I'm analyzing a double-blind, placebo controlled RCT using an ANCOVA in R, where the predicted "treatment effect" shows up before the treatment has occurred!
The goal of the study is to determine if treating a disease reduces a particular behavior. Folks with both the disease and the behavior were randomized 50-50 into treatment and placebo control arms.
As predicted there was a significant interaction between the intervention and baseline disease state (all variables are interval, except for "intervention", which is a two-level factor variable identifying treatment vs. control group):
MODEL 1: Call: lm(formula = follow_up_behavior ~ baseline_behavior + baseline_disease * intervention, data = d) Estimate Std. Error t value Pr(>|t|) (Intercept) 11.28464 0.51177 22.050 <2e-16 *** baseline_behavior 0.77872 0.05112 15.234 <2e-16 *** baseline_disease 0.36726 0.23110 1.589 0.1146 interventiontreatment 0.74738 0.70254 1.064 0.2895 baseline_disease:interventiontreatment -0.64681 0.31374 -2.062 0.0414 *
The interaction was predicted because the intervention is a very effective treatment of the disease, but baseline disease state varies along a continuum from near 0 to very high. Hence, folks with high baseline disease got the biggest benefit from the treatment, and should therefore have had the biggest reduction in the behavioral response. So far so good.
On a lark, I ran a very similar model of baseline behavior:
MODEL 2: Call: lm(formula = baseline_behavior ~ baseline_disease * intervention, data = d) Estimate Std. Error t value Pr(>|t|) (Intercept) -0.6350 0.7620 -0.833 0.4062 baseline_disease 0.7422 0.5016 1.480 0.1415 interventiontreatment 1.1941 1.0611 1.125 0.2626 baseline_disease:interventiontreatment -1.3320 0.6510 -2.046 0.0428 *
As you can see, there is a very similar significant interaction between disease state and intervention group, even though though the intervention has not yet occurred. This would seem to be a failure of randomization.
My primary concern is that because follow_up_behavior is very highly correlated with baseline_behavior, the significant interaction in the first model is due to the pre-existing interaction seen in the second model, and is therefore not a consequence of the intervention.
My questions are:
Do I actually have a problem?
If so, does including baseline_behavior as a control variable in model 1 fix the problem, i.e., guarantee that the significant interaction in this model is not a consequence of the pre-existing interaction seen in model 2 but is instead due to the intervention?
If including baseline_behavior as a control is insufficient, is there anything I can do salvage the study?
Many thanks in advance for any help or insights.