Halperin M, Hamdy M I, Thall P F
Biostatistics Center, Statistics/Computer and Information Systems Department, George Washington University, Rockville, Maryland 20852.
Biometrics. 1989 Jun;45(2):509-21.
Halperin, Gilbert, and Lachin (1987, Biometrics 43, 71-80) obtain confidence intervals for Pr(X less than Y) based on the two-sample Wilcoxon statistic for continuous data. Their approach is applied here to ordered categorical data and right-censored continuous data, using the generalization zeta = Pr(X less than Y) + 1/2Pr(X = Y) to account for ties. Deviations from nominal coverage probability for various sample sizes and values of zeta are obtained via simulation of either three or six ordered categories based on underlying Poisson or exponential distributions. The simulation results indicate that the proposed method performs quite well, and it is apparently superior to the approach of Hochberg (1981, Communications in Statistics--Theory and Methods A10, 1719-1732) for values of zeta far from 1/2.
哈尔珀林、吉尔伯特和拉钦（1987年，《生物统计学》43卷，71 - 80页）基于连续数据的两样本威尔科克森统计量获得了Pr(X小于Y)的置信区间。他们的方法在此应用于有序分类数据和右删失连续数据，使用广义zeta = Pr(X小于Y) + 1/2Pr(X = Y)来处理 ties。通过基于潜在泊松或指数分布对三个或六个有序类别进行模拟，得到了不同样本量和zeta值下与名义覆盖概率的偏差。模拟结果表明，所提出的方法表现相当好，并且对于远离1/2的zeta值，它明显优于霍赫贝格（1981年，《统计通信——理论与方法》A10卷，1719 - 1732页）的方法。
