# Thread: How to compare repeated measurements

1. ## How to compare repeated measurements

Okay, I have one group of patients.

This is a hypothetical example:

drug A and B are drugs that decrease puls rate.

After application of drug A, puls rate is measured 10 times with an interval of 1 minute.

3 months later, the same group of patients receives drug B, puls rate is measured 10 times with an interval of 1 minute.

How can I compare this paired data - to find out, if puls rate in group 1 decreases more / less slowly than in group B? What is the best figure choice to show the data?

Thank you so much, for your help!

I tried to do it with ANOVA - but did not succeed...

2. ## Re: How to compare repeated measurements

Hi med, I think what you want to do is compare the linear trends in pulse rate over time between the two drugs. I think doing this will be most straightforward in a repeated measures ANOVA framework. To do this, first compute two linear contrasts for each person, lin_A being the linear trend for Drug A and lin_B being the linear trend for Drug B, as:

lin_A = -4.5*t1_A - 3.5*t2_A - 2.5*t3_A - 1.5*t4_A - 0.5*t5_A + 0.5*t6_A + 1.5*t7_A + 2.5*t8_A + 3.5*t9_A + 4.5*t10_A
lin_B = -4.5*t1_B - 3.5*t2_B - 2.5*t3_B - 1.5*t4_B - 0.5*t5_B + 0.5*t6_B + 1.5*t7_B + 2.5*t8_B + 3.5*t9_B + 4.5*t10_B

Where ti_X is the ith pulse measurement in time under drug X (A or B). Given your balanced design, these lin scores will be equivalent (up to a multiplicative constant) to the regression coefficients you would get by running separate within-participant regressions on the centered time interval variable for both drugs for each person.

Second, compute a difference score between these two lin scores for each person, e.g., lin_diff = lin_A - lin_B.

Finally, the actual analysis consists simply of a one-sample t-test examining whether these lin_diff scores are significantly different from 0 on average. The procedure I have outlined is the piecemeal version of a repeated-measures ANOVA.

3. ## The Following User Says Thank You to Jake For This Useful Post:

med1234 (06-25-2012)

4. ## Re: How to compare repeated measurements

Great!

Thank you so much... how are you getting to the numbers -4.5, -3.5, -2.5 etc.? How would they change, if I change the experimental settings e.g. to measurements every 3 minutes for 30 minutes (11 measurements in total for one patient and drug), how would I have to change these numbers?

Apart from that your approach seems quite clear... For the statistical analysis section of a paper, do I have to call this approach "Groups have been compared by repeated measurements ANOVA", or how would you describe such an approach in statistical language?

5. ## Re: How to compare repeated measurements

The contrast weights were chosen simply because they sum to 0, and also because they have an interval spacing of 1. The latter property I personally find appealing but it does not really add anything substantive, the important thing is just that they sum to 0. So another option would be -9, -7, ..., 7, 9. If you used a design with 11 measurements instead of 10, you would place the centermost measurement (i.e., the 6th measurement) at 0 and have an equal number of weights above and below 0. Again, the principle is that all of the weights sum to 0.

I would just describe the procedure as repeated measures ANOVA. The little details of how you carried it out are not important in my opinion.

6. ## Re: How to compare repeated measurements

Hi.
I have also been doing repeated measurements. I've concluded that AUC is a good way to compare these curves. I've measured glucose concentration in the blood 7 times over a period of 180 minutes. I've done this at 3 different occacions. I've drawn a line for each subject and calculated AUC for each. Then compared AUCs with each others by t-test (I have 2 different treatment groups at the same time - so my subjects are not paired).

For your experiment, I would draw a line for each subject over time, then calculate AUC (area under the curve) for each subject. Then do the same for the test 3 months later. Then perform a paired t-test between the AUCs (1 column for AUCs at first test and 1 column for AUCs at test 3 months later).
What do you think about this? I am not very good with statistics, just giving a suggestion and hope someone else can answer if this sounds like a good idea...

7. ## Re: How to compare repeated measurements

Dear all

As far as I understand the described experiment is a typical situation occurring in drug development. I would suggest to apply so-called “indirect response models” to describe the data. These models are frequently applied in the last 15 years and are actually state-of-the-art and I think that they are appropriate for your situation.

The idea is to obtain pharmacological parameter by these models. Then you are e.g. able to calculate the AUC (more or less in the same way as suggested by Amana but based on continuous functions and not only on the data). The advantage of the “indirect response model” approach is that you eventually could perform simulations, that means, you could compare arbitrary dosing regimens.

What I think you actually want to do is a so-called Population Pharmacokinetic/Pharmacodynamic approach but I am aware that doing this for the first is not easy. However, depending on how familiar you are with PKPD I would strongly recommend also with respect to publication to apply IDR models combined with an AUC analysis.

I did not really understand the idea from Jake but depending where you will publish a “hand-made” analysis could be crucial.

EDIT: Finally, to summarize and answer your question: Calculate the AUC (area under the curve = difference between baseline and effect) as suggested by Amana! This is a well-accepted value!
More precisely, it is a typical parameter to describe an effect of a drug and is traditionally used to compare dose-effect relationship. However, to make things not to easy, AUC is independent of the dynamic of the effect in time and therefore, nowadays criticized.

8. ## Re: How to compare repeated measurements

Hi, i find this discussion very helpful. One question: when calculating the p of the contrasts (for say the simple effect) would it be necessary to account for bonferroni correction?

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