21.0 years) received the MTT in order of gradually decreasing complexity. For subjects who received the MTT in order of increasing difficulty, 62% in both age groups performed all eight tasks without any Errors in the motor components. Among those making Errors, the proportion of subjects that made motor Errors increased significantly as the tasks became more complex (F(1,7)=2.66, P<0.05). This increase differed across the two groups (significant interaction of Group by Task; F(1,7)=3.07, P=0.01) because more elderly subjects produced motor Errors during the most complex tasks. Cognitive Errors increased even more than motor Errors with task complexity, and this increase was most pronounced in young subjects (significant interaction of Group by Error Type by Task; F(1,1,7)=3.85, P=0.001). Only eight young (16%) and four elderly subjects (30.8%) performed the MTT without any motor or cognitive Errors, again suggesting that more young subjects made cognitive Errors. Among subjects who received the MTT in reverse order, motor errors were more common than among subjects who received the MTT in order of increasing complexity (F(1,7)=5.90, P<0.05), particularly during the two most difficult tasks. The elderly performed all tasks slower than the young subjects. We conclude that the MTT is a new balance test based upon a multiple task design that resembles everyday situations. Performance by healthy subjects revealed interesting insights into normal postural strategies. For complex postural tasks, healthy subjects favour execution of motor components over execution of a cognitive component ("posture first" strategy). Young subjects were more inclined than elderly subjects to use this strategy. Motor learning influenced performance among subjects who received the MTT in order of increasing difficulty. Further studies must determine whether the MTT can be used to evaluate balance disorders.

Accidental Falls↗

[Method for calculating the distribution of randomly expected scores in a false-true-do not know-type of test].

Multiple choice tests have been used widely in the evaluation of knowledge. The lowest passing limit is generally chosen arbitrarily. Better and more objective criteria may arise from analyzing the distribution of correct and incorrect answers as expected by chance. In order to calculate the distribution of correct answers and the difference between correct and incorrect answers (core) we propose the use of a method based on a gaussian distribution. The distribution of scores expected by chance is approximated by a gaussian distribution with a mean of zero and a standard deviation SD = square root of n(pA + pE), and the distribution of the total number of correct answers has a mean of npA and SD = square root of npApE, where n is the total number of questions, and pA and pE are the probabilities of having a correct and an incorrect answer, respectively. The formulae are applicable to questions type false/true/do not know and to the more common type of one correct in five options. Once the chance distribution is known, it can be compared with the distribution of scores or correct answers obtained, which can then be used to separate people in two groups: those that answer the test as expected or worse than expected by chance, and those that answer the test better than expected by chance. The first group should not be passed. The passing of individuals in the second group can be decided by additional criteria.

Educational Measurement↗

Writing a multiple-choice test question.

Multiple-choice test questions are the most widely used and highly regarded of the presently available objective or selective test items. They can be used to test all levels of learning and are applicable to the measurement of most important educational outcomes. Although it is difficult to construct these questions well, they are versatile and can be used in settings involving large numbers of students.

Education, Medical, Graduate↗

Peritz' F test: basic program of a robust multiple comparison test for statistical analysis of all differences among group means.

Peritz' F test has previously been found to be the most robust statistical multiple comparison test able to hold all comparisons among group means to a given experimentwise error rate. A BASIC program which will perform this test quickly on a desk-top microcomputer, needing fewer than 11 kbytes of RAM memory, is presented. The program is run in the author's laboratory using an inexpensive VIC-20 computer.

Computers↗

Evaluation of the microcolumn technology for pretransfusion testing in multiple myeloma patients.

OBJECTIVE: Microcolumn tests are useful for serological investigations, although because of their high sensitivity, false-positive results might be expected, e.g. in hypergammaglobulinemia. The aim of this study was to evaluate these tests in multiple myeloma. METHODS: Pretransfusion testing was done in 80 patients with multiple myeloma using microcolumn and traditional tube tests. RESULTS: All sera were negative in microcolumn indirect antiglobulin test and enzyme test, positive in 58% of samples in the enzyme tube test. The microcolumn direct antiglobulin test was positive in about 40% of samples but never in the tube direct antiglobulin test. This was not due to the presence of autoantibodies but to nonspecific binding of immunoglobulins related to their concentration in sera. CONCLUSION: Microcolumn tests appeared to be useful for pretransfusion testing in multiple myeloma in spite of positive autocontrols.

Adult↗

Semi-supervised discovery of differential genes.

BACKGROUND: Various statistical scores have been proposed for evaluating the significance of genes that may exhibit differential expression between two or more controlled conditions. However, in many clinical studies to detect clinical marker genes for example, the conditions have not necessarily been controlled well, thus condition labels are sometimes hard to obtain due to physical, financial, and time costs. In such a situation, we can consider an unsupervised case where labels are not available or a semi-supervised case where labels are available for a part of the whole sample set, rather than a well-studied supervised case where all samples have their labels. RESULTS: We assume a latent variable model for the expression of active genes and apply the optimal discovery procedure (ODP) proposed by Storey (2005) to the model. Our latent variable model allows gene significance scores to be applied to unsupervised and semi-supervised cases. The ODP framework improves detectability by sharing the estimated parameters of null and alternative models of multiple tests over multiple genes. A theoretical consideration leads to two different interpretations of the latent variable, i.e., it only implicitly affects the alternative model through the model parameters, or it is explicitly included in the alternative model, so that the interpretations correspond to two different implementations of ODP. By comparing the two implementations through experiments with simulation data, we have found that sharing the latent variable estimation is effective for increasing the detectability of truly active genes. We also show that the unsupervised and semi-supervised rating of genes, which takes into account the samples without condition labels, can improve detection of active genes in real gene discovery problems. CONCLUSION: The experimental results indicate that the ODP framework is effective for hypotheses including latent variables and is further improved by sharing the estimations of hidden variables over multiple tests.

Algorithms↗

Gatekeeping procedures in dose-response clinical trials based on the Dunnett test.

This paper discusses multiple testing procedures in dose-response clinical trials with primary and secondary endpoints. A general gatekeeping framework for constructing multiple tests is proposed, which extends the Dunnett test [Journal of the American Statistical Association 1955; 50: 1096-1121] and Bonferroni-based gatekeeping tests developed by Dmitrienko et al. [Statistics in Medicine 2003; 22:2387-2400]. The proposed procedure accounts for the hierarchical structure of the testing problem; for example, it restricts testing of secondary endpoints to the doses for which the primary endpoint is significant. The multiple testing approach is illustrated using a dose-response clinical trial in patients with diabetes. Monte-Carlo simulations demonstrate that the proposed procedure provides a power advantage over the Bonferroni gatekeeping procedure. The power gain generally increases with increasing correlation among the endpoints, especially when all primary dose-control comparisons are significant.

Clinical Trials as Topic↗

[Multiple significance tests and their importance in the judging of results. A quality analysis of the journal Strahlentherapie und Onkologie].

BACKGROUND: The statistical quality of the contributions to "Strahlentherapie und Onkologie" is assessed, aiming for improvement of the journal and consequently its impact factor. MATERIAL AND METHODS: All 181 articles published during 1998 and 1999 in the categories "review", "original contribution", and "short communication" were analyzed concerning the appropriate use of multiple tests. RESULT: One hundred and four publications were excluded from analysis, because they did not contain quantitative data or because no or only 1 statistical test was performed. In 77 publications multiple tests were done which was adequately considered in only 3 of these papers, corresponding to a fraction of 4% (95% CI: 0.8 to 11%). CONCLUSION: Authors, peer reviewers, and editors could contribute to improve the quality of the journal by setting value on correction for multiple tests.

Bibliometrics↗

Controlling the proportion of false positives in multiple dependent tests.

Genome scan mapping experiments involve multiple tests of significance. Thus, controlling the error rate in such experiments is important. Simple extension of classical concepts results in attempts to control the genomewise error rate (GWER), i.e., the probability of even a single false positive among all tests. This results in very stringent comparisonwise error rates (CWER) and, consequently, low experimental power. We here present an approach based on controlling the proportion of false positives (PFP) among all positive test results. The CWER needed to attain a desired PFP level does not depend on the correlation among the tests or on the number of tests as in other approaches. To estimate the PFP it is necessary to estimate the proportion of true null hypotheses. Here we show how this can be estimated directly from experimental results. The PFP approach is similar to the false discovery rate (FDR) and positive false discovery rate (pFDR) approaches. For a fixed CWER, we have estimated PFP, FDR, pFDR, and GWER through simulation under a variety of models to illustrate practical and philosophical similarities and differences among the methods.

Chromosome Mapping↗

Evaluating hypotheses on the origin and evolution of the New Zealand alpine cicadas (Maoricicada) using multiple-comparison tests of tree topology.

The statistical testing of alternative phylogenetic trees is central to evaluating competing evolutionary hypotheses. Fleming proposed that the New Zealand cicada species Maoricicada iolanthe is the sister species to the major radiation of both low-altitude and montane Maoricicada species. However, using 1,520 bp of mitochondrial DNA sequence data from the cytochrome oxidase subunit I, tRNA aspartic acid, and the ATPase subunit 6 and 8 genes, we inferred that both M. iolanthe and another low-altitude species, Maoricicada campbelli, are nested within the montane Maoricicada radiation. Therefore, we examined the stability of the inferred phylogenetic placement of these two species using the newly developed Shimodaira-Hasegawa test (SH test) implemented in a maximum-likelihood framework. The SH test has two advantages over the more commonly used Kishino-Hasegawa (KH) and Templeton tests. First, the SH test simultaneously compares multiple topologies and corrects the corresponding P: values to accommodate the multiplicity of testing. Second, the SH test is correct when applied to a posteriori hypotheses, unlike the KH test, because it readjusts the expectation of the null hypothesis (that two trees are not different) accordingly. The comparison of P: values estimated under the assumptions of both the KH test and the SH test clearly demonstrate that the KH test has the potential to be misleading when the issue of comparing of a posteriori hypotheses is ignored and when multiple comparisons are not taken into account. The SH test, in combination with a variety of character-weighting schemes applied to our data, reveals a surprising amount of ambiguity in the phylogenetic placement of M. iolanthe and M. campbelli.

Animals↗

HLA-DR3 associated genetic control of response to multiple skin tests with new tuberculins.

Multiple skin testing with mycobacterial antigenic preparations reveals distinct reaction patterns, which might be relevant to the development of mycobacterial disease in man. Previous work has shown that HLA-DR associated factors correlate with the position of a leprosy patient in the immunopathological spectrum of leprosy. This study was undertaken to see whether these skin test patterns in healthy persons do show any association with HLA-DR types. Out of a group of 74 healthy Caucasoid individuals HLA-DR3 was observed to be absent from the 16 individuals who did not respond to any of the mycobacterial antigens tested. This is a striking difference from the distribution of HLA-DR3 both among the 17 individuals who responded to all mycobacterial antigens tested (P = 0.005) and the 41 individuals who responded to some but not all antigens (P = 0.015). These data show that an HLA-DR3 associated genetic factor controls, albeit indirectly, skin test responsiveness to mycobacterial antigens. It may be significant that this same HLA-DR determinant is implicated in deciding the type of disease to be developed by a leprosy patient.

Genes, MHC Class II↗

Changes in non-specific immune responses induced by repeated delayed-type hypersensitivity skin testing with multiple antigens.

Delayed-type hypersensitivity (DTH) responses following in vivo multiple-antigen skin testing in healthy individuals have been well described as indicators of immune responsiveness. In contrast, little information is available about how repeated in vivo multiple antigen skin testing could effect major non-specific parameters of immune responses. In a prospective study of 22 healthy adult volunteers, DTH skin tests were performed 6 times at 4-week intervals over a 28-week course. Prior to each skin test, blood specimens were collected and evaluated by in vitro assays of non-specific parameters related to humoral and cell-mediated immune (CMI) responses. Sustained effects of repeated skin tests in the volunteers included decreased numbers of circulating polymorphonuclear leukocytes (PMNLs), increased serum IgM levels and decreased DTH responses in those individuals originally designated as high DTH responders. Increased lymphocyte transformation with PHA was transiently observed in the study group at 4-12 weeks into the study. In contrast, numbers of T, B and total lymphocytes, levels of IgG, IgA, and circulating immune complexes, and serum blocking activity did not change. This study suggests that few alterations in non-specific immune parameters may be expected to occur in normal, adult individuals as a result of repeated multiple-antigen skin tests.

Adolescent↗

Confidence intervals and p-values for Williams' and other step-down multiple comparison tests against control.

When single-step multiple comparison tests against control, such as Dunnett's test, are used, p-values and confidence intervals can be reported. However, Williams' test and other step-down multiple comparison tests only provide results in terms of statistical significance. In this paper, approximate confidence intervals are proposed for some step-down multiple comparison tests and their coverage properties are assessed by simulation; p-values are readily calculated. The proposed simultaneous confidence intervals associated with Williams' test, Dunnett's step-down test, and the closed t test are all found to have good coverage, typically between 94% and 96% for a nominal value of 95%. Thus practicing statisticians can now quote p-values for these tests and use simple confidence intervals to aid interpretation of test results.

Computer Simulation↗