# RCT - baseline measures and group x time interaction without main effect for group?

I understand there is a general consensus amongst statisticians not to use change from baseline as an estimate of treatment effect and the head-to-head comparison, adjusted for baseline, is what we should be most interested in when formulating an RCT. However, there also seems a consistent push by researchers/clinicians to provide change from baseline estimates across treatment groups. If a ‘second’ baseline is taken very soon after the first this tends to placate everyone because you can then control for the first baseline and include the second as the first outcome measure, allowing change contrasts from early in the study to be calculated. But this can be problematic if the first post-baseline measure happens some time (e.g. months?) after.

My question is two parts:

1. When designing an RCT, how many of you suggest to take a second baseline routinely? Or is this something that tends not to be done in practice?
2. If you are presented with data where change from baseline is of interest but adjusting for baseline means comparisons might only be conducted from a first point much later in the future, do any of you use the approach of simply not including the main effect for treatment group in the model? (but including the main effect for time and the group x time interaction - see below) This approach thus forces the treatment groups to be equal at baseline and has the added advantage of allowing you retain the baseline measure in the outcome vector. Not sure what the inherent disadvantages are.

Interested in people’s thoughts.

(Section 2.1.2 - Method 2)

https://content.sph.harvard.edu/fitzmaur/ala2e/

(Pages 128 to 134 if you happen to have this book)

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We need to refuse to compute change from baseline. Among other things it assumes that Y is perfectly transformed before doing the subtraction. It does not represent the raw data in need of analysis. And very few studies collect the second baseline needed. Note that the second baseline must be a real baseline. For example one must screen patients and take those who qualify (e.g., those with X > c) then wait a few weeks to collect a less regression-to-the-mean-affected X to use as the baseline, then randomize patients.

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Frison and Pocock Stat Med 1992 is the seminal paper. Repeat baseline if and when baseline measures vary, so that taking an average of several measures reduces variance. There are only rare cases where you don’t include the main effect. For instance, if you are comparing weight loss over time in two groups, a main effect would suggest that, 10 seconds after randomization, patients receiving diet 1 are 10 lbs lighter than those on diet 2.

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This also points out the usual need for treatment \times time interaction. That raises the difficult question of forming the exact estimand. The combined multiple parameter test of treatment main effect combined with treatment \times time interaction tests whether treatment has an effect at any time, but diffuses the power a bit. The test for treatment difference at the final follow-up is usually very relevant (it’s the only thing relevant in a weight loss study, I’d posit) and will have lower power than testing for the average treatment effect over time. After all these years I don’t think we’ve settled this.

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I actually like to split this up into two questions: 1) Does the treatment have an effect? 2) Does the treatment effect change over time?

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Thank you Frank and Andrew,

Do I take that to mean that even if you take another baseline measure before randomisation, you would adjust using the second baseline and not the first (i.e. essentially ignore the first measure)? If that’s the case I incorrectly assumed one could adjust using the first measure and then include the second (and all post-randomisation measures) in the outcome vector.

If I understand your last post Andrew, then:

1. Does the treatment have an effect? - can be answered in an adjusted analysis by directly comparing treatment groups at a specific point in time, and
2. Does the treatment effect change over time? - is answered by inspecting the group x time interaction term.

I guess what I’m asking is, is there a valid way to estimate the difference in the treatment effect over time, where you are interested in the relative change from baseline and not the first post-baseline measure? e.g. you have 3 measures - a baseline (time = 0), time = 6 months and time = 12 months. If you adjust for baseline, you can perform contrasts of the outcome in treatment and control groups at 6 months and at 12 months, but there will be only one interaction term giving the relative change in the treatment from 6 months to 12 months. How do you design an experiment and analyses that allow you to validly assess both head-to-head effects and relative differences in treatment effect over time, from baseline (without using change as an outcome measure)?

Adjusting for baseline and using change scores as the outcome is one way - although not recommended as Frank has pointed out. Specifying a group x time interaction but without the main effect of group seems to be another way that is recommended in various texts, but I get the impression is not applied very often.

Apologies if this is obvious, but I don’t understand this the way I want to be able to.

Thank you.

The second baseline is to somewhat cancel regression to the mean effects. You have two choices:

• covariate adjust only for the second baseline
• covariate adjust for both baselines. The first baseline is very likely to have a weaker effect than the second. This includes as a special case adjusting for the average of the two baselines.

The way to properly assess change from baseline is, if you only adjust for the second baseline, to set the baseline to a grid of values, and for each one of them plot the baseline value vs. the estimated follow-up value (one estimate for each treatment). You can take the difference if you want, but that sort of assumes the coefficient of baseline is 1.0.

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