The Use of Balanced Incomplete Block Designs in Comparative Bioavailability Trials

SUMMARY In a comparative bioavailability trial it is customary to employ a cross-over design in which each subject receives each of the formulations of the drug in turn. After administration of each formulation, blood samples are obtained at various sampling times and are assayed for drug concentration. A number of reasons why it may not always be convenient to administer all formulations to each subject are suggested and the use of incomplete block designs is proposed. Selection of characteristics of the blood-level sequence for analysis is discussed and a test of the validity of a univariate analysis of variance of the repeated measurements of blood drug concentrations over time is given. The general form of the analysis of variance is displayed and illustrated by an actual trial comparing four formulations of lithium carbonate. A comparative bioavailability trial is one in which different formulations of a drug are administered to a number of subjects and blood samples are obtained at various times following administration. Assay of the drug in the blood samples gives, for each administration of a formulation to a given subject, a sequence of concentrations of drug in the blood (blood levels). The purpose of such trials is to compare the in vivo performances of the different formulations. When assay methods for the drug in the blood are not feasible, the alternative approach of collecting and assaying urine samples during various periods following administration is often used. While the discussion of this paper is conducted in terms of blood levels, there are simple extensions of the proposed methods to drug concentration in urine samples. The cross-over concept is widely used in bioavailability trials. In a cross-over trial each subject receives each of the formulations in turn, with an appropriate wash-out period intervening between administration of the different formulations. The order of administration of the formulations to the subjects is usually arranged so that the design constitutes a series of Latin squares. The reason for the cross-over concept is readily apparent: the biological variation among subjects, for example, with respect to metabolism, is usually considerable, and use of a cross-over design enables one to remove subject effect from the error variance thus obtaining a more sensitive test. The advantages of the cross-over concept still obtain, however, even if each subject does not receive all of the formulations provided that he receives at least two of them. The possibility thus exists of retaining the advantages of the cross-over while designing bioavailability trials as incomplete block designs. Some of the advantages of employing balanced incomplete block designs will be discussed, together with a suggested method of analysis. 319