### Regression to the mean?

#### Posted by agbarnett on 08 Sep 2012 at 06:00 GMT

The stronger effects in those with lower baseline scores sounds suspiciously like regression to the mean. It shouldn't be an issue because there is a control group. However, to rule it out I would try a linear regression model with follow-up as the dependent variable and baseline and treatment group as independent variables using the entire sample (analysis of covariance). You could then add an interaction between treatment and low baseline score.

No competing interests declared.

### RE: Regression to the mean?

#### AJRichardson replied to agbarnett on 13 Sep 2012 at 10:52 GMT

Many thanks for your comments. As you say, this was a placebo-controlled trial – so although the issue you raise of ‘regression to the mean’ is an interesting one, it does not negate the treatment effects we have reported.

We did carry out and report a subgroup interaction test, as you will have seen, which partially addresses your question. This indicated that the effect of active treatment on reading found in the main subgroup (initial reading ≤ 20th centile) was not due to chance.

However, this did not make use of the full variance in baseline reading scores (as children were simply classified on initial reading into two groups). We also used an analysis of the “change scores” rather than using the follow-up results in contrast to the baseline assessments.

We have now carried out the analyses you have helpfully suggested, with the following results:

TEST OF REGRESSION TO THE MEAN - Whole sample (n=362)

Dependent Variable:
Variable: Coeff: S.E. T P-value
Reading (at baseline) 1.02 0 .053 19.44 0.000
Treatment (0/1) 15.46 6.068 2.55 0.011
Interaction -0.18 0 .071 -2.51 0.013
Constant -0.60 4.464 -0.13 0.894

As you can see, there is an effect of baseline reading, and also a significant interaction between this and the treatment, indicating that there is indeed some regression to the mean.
However, this does not account for the positive effect of the treatment, as this remains significant when controlling for the interaction.

Competing interests declared: Corresponding author of the paper

### RE: RE: Regression to the mean?

#### agbarnett replied to AJRichardson on 15 Sep 2012 at 02:04 GMT

Perfect, thanks.

The only odd thing is the coefficient for baseline of 1.02. When follow-up score is the dependent variable this coefficient is usually between 0 and 1, and is interpretable as the (adjusted) correlation between baseline and follow-up. Perhaps this was because the follow-up was standardised, but the baseline wasn't?

Also, to give an adjusted treatment effect that is more comparble to those in the paper it might be worth subtracting the mean baseline from the baseline scores, and then using this centred baseline variable as both a main effect and in the Treatment interaction. This should give the adjusted treatment effect for an average baseline score.

No competing interests declared.