Assessing the effect of a treatment when subjects are growing at different rates

The analysis of covariance is often used in the context of premeasure/postmeasure designs to compare treatment and control groups in both randomized [1] and nonrandomized [2] studies. The intent is to adjust the difference between the changes in the 2 groups for any difference which might exist at baseline, i.e., for any difference between the premeasures in the 2 groups. An important assumption underlying the use of the analysis of covariance is that the slopes of the lines for the regression of the postmeasure on the premeasure in the 2 groups are equal. In this paper we describe a program which can be used to test the hypothesis of equal slopes; and performs an alternative analysis which does not depend on this assumption. This is done in the context of comparing treatment and control groups with respect to a measurement subject to natural maturation as in [3]. Equal slopes in this context means equal growth rates; unequal slopes implies that the 2 groups are growing at different rates. The method, known as the Johnson-Neyman procedure [4] is, however, more general than this, and can be used in any two-sample comparison where an alternative to the usual analysis of covariance is deemed appropriate. The procedure identifies a 'region of significance' which is especially useful in practice. This region consists of a set of values of the premeasure for which the treatment and the control groups are significantly different with respect to the postmeasure.