Step-up Procedure Research Articles

A self-calibrating instrument current transformer

This paper presents the development of a self-calibrating transformer for using as a primary standard in the Uruguayan National Metrology Institute. Nominal ratios go from 5A/5A to 2000A/5A. The primary windings are divided in groups to allow different ratios by changing their combinations in series–parallel connections, so that the errors remain the same. In ratio 1 (5A/5A) the transformer can be calibrated without any external standard, and a step-up procedure is proposed. Low errors are achieved by using a modified zero-flux technique.

The Interval Property in Multiple Testing of Pairwise Differences

The usual step-down and step-up multiple testing procedures most often lack an important intuitive, practical, and theoretical property called the interval property. In short, the interval property is simply that for an individual hypothesis, among the several to be tested, the acceptance sections of relevant statistics are intervals. Lack of the interval property is a serious shortcoming. This shortcoming is demonstrated for testing various pairwise comparisons in multinomial models, multivariate normal models and in nonparametric models. Residual based stepwise multiple testing procedures that do have the interval property are offered in all these cases.

Development and Validation of a Behavioral Acclimation Protocol for Cats to Respiration Chambers Used for Indirect Calorimetry Studies

Cats exposed to novel environments initiate stress responses by behavioral and physiological changes that modify metabolism and lead to the collection of unreliable data. Fourteen cats (10 ± 2 months) were subjected to an 11-week acclimation procedure to adapt to restriction within chambers used for indirect calorimetry studies. Cats were acclimated to chambers in their home environments, to chambers in the study room, and to increasing periods of restriction within chambers. Ten additional cats (11 ± 1 month), used as controls, were subjected to a single 5-hr restriction without any prior exposure. Stress level, feed intake, fearfulness, and eliminations were recorded. Latencies to approach a novel object peaked on Weeks 4 and 8 (p < .05). Cat-Stress-Scores (CSS) declined with exposure and on Week 11, stress levels were low and consistent (p < .05). CSS was greater in unacclimated versus acclimated cats (p < .05). In conclusion, acclimation protocols prepare cats for repeated, temporary restriction within chambers, whereas short acclimations do not. A step-up acclimation procedure with behavioral indices of stress should be utilized to prepare cats for research that necessitates restriction.

Step-up procedure controlling generalized family-wise error rate

This paper aims at developing a powerful step-up procedure controlling the generalized family-wise error rate (k-FWER) in multiple hypotheses testing, based on the least favorable configuration of k-FWER. Simulation studies suggest improvement over some existing methods.

A Package to Study the Performance of Step-Up and Step-Down Test Procedures

The package can be used to analyze the performance of step-up and step-down procedures. It can be used to compare powers, calculate the “false discovery rate”, to study the effects of reduced step procedures, and to calculate P [U ≤ k], where U is the number of rejected true hypotheses. It can be used to determine the maximum number of steps that can be made and still guarantee (with a given probability) that the number of false rejections will not exceed some specified number. The test statistics are assumed to have a multivariate-t distribution. Examples are included.

Using information mining of the medical literature to improve drug safety

Prescription drugs can be associated with adverse effects (AEs) that are unrecognized despite evidence in the medical literature, as shown by rofecoxib's late recall in 2004. We assessed whether applying information mining to PubMed could reveal major drug-AE associations if articles testing whether drugs cause AEs are over-represented in the literature. MEDLINE citations published between 1949 and September 2009 were retrieved if they mentioned one of 38 drugs and one of 55 AEs. A statistical document classifier (using MeSH index terms) was constructed to remove irrelevant articles unlikely to test whether a drug caused an AE. The remaining relevant articles were analyzed using a disproportionality analysis that identified drug-AE associations (signals of disproportionate reporting) using step-up procedures developed to control the familywise type I error rate. Sensitivity and positive predictive value (PPV) for empirical drug-AE associations as judged against drug-AE associations subject to FDA warnings. In testing, the statistical document classifier identified relevant articles with 81% sensitivity and 87% PPV. Using data filtered by the statistical document classifier, base-case models showed 64.9% sensitivity and 42.4% PPV for detecting FDA warnings. Base-case models discovered 54% of all detected FDA warnings using literature published before warnings. For example, the rofecoxib-heart disease association was evident using literature published before 2002. Analyses incorporating literature mentioning AEs common to the drug class of interest yielded 71.4% sensitivity and 40.7% PPV. Results from large-scale literature retrieval and analysis (literature mining) compared favorably with and could complement current drug safety methods.

Exact calculations for false discovery proportion with application to least favorable configurations

In a context of multiple hypothesis testing, we provide several new exact calculations related to the false discovery proportion (FDP) of step-up and step-down procedures. For step-up procedures, we show that the number of erroneous rejections conditionally on the rejection number is simply a binomial variable, which leads to explicit computations of the c.d.f., the {$s$-th} moment and the mean of the FDP, the latter corresponding to the false discovery rate (FDR). For step-down procedures, we derive what is to our knowledge the first explicit formula for the FDR valid for any alternative c.d.f. of the $p$-values. We also derive explicit computations of the power for both step-up and step-down procedures. These formulas are "explicit" in the sense that they only involve the parameters of the model and the c.d.f. of the order statistics of i.i.d. uniform variables. The $p$-values are assumed either independent or coming from an equicorrelated multivariate normal model and an additional mixture model for the true/false hypotheses is used. This new approach is used to investigate new results which are of interest in their own right, related to least/most favorable configurations for the FDR and the variance of the FDP.

Sample size determination in step‐up testing procedures for multiple comparisons with a control

Step-up procedures have been shown to be powerful testing methods in clinical trials for comparisons of several treatments with a control. In this paper, a determination of the optimal sample size for a step-up procedure that allows a pre-specified power level to be attained is discussed. Various definitions of power, such as all-pairs power, any-pair power, per-pair power and average power, in one- and two-sided tests are considered. An extensive numerical study confirms that square root allocation of sample size among treatments provides a better approximation of the optimal sample size relative to equal allocation. Based on square root allocation, tables are constructed, and users can conveniently obtain the approximate required sample size for the selected configurations of parameters and power. For clinical studies with difficulties in recruiting patients or when additional subjects lead to a significant increase in cost, a more precise computation of the required sample size is recommended. In such circumstances, our proposed procedure may be adopted to obtain the optimal sample size. It is also found that, contrary to conventional belief, the optimal allocation may considerably reduce the total sample size requirement in certain cases. The determination of the required sample sizes using both allocation rules are illustrated with two examples in clinical studies.

On stepwise control of the generalized familywise error rate

A classical approach for dealing with a multiple testing problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of at least one false rejection. In many applications, one might be willing to tolerate more than one false rejection provided the number of such cases is controlled, thereby increasing the ability of a procedure to detect false null hypotheses. This suggests replacing control of the FWER by controlling the probability of k or more false rejections, which is called the k-FWER. In this article, a unified approach is presented for deriving the k-FWER controlling procedures. We first generalize the well-known closure principle in the context of the FWER to the case of controlling the k-FWER. Then, we discuss how to derive the k-FWER controlling stepup procedures based on marginal p-values using this principle. We show that, under certain conditions, generalized closed testing procedures can be reduced to stepup procedures, and any stepup procedure is equivalent to a generalized closed testing procedure. Finally, we generalize the well-known Hommel procedure in two directions, and show that any generalized Hommel procedure is equivalent to a generalized closed testing procedure with the same critical values.

Testing multiple outcomes in repeated measures designs.

This study investigates procedures for controlling the familywise error rate (FWR) when testing hypotheses about multiple, correlated outcome variables in repeated measures (RM) designs. A content analysis of RM research articles published in 4 psychology journals revealed that 3 quarters of studies tested hypotheses about 2 or more outcome variables. Several procedures originally proposed for testing multiple outcomes in 2-group designs are extended to 2-group RM designs. The investigated procedures include 2 modified Bonferroni procedures that adjust the level of significance, alpha, for the effective number of outcomes and a permutation step-down (PSD) procedure. The FWR, any-variable power, and all-variable power are investigated in a Monte Carlo study. One modified Bonferroni procedure frequently resulted in inflated FWRs, whereas the PSD procedure controlled the FWR. The PSD procedure could be substantially more powerful than the conventional Bonferroni procedure, which does not account for dependencies among the outcome variables. However, the difference in power between the PSD procedure, which does account for these dependencies, and Hochberg's step-up procedure, which does not, were negligible. A numeric example illustrates implementation of these multiple-testing procedures.

From Defibrillation Theory to Clinical Implications

Our defibrillation theory claims that the mean voltage threshold is a hyperbolic function of pulse duration and that voltages below rheobase should be avoided as being counterproductive. Truncation of the pulse just at rheobase level yields minimal stored energy thresholds. To verify or falsify this theory, animal experiments were carried out. In two animal experiments, 212 defibrillation thresholds in 22 swine were determined with different biphasic pulses of which 92 were optimally truncated in phase 1. Step-up test procedure was used with the first successful shock defined as "threshold." Experimental proof is gained that truncation according to "rheobase condition" shows lowest stored energy. A ranking order of stored energy thresholds demonstrates that (1) lower output capacitances reduce needed energy, and (2) pulse durations shorter or longer than optimal increase needed energy. The voltage-pulse-content threshold is linearly correlated with pulse duration. Truncation above or below rheobase increases the stored energy threshold. Voltage averaged during pulse duration is a hyperbolic function of pulse duration. The stored energy is reduced with decreasing output capacitance. The experimental results do not only fully verify our theory, they also suggest clinical implications: (1) the current usage of the "constant tilt concept" in implantable cardioverter defibrillator (ICD) should be abandoned in favor of "optimal truncation concept," (2) an algorithm developed for calculating optimal truncation proved to be useful so that incorporation into ICD for automatic adjustment is recommended, and (3) the output capacitance should be reduced from about 100 microF to 60 to 70 microF.

Flexible Regression Model Selection for Survival Probabilities: With Application to AIDS

Clinicians are often interested in the effect of covariates on survival probabilities at prespecified study times. Because different factors can be associated with the risk of short- and long-term failure, a flexible modeling strategy is pursued. Given a set of multiple candidate working models, an objective methodology is proposed that aims to construct consistent and asymptotically normal estimators of regression coefficients and average prediction error for each working model, that are free from the nuisance censoring variable. It requires the conditional distribution of censoring given covariates to be modeled. The model selection strategy uses stepup or stepdown multiple hypothesis testing procedures that control either the proportion of false positives or generalized familywise error rate when comparing models based on estimates of average prediction error. The context can actually be cast as a missing data problem, where augmented inverse probability weighted complete case estimators of regression coefficients and prediction error can be used (Tsiatis, 2006, Semiparametric Theory and Missing Data). A simulation study and an interesting analysis of a recent AIDS trial are provided.

An adaptive step-down procedure with proven FDR control under independence

In this work we study an adaptive step-down procedure for testing m hypotheses. It stems from the repeated use of the false discovery rate controlling the linear step-up procedure (sometimes called BH), and makes use of the critical constants iq/[(m+1−i(1−q)], i=1, …, m. Motivated by its success as a model selection procedure, as well as by its asymptotic optimality, we are interested in its false discovery rate (FDR) controlling properties for a finite number of hypotheses. We prove this step-down procedure controls the FDR at level q for independent test statistics. We then numerically compare it with two other procedures with proven FDR control under independence, both in terms of power under independence and FDR control under positive dependence.

Step-Up Tests for Comparing Several Exponential Populations with Control: Location Case

SYNOPTIC ABSTRACTLet π1…, πk be k treatments/ populations which are to be compared with a control treatment π0. We assume that an observation from population πi follows exponential distribution with probability density function (pdf) , where IA(.) is an indicator function of event A, θ is the common scale parameter and μi is the location parameter, (i = 0, 1, … k. In this paper, the problem of comparing several exponential populations/treatments with a control, in terms of their location parameters, is addressed by simultaneously testing k hypotheses on differences γi = πi, i = 1, …, k by using a step-up test procedure. A method for computing exact critical constants, which control the Type-I family-wise error rate at a preassigned level α, is discussed for one-sided and two-sided testing problems. The required constants are tabulated for specific values of the Type-I family-wise error rate and application of these constants to Pareto probability model is discussed.

A Method to Compute Multiplicity Corrected Confidence Intervals for Odds Ratios and Other Relative Effect Estimates

Epidemiological studies commonly test multiple null hypotheses. In some situations it may be appropriate to account for multiplicity using statistical methodology rather than simply interpreting results with greater caution as the number of comparisons increases. Given the one-to-one relationship that exists between confidence intervals and hypothesis tests, we derive a method based upon the Hochberg step-up procedure to obtain multiplicity corrected confidence intervals (CI) for odds ratios (OR) and by analogy for other relative effect estimates. In contrast to previously published methods that explicitly assume knowledge of P values, this method only requires that relative effect estimates and corresponding CI be known for each comparison to obtain multiplicity corrected CI.

Estudo prospectivo comparativo de duas modalidades de posicionamento do sensor de phmetria esofágica prolongada: por manometria esofágica e pela viragem do Ph

By internationally accepted standardization, the esophageal pH-meter distal sensor is positioned 5 cm above the superior border of the lower esophageal sphincter, identified by esophageal manometry. However, several authors suggest alternative positioning techniques that leave out the manometry; among such techniques, the pH step-up is the one to be pointed out. This subject is controversial; some publications state that the step-up technique is not reliable while some others consider it reliable. Considering the existent controversy and the small number of prospective works with suitable sample and methodology, we have idealized the present study, that aims the evaluation of the suitability of the pH-meter distal sensor positioning based on the step-up technique, by analyzing the presence, the type and the degree of the error of positioning that such technique provides and the influence of the position adopted by the patient during the procedure. One thousand and thirty one patients conducted to the esophageal pH-meter procedure were studied in a prospective way. During the clinical interview, the demographic data and the presented clinical complaints were registered. All the patients were submitted to both esophageal manometry in order to localize the lower esophageal sphincter and the pH step-up technique, that consists of the introduction of the pH-meter sensor in the gastric chamber and in the sensor's gradual traction until the pH steps up to levels over 4. The step-up point was identified by two distinct ways, characterizing two study groups: with the sitting patient (group I - 450 patients) and with the patient in supine position (group II - 581 patients). After the step-up point identification, the pH-meter distal sensor was placed in the standard position (based on the sphincter manometric placement). It was registered where the pH sensor would be positioned if the step-up technique were adopted. To evaluate the positioning suitability, the error was considered to be represented by the difference (in centimeters) between the suitable placement (manometry) and the one that would be adopted in case the step-up technique were adopted. The positioning error was considered rough if it were larger than 2 cm. The most frequent type of error was also analyzed (if above or below the standard position). It was observed that if the step-up technique were adopted, there would be error in the sensor positioning in 945 patients (91.6%). In terms of error degree, there would be a rough error in 597 (63.2%) cases. Concerning the type of error, the sensor would be positioned below the standard place in 857 (90.7%) patients. As to the interference of the position adopted by the patient during the step-up technique, it was observed that there was no significant difference among the groups of study in any of the analyzed parameters. 1. The positioning of the pH-meter distal sensor by the step-up technique is not reliable; 2. the step-up technique provides expressive error margin; 3. the most common type of error that such technique mode provides is the placement of the sensor below the standard positioning, which may overestimate the reflux occurrence; 4. there is no influence in the position adopted by the patient during the pH step-up technique procedure, in terms of method efficiency.

Adaptive control of the false discovery rate in voxel‐based morphometry

Voxel-based morphometry (VBM) is widely used as a high-resolution approach to understanding the relationship between anatomical structures and variables of interest. Controlling for the false discovery rate (FDR) is an attractive choice for thresholding the resulting statistical maps and has been commonly used in fMRI studies. However, we caution against the use of nonadaptive FDR control procedures, such as the most commonly used Benjamini-Hochberg procedure (B-H), in VBM analyses. This is because, in VBM analyses, specific risk factors may be associated with volume change in a global, rather than local, manner, which means the proportion of truly associated voxels among all voxels is large. In such a case, the achieved FDR obtained by nonadaptive procedures can be substantially lower than the nominal, or controlled, level. Such conservatism deprives researchers of power for detecting true associations. In this article, we advocate for the use of adaptive FDR control in VBM-type analyses. Specifically, we examine two representative adaptive procedures: the two-stage step-up procedure by Benjamini, Krieger and Yekutieli (2006: Biometrika 93:491-507) and the procedure of Storey and Tibshirani ([2003]: Proc Natl Acad Sci USA 100:9440-9445). We demonstrate mathematically, with simulations, and with a data example that these procedures provide improved performance over the B-H procedure.

Metrology of Viscosity: Have We Learned Enough?

Viscosity is one of the most important properties for many technological and scientific applications, and therefore it has been the subject of an enormous effort of measurement, correlation, and interpretation. This effort is completely inconsistent with the fact that it is probably the fluid property with less independent reference values that can be used by most of the everyday users as guidance, calibration, or designing tools. The only accepted standard, the viscosity of pure water at 20 °C, is unsatisfactory because the viscosity among different fluids can vary by a factor of 1014. Its application in the current step-up procedures to produce certified reference materials of higher viscosity, although useful for industrial purposes, degrades the desired small uncertainty of these values. An analysis of the metrology status for Newtonian liquids viscosity, including the best available measurement methods, applicable ranges, existing reference data, uncertainties, and traceability of the measurements to the SI, is made. The discussion assumes in general the internationally accepted definitions of uncertainty.

Resampling‐Based Empirical Bayes Multiple Testing Procedures for Controlling Generalized Tail Probability and Expected Value Error Rates: Focus on the False Discovery Rate and Simulation Study

This article proposes resampling-based empirical Bayes multiple testing procedures for controlling a broad class of Type I error rates, defined as generalized tail probability (gTP) error rates, gTP (q,g) = Pr(g (V(n),S(n)) > q), and generalized expected value (gEV) error rates, gEV (g) = E [g (V(n),S(n))], for arbitrary functions g (V(n),S(n)) of the numbers of false positives V(n) and true positives S(n). Of particular interest are error rates based on the proportion g (V(n),S(n)) = V(n) /(V(n) + S(n)) of Type I errors among the rejected hypotheses, such as the false discovery rate (FDR), FDR = E [V(n) /(V(n) + S(n))]. The proposed procedures offer several advantages over existing methods. They provide Type I error control for general data generating distributions, with arbitrary dependence structures among variables. Gains in power are achieved by deriving rejection regions based on guessed sets of true null hypotheses and null test statistics randomly sampled from joint distributions that account for the dependence structure of the data. The Type I error and power properties of an FDR-controlling version of the resampling-based empirical Bayes approach are investigated and compared to those of widely-used FDR-controlling linear step-up procedures in a simulation study. The Type I error and power trade-off achieved by the empirical Bayes procedures under a variety of testing scenarios allows this approach to be competitive with or outperform the Storey and Tibshirani (2003) linear step-up procedure, as an alternative to the classical Benjamini and Hochberg (1995) procedure.

Step-Up Procedure for Multiple Comparison with a Control for Multivariate Normal Means

In this study, we consider the multiple comparison with a control for multivariate normal means. Specifically, we construct a step-up procedure by referring to Dunnett and Tamhane (1992). We derive recursive formulae for determining the critical values of the step-up procedure for a specified significance level. Then we formulate the power of the test. Finally, we compare the step-up procedure with the single-step procedure proposed by Nakamura and Imada (2005) and the step-down procedure proposed by Imada and Douke (2007) in terms of numerical examples regarding the power of the test.