A: These terms have been around a very long time. Basically, a moderator suggests on whom or under what conditions a treatment produces its effect. A mediator, in contrast, suggests how and why a treatment produces its effect. The problem is that the way the terms have been used has been inconsistent and imprecise, so if you ask a roomful of researchers, "What do you mean by a moderator?," "What do you mean by a mediator?" you would get multiple definitions.

The first major step in achieving some clarification on the issue was in 1986, when Baron and Kenny wrote a seminal paper on this topic; however, in the years since, what we've found is that if you follow the actual analytical procedures that were suggested by Baron and Kenny, you still end up confused as to which is which. The actual analyses were not specifically designed to clarify the definition between the two.

What Dr. Kupfer and I have been trying to do in the last number of years is to extend the Baron-Kenny Model; we're calling it the MacArthur Model. We're not deviating from the conceptual underlying model, but trying to come up with the analytic procedures and the specific definitions that are needed to make it absolutely clear what the relationships between the two might be.

A: In your equation, you have the moderator, the mediator, the treatment (T), and an outcome (O). The moderator must satisfy the following three conditions:

1) It precedes T temporally.
That's easy to determine in a randomized clinical trial because any baseline measure, pre-randomization measure, by definition has to precede T, so in randomized clinical trials, moderators are baseline variables.

2) It is independent of T.
Again, in RCT's this is easy because with randomization, basically any baseline variable is independent of the choice of treatment.

3) The effect of T on O varies depending on its value.

Potential moderators in all RCTs include:
- site
- sociodemographics(i.e. gender, age, ethnicity)
- genotype
- baseline clinical characteristics (i.e. co-morbidity, disease severity)

In contrast, a variable mediates the effect of treatment on an outcome if three conditions are met:

1) It is an event or a change that happens during treatment.
Automatically, you can see that you can't have something that is both a moderator and a mediator, since a moderator has to precede treatment, it's a baseline variable, and a mediator has to follow treatment, a change or event that happens during treatment.

2) It has to be correlated with the treatment.
It is an outcome of the treatment, and again that is another distinction between a moderator and a mediator. Moderators do not correlate with treatment. Mediators do.

3) It explains all or part of the effect of T on the outcome measure.

A: There are a number of fallacies out there about interactions. Some researchers think that if you're not interested in the interaction, it's OK to leave it out of the model. Well, that's not true. The interaction has to go someplace. If it exists in the population, and you don't include it in the model, it will do two things. A portion of it will be remapped into the coefficients that you've included in the model thereby increasing Type I error, and the rest of it will go into the error, which will increase Type II error. Now Type I and Type II errors tend to go on a seesaw; you do something that lifts one and drops the other. This is one of the few cases where both ends of the seesaw go up at the same time. It's really a bad idea. The only reason for excluding an interaction from the model is because you have good reason to believe it doesn't exist in the population.

The other sort of fallacy is the notion that you could test the interaction, and if you found it to be non-significant, you could just leave it out of the model. The problem here is that the sample size you need to get adequate power to detect the interaction is usually larger than the sample size you need to detect the main effect, and as a result, when you find a non-significant interaction, it is not assurance that the interaction is zero. It should be still included in the model.

Finally, people say that there is loss of power to detect the effect of the treatment if you include the interaction. The logic here is good. When you include the interaction, you're going to lose some degrees of freedom, and people tend to think of degrees of freedom as being the major determinant of power. The major determinant of power is the effect size, not the degrees of freedom, and very frequently, including the interaction actually increases the power, even while it decreases the degrees of freedom.