Empirical likelihood against chi-squared-based tests for ordered alternatives

M. C. Pardo, Y. Lu, A. M. Franco Pereira

In phase I or even phase II trials, multiple dose levels are tested for either safety or efficacy. A stochastic order or an umbrella shape dose relationship is often biologically justified. The contribution of this work is to define empirical likelihood and chi-squared-based test statistics for stochastic and umbrella orderings. The asymptotic null distribution of the proposed statistics is obtained. Statistical powers of the proposed tests are computed via simulation studies and compared to those of the existing tests. Furthermore, Type-I error robustness of the proposed and existing tests are studied also via simulation. Finally, our proposals are illustrated with several real data sets.

Keywords: empirical likelihood test statistic chi-squared test statistic umbrella ordering stochastic ordering

F. Ruggeri, M. Sánchez Sánchez, M. Á. Sordo Díaz, A. Suárez Llorens

A. Arriaza Gomez, M. Á. Sordo Díaz

A. Castaño Martínez, G. Pigueiras Voces, M. Á. Sordo Díaz