Analysis of Rank Measures of Association for Ordinal Data from Longitudinal Studies

Carr, Gregory J.; Hafner, Kerry B.; Koch, Gary G.

doi:10.2307/2289669

Cited by 16 publications

(14 citation statements)

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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: 89%

“…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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Section: Discussionmentioning

confidence: 89%

Section: Discussionmentioning

confidence: 99%

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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“…(2), Dˆ is a diagonal matrix with the quantitiesˆ = Dˆ 1 −ˆ on the main diagonal (with D a generally representing a diagonal matrix with a on the diagonal). As noted in Koch (1998, 1999), the logit transformation producing f is comparable to the Fisher (1925) transformation of Somers' (1962) version of the Kendall tau rank correlation and thereby enhances applicability of multivariate normal approximations via central limit theory; see Carr et al (1989). When the responses for groups i and i during period k have non-negative continuous distributions that are in the proportional hazards family with hazard ratio ii k for group i versus group i, then ii k = 0 − d dy S ik y S ik y ii k dy = 1/ 1 + ii k where S ik y represents the "survivorship function" for group i at period k (i.e., probabilities of response ≥y).…”

Section: Methodsmentioning

confidence: 95%

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

Kawaguchi

Koch

2010

Journal of Biopharmaceutical Statistics

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This paper discusses the application of multivariate Mann-Whitney estimators to the comparison of two treatments for a strictly ordinal response variable in a crossover study with four sequence groups and three periods. Ways of managing randomly missing data and nonparametric covariance adjustment for no differences among groups for a baseline period have consideration as well. Estimators pertaining to treatment comparisons in linear logistic models for the Mann-Whitney estimators have determination through a Bradley-Terry model for dimension reduction and weighted least squares. These estimators can be the basis for both statistical tests and confidence intervals. The methods in this paper have their results presented for an example. Simulation studies for the methods show that they have reasonable control of type 1 error and power.

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“…One way to address the dilemmas for parametric model fitting involves using a nonparametric method for the primary evaluation of treatment comparisons (4,10,11), and then the supportive use of a parametric model to describe the nature and extent of treatment effects and to evaluate the homogeneity of treatment effects across subgroups (10,11,12). It should be noted that using a parametric model in a supportive secondary role may require a posteriori modification in order to improve compatibility with the observed data.…”

Section: Methodsmentioning

confidence: 99%

Nonparametric Analysis of Covariance and Its Role in Noninferiority Clinical Trials

Koch

Tangen

1999

Drug Information J

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Some randomized clinical trials are conducted to compare test treatment, an active reference control, and placebo with the objectives of demonstrating that test treatment is not inferior to reference control, and to show that both test treatment and reference control are better than placebo. We typically want to adjust for covariables that are strongly associated with the response of interest in order to gain variance reduction, to adjust for random imbalances of covariables, and to clarify the degree to which differences between randomized groups are due to treatments rather than other factors associated with response.Parametric modeling is often used to evaluate the relationship between covariables and the conditional distributions of response given the covariables. There can be concerns, however; about model assumptions, and they are not always straightforward to assess. An alternative is to use a nonparametric method for the primary evaluation of treatment comparisons. The nonparametric method is performed through linear models for (unconditional) differences between treatment groups for means of response criteria (or functions of such means) and covariables jointly with specifications that adjust random differences for means of covariables to zero. This paper discusses the role of nonparametric analysis of covariance in clinical trials to compare test treatment, an active reference control, and placebo with three examples.

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Analysis of Rank Measures of Association for Ordinal Data from Longitudinal Studies

Cited by 16 publications

References 0 publications

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

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

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

Nonparametric Analysis of Covariance and Its Role in Noninferiority Clinical Trials

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