The behavior of the P-value when the alternative hypothesis is true

The P-value is a random variable derived from the distribution of the test statistic used to analyze a data set and to test a null hypothesis. Under the null hypothesis, the P-value based on a continuous test statistic has a uniform distribution over the interval [0, 1], regardless of the sample size of the experiment. In contrast, the distribution of the P-value under the alternative hypothesis is a function of both sample size and the true value or range of true values of the tested parameter. The characteristics, such as mean and percentiles, of the P-value distribution can give valuable insight into how the P-value behaves for a variety of parameter values and sample sizes. Potential applications of the P-value distribution under the alternative hypothesis to the design, analysis, and interpretation of results of clinical trials are considered.

Evaluation of experiments with adaptive interim analyses

A general method for statistical testing in experiments with an adaptive interim analysis is proposed. The method is based on the observed error probabilities from the disjoint subsamples before and after the interim analysis. Formally, an intersection of individual null hypotheses is tested by combining the two p-values into a global test statistic. Stopping rules for Fisher's product criterion in terms of critical limits for the p-value in the first subsample are introduced, including early stopping in the case of missing effects. The control of qualitative treatment-stage interactions is considered. A generalization to three stages is outlined. The loss of power when using the product criterion instead of the optimal classical test on the whole sample is calculated for the test of the mean of a normal distribution, depending on increasing proportions of the first subsample in relation to the total sample size. An upper bound on the loss of power due to early stopping is derived. A general example is presented and rules for assessing the sample size in the second stage of the trial are given. The problems of interpretation and precautions to be taken for applications are discussed. Finally, the sources of bias for estimation in such designs are described.

[Cardiovascular effects produced by prophylactic digitalization during introduction of anaesthesia (author's transl)]

The narrow field of non-controversial indications concerning the application of digitalis glycosides is pointed out. Problems of routine digitalization of older patients not suffering from cardiac insuffiency are discussed with special regard to preparing them for operations. Up to now, from the viewpoint of anaesthesiologists no benefits of prophylactic digitalization have been found. In a retrospective computerized study, clinical hemodynamic parameters during introduction of anaesthesia have been investigated by means of anaesthetic data recorded during three years. Nondigitalized patients older than fifty years showed satisfactory cardiac functions, whereas prophylactically digitalized patients--compared with the control group--have been treated with plasma expanders earlier and at a double rate. Furthermore, higher heart frequencies and greater tendency to arrythmias were observed. Consequently, prophylactic digitalization cannot be recommended in general.