Multivariate Mann–Whitney Estimators for the Comparison of Two Treatments in a Three-Period Crossover Study with Randomly Missing Data

Kawaguchi, Atsushı; Koch, Gary G.

doi:10.1080/10543401003618108

Cited by 13 publications

(10 citation statements)

References 14 publications

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“…The comparison of HRV parameters between girls and boys was made with the non-parametric Mann-Whitney test. To address the issue of potential interaction between age and children's sex in the Man-Whitney test we controlled for the age factor by carrying out the stratified van Elteren's test, which is an extension of the Man-Whitney test (Kawaguchi and Koch, 2010, 2015). All children were divided into three age groups, i.e., 3–6 years old corresponding to early childhood (Group 1); 7–12 years old corresponding to preadolescence (Group 2); and 13–18 years old, i.e., adolescence (Group 3).…”

Section: Methodsmentioning

confidence: 99%

Measures of Heart Rate Variability in 24-h ECGs Depend on Age but Not Gender of Healthy Children

et al. 2017

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Many methods computing heart rate variability (HRV) have been applied in studies in children. Not all of these methods have a comprehensive physiological interpretation, and not all of studies are in agreement with the Task Force Standards on HRV from 1996, and the New Joint Position Statement on the advances of HRV from 2015. The study aim was to analyse HRV in the 24-h ECGs of healthy children by the Poincare plots and Lomb-Scargle periodograms, and to follow proper HRV recommendations. Additionally, we investigated the associations between age, children's sex and measured HRV indices. One hundred healthy children, aged 3–18 underwent 24-h ECG Holter monitoring. HRV was analyzed by the Poincaré plots and spectral by Lomb-Scargle periodograms of RR intervals. The Mann-Whitney test was used to compare sex differences in HRV, the van Elteren's test was used to correct for the age-gender interaction, and non-parametric Spearman correlation was applied to analyse the association between age and HRV indices. None of the HRV measures differed significantly between boys and girls. None of the HRV indices was modified by the age-gender interaction. There were statistically significant associations of age with measures of ultra-low (rho = 0.42; p < 0.0001), very low (rho = 0.35; p = 00004) and low (rho = 0.30; p = 0.0028) frequency powers, the ratio of the low to high frequency power (rho = 0.38; p = 0.0001), indices of long-term (SD2; rho = 0.37; p = 0.0002) and total (SDNN; rho = 0.33; p = 0.0008) HRV, and the contribution of the long-term HRV to total HRV (CL; rho = 0.32; p = 0.0012). In general, HRV parameters derived from the analyses of Poincaré plots and Lomb-Scargle periodograms appear not to be affected by gender, however, most of them increase with age in the 24-h ECG recordings in healthy children.

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Section: Methodsmentioning

confidence: 99%

Measures of Heart Rate Variability in 24-h ECGs Depend on Age but Not Gender of Healthy Children

et al. 2017

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“…Also, simulation studies of Carr et al (1989) and Kawaguchi and Koch (2010) support somewhat better statistical properties for the use of this logit transformation than the actual Mann-Whitney estimator when the actual MannWhitney estimator is further from its null value of 0.5. Another strategy that can improve the statistical properties of the methods in this article for adjusted MannWhitney estimators is to multiply the applicable covariance matrices by (N − 1)/(N − q − r − M) and then to use t distributions with d.f.…”

Section: Discussionmentioning

confidence: 86%

“…= (N − q − r − M) for confidence intervals and F distributions with d.f. = (c, N − q − r − M) for testing contrasts with rank c. Simulation studies concerning these modifications were discussed by Kawaguchi and Koch (2010) for a version of the methods in this article for a crossover study with four groups and no stratification.…”

Section: Discussionmentioning

confidence: 98%

“…As noted by Carr, Hafner, and Koch (1989), Koch (1998, 1999), and Kawaguchi and Koch (2010), such logit transformations correspond to the Fisher (1925) transformation of Somers' version of the Kendall Tau rank correlation coefficient. Also, simulation studies of Carr et al (1989) and Kawaguchi and Koch (2010) support somewhat better statistical properties for the use of this logit transformation than the actual Mann-Whitney estimator when the actual MannWhitney estimator is further from its null value of 0.5.…”

Section: Discussionmentioning

confidence: 99%

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Stratified Multivariate Mann–Whitney Estimators for the Comparison of Two Treatments with Randomization Based Covariance Adjustment

Kawaguchi

Koch²,

Wang

2011

Statistics in Biopharmaceutical Research

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Methodology for comparing two randomly assigned treatments for strictly ordinal response variables has been discussed throughout the literature on multivariate Mann-Whitney estimators with stratification adjustment. Although such estimators can be computed directly as weighted linear combinations of within-stratum Mann-Whitney estimators, consistent estimation of their covariance matrix is done using methods for multivariate U-statistics. The scope of these methods includes ways of managing randomly missing data and ways to invoke randomization-based covariance adjustment for no differences between treatments for background or baseline covariables. The assessment of treatment differences can be done using confidence intervals or statistical tests for the adjusted Mann-Whitney estimators. The methods in this article are illustrated using three examples. The first example is a randomized clinical trial with eight strata and a univariate ordinal response variable. The second example is a randomized clinical trial with four strata, two covariables, and four ordinal response variables. The third example is a randomized two-period crossover clinical trial with four strata, three covariables (as age, screening, first baseline), three response variables (as first period response, second baseline, second period response), and missing data. For these examples, the results are interpretable through the probability of better outcomes for one treatment over the other.

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“…In crossover design, as one patient can receive more than one treatment during the trial, proper use of intra-subject comparison (for example, Wallenstein and Fisher, 1977;Hafner et al, 1988;Elswick and Uthoff, 1989;Putt and Chinchilli, 2004) reduces the bias due to different subjects and at the same time may give larger power than that obtained from inter-subject comparison (for example, Koch, 1972;Jung and Koch, 1999;Kawaguchi et al, 2009;Kawaguchi and Koch, 2010) while testing for the difference between treatment effects. On the other hand, intra-subject evaluation becomes impracticable in the presence of possible carryover effects especially for multiperiod crossover design accounting a large number of parameters.…”

Section: Testsmentioning

confidence: 99%

Three‐period, two‐treatment crossover design under long‐term carryover effect

Chatterjee¹,

Bandyopadhyay

2017

Statistica Neerlandica

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The paper describes non‐parametric approach for analysis of a three‐period, two‐treatment, four‐sequence crossover design in which test procedure for interchangeability of the treatment effects is obtained. The proposed procedure is based on a non‐parametric model, which incorporates, along with the direct treatment effects and the usual carryover effects, the long‐term carryover effects. Relevant competitors are obtained. Related asymptotic results are given. By performing simulation study, we compared the procedures with respect to type I error rate and power. Furthermore, confidence intervals for treatment differences are studied. The procedures are illustrated with a data study.

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Multivariate Mann–Whitney Estimators for the Comparison of Two Treatments in a Three-Period Crossover Study with Randomly Missing Data

Cited by 13 publications

References 14 publications

Measures of Heart Rate Variability in 24-h ECGs Depend on Age but Not Gender of Healthy Children

Measures of Heart Rate Variability in 24-h ECGs Depend on Age but Not Gender of Healthy Children

Stratified Multivariate Mann–Whitney Estimators for the Comparison of Two Treatments with Randomization Based Covariance Adjustment

Three‐period, two‐treatment crossover design under long‐term carryover effect

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