A note on the interpretation of results of supplementation trials

In a supplementation trial to study the effect of the supplemental treatment on some response variable of interest, the variable is often measured twice from each subject, namely; before (x) and after (y) the trial period. The difference between y and x (Z = y - x) is then computed for each subject. The Z and x values are the primary data for statistical analysis. The objective of the study is to obtain an unbiased estimate of the "average effect" of the supplemental treatment on the response variable. When x is not comparable in the two groups (supplementation versus no supplementation) but x and Z are similarly correlated in the two groups, then an unbiased estimate of the average effect is obtained by the usual method of covariance adjustment of x. However, when x and Z are not similarly correlated in the two groups, a modified method of adjustment of x is needed to obtain an unbiased estimate of the average effect. The modified method is given in this note. Furthermore, the statistical implication of the average effect so obtained is discussed.