Experiments in which the treatments are composed of a series of doses of a compound and a zero dose control are often used in animal toxicity studies. A test procedure is proposed to assess trends in the response variable. The notion of a no-statistical-significance-of-trend (NOSTASOT) dose is introduced, and questions of multiplicity of statistical tests in this context are addressed.

Statistical analysis of difference between groups in change for some variable, adjusting for initial value, is complicated by the presence of intra-individual variation in that variable. We estimate here the asymptotic bias that results from calculating the adjusted between-group difference by ordinary least squares (OLS) from observed data. We also present explicit formulae that use the OLS estimates, the difference between treatment groups in mean initial values, and a measure of the intra-individual variation to compute a corrected estimator and its variance. Alternatively, we can use OLS on transformed data to obtain unbiased estimates, in which we replace initial observed values by conditional Stein estimates of true values. We illustrate the results with data from an observational study and a clinical trial.

'Qualitative' or 'crossover' interactions arise when a new treatment, compared with a control treatment, is beneficial in some subsets of patients and harmful in other subsets. We present a new range test for crossover interactions and compare it with the likelihood ratio test developed by Gail and Simon. The range test has greater power when the new treatment is harmful in only a few subsets, whereas the likelihood ratio test has greater power when the new treatment is harmful in several subsets. We provide power tables for both tests to facilitate sample size calculations for designing experiments to detect qualitative interactions and for interpreting the results of clinical trials.

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In a pharmacokinetic drug interaction study, the purpose is to determine whether the coadministration of a drug A with a second drug B alters the absorption/distribution/metabolism/elimination profile of either drug. While the usual design for such studies is a three-period crossover, it cannot be analyzed as such, because the plasma-level data of drug B will be 0 when drug A is given alone, and vice versa. The easiest way to proceed is to do two sets of paired analyses, one on the absorption profile of A (A vs AB), and the other on the absorption profile of B (B vs AB). A complete separation of the total sources of variation and degrees of freedom is presented along with a numerical example.