Change scores vs ANCOVA vs repeated measures - how could I have done this better?

[Paul Sanfilippo]

Hi Group,

I was asked to analyse some data last year and after now reading more about repeated measures and longitudinal analysis, think I could approached the problem in a better way. I have tried searching through previous posts on this forum, as I realise this question tends to come up a bit, but I'm still a little confused.

Essentially, this was a 2 group (treatment/control) RCT with a continuous outcome measured at baseline, then every month thereafter for 24 months. The question we were interested in addressing was to assess the change in outcome from baseline (compared across the two groups) at 6 months, 12 months and 24 months.

I performed a t-test of the change scores - i.e. 3 t-tests (6 months - baseline, 12 months - baseline, 24 months - baseline). Please be gentle, but how could/should I have done this to make more efficient use of the data in answering the question? And, is the way that I've done it, necessarily incorrect?

Change scores vs ANCOVA are really addressing different questions, aren't they? The former looks at the difference, while the latter looks at the outcome at that point (controlling for the baseline). Perhaps I should have used some sort of repeated measures design.

Thanking you in advance for your thoughts,

Paul

[Swank, Paul R]

A mixed growth model.

Sent from my iPad

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[Rajeev Kumar]

You can apply linear mixed model and select appropriate correlation structure.  

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Dr. Rajeev Kumar, PhD

Scientist -II (Statistics)

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Dr. BRA I.R.CH, AIIMS

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[Munyaradzi Dimairo]

Let's step back a bit. What is the research question of interest? Effect at time x or averaged effect over time horizon? This will influence the approach to use. For instance, if the latter, then a longitudinal approach is appropriate.

Second, there are two versions of ANCOVA that give you exactly the same result except the y intercept which is a nuisance parameter. 

1) analysis of change scores adjusted for baseline

2) analysis of outcome scores adjusted for baseline

So when you say change scores it may confuse others because it could mean with or without baseline adjustment. 

Best wishes 

Munya 

[Paul Sanfilippo]

Thanks for the replies everyone.

Munya, your response has helped clarify things for me. We were more interested in the effect observed at those time points, rather than an averaged effect I think.

Also, I didn't realise that with ANCOVA. I thought the main approach was outcome scores adjusted for baseline.

Thank you,

Paul

On Tuesday, February 6, 2018 at 5:26:07 PM UTC+11, Munya Dimairo wrote:

Let's step back a bit. What is the research question of interest? Effect at time x or averaged effect over time horizon? This will influence the approach to use. For instance, if the latter, then a longitudinal approach is appropriate.

Second, there are two versions of ANCOVA that give you exactly the same result except the y intercept which is a nuisance parameter. 

1) analysis of change scores adjusted for baseline

2) analysis of outcome scores adjusted for baseline

So when you say change scores it may confuse others because it could mean with or without baseline adjustment. 

Best wishes 

Munya 

On 6 Feb 2018 05:13, "Rajeev Kumar" <rajeev.kum...@gmail.com> wrote:

You can apply linear mixed model and select appropriate correlation structure.  

On Tue, Feb 6, 2018 at 7:02 AM, Swank, Paul R <Paul.R...@uth.tmc.edu> wrote:

A mixed growth model.

Sent from my iPad

On Feb 5, 2018, at 7:18 PM, Paul Sanfilippo <prs...@gmail.com> wrote:

Hi Group,

I was asked to analyse some data last year and after now reading more about repeated measures and longitudinal analysis, think I could approached the problem in a better way. I have tried searching through previous posts on this forum, as I realise this question tends to come up a bit, but I'm still a little confused.

Essentially, this was a 2 group (treatment/control) RCT with a continuous outcome measured at baseline, then every month thereafter for 24 months. The question we were interested in addressing was to assess the change in outcome from baseline (compared across the two groups) at 6 months, 12 months and 24 months.

I performed a t-test of the change scores - i.e. 3 t-tests (6 months - baseline, 12 months - baseline, 24 months - baseline). Please be gentle, but how could/should I have done this to make more efficient use of the data in answering the question? And, is the way that I've done it, necessarily incorrect?

Change scores vs ANCOVA are really addressing different questions, aren't they? The former looks at the difference, while the latter looks at the outcome at that point (controlling for the baseline). Perhaps I should have used some sort of repeated measures design.

Thanking you in advance for your thoughts,

Paul

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Dr. Rajeev Kumar, PhD

Scientist -II (Statistics)

Room No 24, Delhi Cancer Registry
Dr. BRA I.R.CH, AIIMS

Delhi - 110029

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[Paul Thompson]

the basic approach is the mixed or multilevel model. The question of what is to be done with the initial baseline value is secondary. 

It is suboptimal and actually inappropriate to use multiple t-tests on such data. What is the correct approach? Set up the multilevel model with a categorical time variable, a categorical group variable, a group*time interaction (which usually captures the main hypothesis). 

The appropriate covariance structure must be selected.

Tests of differences at different time points may be done as contrasts. The baseline value may or may not be included in such contrasts.

Paul A. Thompson, Ph.D. PSTAT(R)

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[Paul Sanfilippo]

Thank you Paul,

Ok, I think that makes sense and it does highlight to me how crude my approach was.

So the group*time interaction term would give the averaged effect of whether there was a between group difference over time in changes in the outcome? Then as you say, you would look at contrasts across groups if you wanted to evaluate specific time points.

Thank you again.

Paul

[Paul Thompson]

Yes, that's my view. I do clinical trials, so use the multilevel/mixed model frequently. 

In my opinion, the overall tests (Time, Group, T*G) are almost never of much interest. They are too large, and average over things. 

Rather, I do simple main effects (difference between G at T=6mo) or simple interaction (incorporating a baseline comparison into the comparison at time =6)

In SAS terms, if you have 4 levels (baseline & 3 later values), 

CLASS GROUP TIME;

MODEL DV=GROUP TIME GROUP*TIME;

CONTRAST GROUP 1 -1 GROUP*TIME 1 0 -1 0  -1 0 1 0 ; * simple interation

CONTRAST GROUP 1 -1 GROUP*TIME 0 0 1 0  0 0 -1 0; * simple main effect

Paul A. Thompson

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