Testing equality of correlated slopes in linear regression: An application to clinical cosmetic study.

Testing whether regression lines are parallel is a standard statistical problem when data sets are independent, solvable using conventional least squares theory for observations that are normally distributed and using nonparametric methods otherwise. The case in which the data sets are correlated poses an interesting complication since many alternative procedures become relevant. Such a case of correlated slopes was encountered in a multiple exposure cosmetic clinical study conducted to determine anti-irritation potential of skincare products. Each subject received all three products twice daily at three sites on the forearm. During the product application session, firstly irritant and then irritation reducing skincare products were applied. Data were irritation scores at various follow up time points. According to clinicians, slope of regression of irritation score over time is a good measure of efficacy. With repeated application of irritants, the score increases over time. Anti-irritation products slow down the rate of increase. Lower the slope, higher the efficacy of the treatment. Hence, slopes corresponding to products were to be compared with slope corresponding to ‘placebo’ or baseline product. Various alternative tests are possible. They are (a) Friedman test (b) extra sum of squares test(c) Hotelling T² test with suitable dispersion matrix for errors (d) ANOVA ignoring correlations and (e) an ad hoc procedure named ‘PaD’ test proposed for the present problem. It is a test based on pairwise differences. These methods were compared using simulation and PaD test was found to be more appealing. [ABSTRACT FROM AUTHOR]