An approach to comparing treatments based on repeated measures

Simulating Correlated Ordinal and Discrete Variables with Assigned Marginal Distributions

“…Therefore several multiple comparison approaches have been proposed but the method based on one degree of freedom chi-squared statistic is less informative and the result of the analysis is often difficult to interpret since the degrees of freedom for interaction is usually so large. Therefore the row-and/or column-wise multiple comparisons have been proposed in Hirotsu (1983) and verified to be useful in several occasions as compared with other multiple comparison approaches, see Greenacre (1988) and Hirotsu (1991Hirotsu ( , 1993. The multiple comparison procedure proposed is essentially the Scheffe type based on the generalized squared distances among rows and the reference distribution is that of the largest root of the Wishart matrix.…”

Isotonic Inference

“…The goodness-of-fit χ 2 has been compared with the fitting of the proportionalodds model [51] and its extension [33]; see [20] for details. The Scheffé-type multiple comparison method is applied to the normal distribution model in [21], for classifying subjects based on the upward, flat, and downward tendencies defined by repeated measurements. with the χ 2 ij being the goodness-of-fit χ 2 for the 2 × 2 tables obtained from partitioning and accumulating rows and columns at i = 1, .…”

A classification of circadian blood pressure profiles using a cumulative chi-squared technique

“…The analysis consisted of two mathematical techniques: one was the application of a cumulative chisquared test (see Appendix) to the ordered quantitative data; the other was the utilization of the ® rst-order difference for detecting a serial trend such as an upward,¯at, or downward pattern [10].…”

“…However, if the categories are expressed in a ordinal scale such as ( ± absent), (¡ equivocal) and (z present), a cumulative chi-squared statistic (x *2 ) has been reported to be more powerful as a test-statistic than a standard chisquared statistic (x 2 ) [14,15]. Hirotsu has applied the cumulative chi-squared statistic to ordered quantitative data as well as to ordered categorical data [10]. For instance, the ordered quantitative data of subjects X and Y are denoted by (x1, x2, x3, x4) and (y1, y2, y3, y4), respectively.…”

“…One possible approach would be to classify them based on the concave-convex shape of the circadian variation. To that end, we describe a new method of pro® le analysis for the evaluation of BP variability, which was originally used as a method for the objective determination of the effectiveness of anti-hyperlipidemic therapy [10]. In patients with hypercholesterolemia, Hirotsu identi® ed three patterns of changes in the serum cholesterol concentration after anti-hyperlipidemic treatment into: decreased (i.e.…”