Statistical analysis of drug interactions.

The design of drug interaction experiments focusing on whether to characterize the interaction as addition, antagonism, synergism or potentiation 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. The chi-square or Fisher's exact probability test may be used for quantal data. Additivity is inferred if the null hypothesis is accepted. One infers either antagonism or synergism (depending upon the direction of the deviation from additivity) if the null hypothesis is rejected. If one substance is inactive when given alone the null hypothesis is that it has no effect when given with the other. This is tested using the same techniques as mentioned above, except that there is no need, obviously, to determine relative potency. The isobolographic method for studying drug interactions was compared with those mentioned above. Both approaches have the same conceptual basis. The isobolographic method is more tedious, however, since it entails determination of doses required to cause a specific response, whereas the other methods focus on the responses caused by specific doses. It was cautioned that, whatever the approach, it is the investigator's responsibility to know what assumptions are being made and to take all possible precautions before, during, and after the experiment to ensure that the reported results are meaningful.