# Comparing quantitative parameter between two groups with only one of these having repeated measures

#### Rubber

##### New Member
My question regards the best way of comparing two groups for differences in the levels of several quantitative parameters. Here, for only one of the groups there are 4 repeated measurements at different intervals.

The data
-We have two groups we want to compare: one consists of ~200 patients at 1 timepoint and the other of 50 controls that we have measurements for at ~4 timepoints.
-The measurements of the 200 patients and 50 controls were done in about the same period of time.
-The 50 controls were measured at various times, usually about 3 months apart. However, for each control, this timing was different. This means that the first measurement of a control can be closer to the second measurement of another control than to the first measurement of that other control.
-For all these people we measured several quantitative parameters.
-These quantitative parameters are not normally distributed. But it is not a problem do to something like an inverse rank based transform. I know this type of transform is highly debated, and that opinions vary, but this is not the purpose of my question on this forum.
-We would like to be able to correct for age, gender and BMI

The goal
We want to check of these quantitative parameters are higher or lower for the patient group than they are for the control group.

My “simple” approaches so far
I have been using an ANCOVA, correcting for age, gender and BMI, using the medians of the 50 controls vs the 200 patients. I use the following bit of R code:
Code:
formulaSel = as.formula(‘quantitativeParam~cohortNames+age+BMI+gender’)
#”cohortNames" is a factor containing the information if an individual is a patient or a control, and “quantitativeParam” is our quantitative parameter of interest
results = lm(formulaSel,data = data)
anovaRes = anova(results)
I can of course use this approach on the data with each of the 4 repeated measures separately for the 50 controls. Here I am also able to correct for seasonal changes and linear changes over time. I implemented this using the following bit of R code:
Code:
#Linear model
formulaSel = as.formula('quantitativeParam ~ cohortNames + age + BMI + gender
results = lm(formulaSel,data = data)
valuesAll = summary(results)\$coefficient
I don't think I can use a mixed effect model with as a random effect the "patient-number", since we only have repeated measures for the controls.

The questions
(1) Should I:
-take the mean/median over all 4 timepoints?
-use the timepoints separately?
-use a technique that can take into account the fact that we have repeated measurements for just one of the groups
(2) Is what I am doing valid?
(3) What is the best technique to compare these groups?
Thanks in advance for the input!

Cheers,

Rob

PS. I also posted my question on stackexchange last week, but haven't received any feedback, hence my slightly adjusted post here.
https://stats.stackexchange.com/que...th-only-one-of-these-having-repeated-measures