Testing Ordered Alternatives in the Presence of Incomplete Data

A generalized Jonckheere test against ordered alternatives for repeated measures in randomized blocks

Focusing on statistical methods in patient-reported outcomes, we propose and develop a generalized Jonckheere test against ordered alternatives for repeated measures in a randomized block design. We derive its asymptotic null distribution properties and describe methods for estimating the null distribution for testing the hypothesis. We present a numerical example to illustrate the test procedure.

A Nonparametric Procedure for the Two-Factor Mixed Model with Missing Data

We develop a nonparametric imputation technique to test for the treatment effects in a nonparametric two-factor mixed model with incomplete data. Within each block, an arbitrary covariance structure of the repeated measurements is assumed without the explicit parametrization of the joint multivariate distribution. The number of repeated measurements is uniformly bounded whereas the number of blocks tends to infinity. The essential idea of the nonparametric imputation is to replace the unknown indicator functions of pairwise comparisons by the corresponding empirical distribution functions. The proposed nonparametric imputation method holds valid under the missing completely at random (MCAR) mechanism. We apply the nonparametric imputation on Brunner and Dette's method for the nonparametric two-factor mixed model and this extension results in a weighted partial rank transform statistic. Asymptotic relative efficiency of the nonparametric imputation method with the complete data versus the incomplete data is derived to quantify the efficiency loss due to the missing data. Monte Carlo simulation studies are conducted to demonstrate the validity and power of the proposed method in comparison with other existing methods. A migraine severity score data set is analyzed to demonstrate the application of the proposed method in the analysis of missing data.

Non-parametric test of ordered alternatives in incomplete blocks

Often in medical studies, study subjects become a natural block of observations repeated over a time period. Some subjects miss observations, thus becoming incomplete blocks of observations. We are interested in testing an ordered alternative (or time trend), and propose a non-parametric method to detect a trend in incomplete blocks. Our approach is to estimate the trend by the linear regression method within each block and apply the one-sample Wilcoxon test to the estimated linear trends. The one-sample Wilcoxon test will be sensitive to the trend if it exists. The proposed test statistic is asymptotically normal and consistent. We can also estimate the overall magnitude of the linear trend and its confidence interval by a proper non-parametric method. By Monte Carlo studies, we compare the performance of the proposed test against extended Page and Jonckheere tests. Published in 2000 by John Wiley & Sons, Ltd.