I would like to analyse data from a placebo-controlled within-subject design. For every subject a numeric outcome variable (Y) was measured twice - once following administration of a drug and once following administration of a placebo (order of drug/placebo administration randomized). Also for every subject a numeric covariate was measured once. This covariate does not change with time. It is hypothesized that the covariate might mediate the main-effect of drug in a way that e.g. subjects with higher values of the covariate experience greater changes of Y following drug-administration as compared to subjects with lower values of the covariate. What would be the most appropriate way of investigating the main-effect of drug and whether numeric covariates mediate this main-effect of drug?
- Compute change scores [(Y_placebo - Y_drug) / Y_placebo]. Then create a linear model with covariates predicting the change score. In this model the intercept would represent the main-effect of drug and the effect of covariates would represent how the covariates are mediating the drug effect.
- Create a linear model with Y_drug as IV and the covariates as well as Y_placebo as predictors.
- Create a linear model with Y as IV, the covariates as between subject factors and the treatment (placebo/drug) as within-subject factor.
Questions:
- What is the best way to analyse such data?
- Are there reasons to prefer one approach over another?
I am aware that this question is closely related to the the very informative post Best practice when analysing pre-post treatment-control designs. However in the presented question I refer to a slightly design in which every subject is tested twice (once with drug, once with placebo) and in which I am interested in the mediating effect of the covariate.
