Analysis of change--are base-line measurements needed? Some statistical comments on a common experimental design

In experiments where the treatment effect is defined as the change of a variable during treatment, one may, under certain circumstances, obtain a higher precision by basing the statistical analysis on the after-treatment measurements alone instead of the change during treatment. The conditions for this are derived and an empirical illustration involving bacterial counts is presented. In the case of a cross-over trial it is found in this particular case that not using the base-line measurements reduces the number of patients needed by approximately 40%. In the case of a completely randomized design, about the same precision is obtained whether or not one utilizes the base-line values.