Testing for a treatment effect in the presence of nonresponders.
Good (1979, Biometrics 35, 483-489) introduced a new randomization test for the two-sample problem where a proportion 1 - p of the treatment group does not respond to the treatment, and suggested that the Wilcoxon test is not effective for this situation. We show to the contrary that the Wilcoxon test is quite useful when p greater than or equal to .6 and point out an error in his definition of a one-tailed randomization test.
Hypothesis Testing in a Mixture Case–Control Model
Summary We consider a problem of testing mixture proportions using two‐sample data, one from group one and the other from a mixture of groups one and two with unknown proportion, λ, for being in group two. Various statistical applications, including microarray study, infectious epidemiological studies, case–control studies with contaminated controls, clinical trials allowing “nonresponders,” genetic studies for gene mutation, and fishery applications can be formulated in this setup. Under the assumption that the log ratio of probability (density) functions from the two groups is linear in the observations, we propose a generalized score test statistic to test the mixture proportion. Under some regularity conditions, it is shown that this statistic converges to a weighted chi‐squared random variable under the null hypothesis of λ= 0, where the weight depends only on the sampling fraction of both groups. The permutation method is used to provide more reliable finite sample approximation. Simulation results and two real data applications are presented.
Stereoselective disposition of ibuprofen enantiomers in infants.
The pharmacokinetics of the enantiomers of ibuprofen were investigated after oral administration of a single 7.6 +/- 0.3 mg kg-1 dose of the racemate in 11 infants. Mean (+/- s.d.) half-lives were 1.6 +/- 0.5 h for S(+) and 1.5 +/- 0.5 h for R(-) and mean (+/- s.d.) AUC values were 31.5 +/- 14.3 mg l-1 h for S(+) and 36.6 +/- 13.8 mg l-1 h for R(-). Since plasma concentrations of the active S(+)-isomer were lower than those reported in adults, a higher dosage might be required in infants.