The design and analysis of experiments for the assessment of drug interactions

Abstract

It was pointed out that all fields of biological research have one feature common: inherent variability. Since this is the case and since it is not feasible to examine the entire population one is interested in, the experimenter is forced to give probability statements concerning any treatment differences observed. In order to do this, it is necessary for the experiment to be designed in such a way that a statistical analysis of the data will yield a valid answer to the question, "What is the probability that the differences observed could have occurred by chance?" The importance of randomization in the selection of the samples was emphasized. The problem of determining the sample size was discussed in relation to Type I (rejecting the null hypothesis when it is true) and Type II (accepting the null hypothesis when it is false) errors. It was suggested that too little attention is given to the possibility of Type II errors in biological research. It was emphasized that the specific question, or questions, one is asking should be precisely formulated prior to the design of the experiment, since hazily formulated ideas are difficult to discuss and virtually impossible to test for correctness. Once the experiment has been designed, both the questions and the design should be critically and logically evaluated for any fallacies. If the investigator has any doubts about the design or the manner in which the data will be analyzed, a statistician should be consulted before the experiment is conducted. A statistician cannot extract meaningful results from data collected with a faulty design. It was emphasized that it is important to know both the dose effect and time effect of each substance on the responses to be measured, in order to provide a rationale for the doses used in the interaction studies and the time after dosing at which the effect is to be measured. The design of drug interaction experiments is based, in part, on whether or not both substances when given alone affect the response. If both substances are active, one determines the potency of one substance relative to the other in affecting the response. This can be done for either quantitative or quantal data. Once the relative potency has been determined, subsequent studies involve combining fractional doses of the substances and comparing the results against those obtained using standard doses of the substances individually. Doses of the combination and the single substances are picked such that equivalent responses should be obtained if the effect of the two together is additive. The null hypothesis is that the two compounds behave as though they were different forms of the same substance, one of which is possibly (depending on the potency ratio) diluted with an inert substance. Equivalence of response can be tested using such parametric tests as Student's t or analysis of variance (or their nonparametric equivalents) for quantitative data. Additivity is inferred if the null hypothesis is accepted...