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.
MODIFIED LIKELIHOOD RATIO TEST FOR HOMOGENEITY IN A TWO-SAMPLE PROBLEM
We consider testing for homogeneity in a two-sample problem in which one of the samples has a mixture structure. The problem arises naturally in many applications such as case-control studies with contaminated controls, or the test of a treatment effect in the presence of nonresponders in biological experiments or clinical trials. In this paper, we suggest using the modified likelihood ratio test (MLRT), which is devised to restore a degree of regularity in the mixture situation. The asymptotic properties of the MLRT statistic are investigated in mixtures of general one-parameter kernels, and in a situation where the kernels have an additional structural parameter. The MLRT statistic is shown to have a simple χ 2 null limiting distribution in both cases and simulations indicate that the MLRT performs better than other tests under a variety of model specifications. The proposed method is also illustrated in an example arising from a trial relating to morphine addiction in rats.
Methylmercury-induced changes in operant discrimination by the pigeon.
Pigeons were trained on a fixed consecutive number schedule of reinforcement, pecking eight or nine times on one key (a run) before making the single response on a second key that was reinforced if the number requirement had been met. A run of fewer than eight or more than nine responses reset the response requirement. They then were given methylmercury chronically until behavioral signs of poisoning occurred. Where possible, recovery was followed. Percentage of reinforcers earned and rate at which the birds pecked both decreased whereas variability of run length increased after enough methylmercury had been given to produce blood mercury concentrations between 13 and 27 ppm. Some birds also showed consistent shortening of run length throughout the time of maximum poisoning. Because ataxia was a common accompaniment of the changes in operant behavior, other methods of producing ataxia (hobbling one foot or dosing with ethanol) were also studied in some birds. The pattern of changes induced with these methods did not match that seen after methylmercury.