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We know from the literature that

  • The Wilcoxon-Mann-Whitney two-sample rank sum test is optimal for detecting simple location shifts when comparing two continuous random variables that each have a logistic distribution
  • The Wilcoxon test is a special case of the semiparametric proportional odds ordinal logistic model, e.g., the numerator of the score test for testing $\beta_{1}=0$ in this model, when there is only a single covariate and it is binary, is exactly the rank sum statistic (this is a generalization of the first bullet)

Do we know that the most general way to state that the Wilcoxon test has optimum power in a given situation with continuous $Y$ is when the two distributions are in proportional odds, e.g., logit$(F(x))$ is parallel to logit$(G(x))$?

As a slight aside, we know that the log-rank statistic, a special case of the Cox proportional hazards semiparametric regression model, has optimum performance when proportional hazards is true (just like its generalization).

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