Dear researchers,
I have some serum data, collected repeatedly, from 24 different subjects. The distribution of most of my data is known, and I can apply generalized estimation equation for my repeated observations. However, the residuals of some of my data do not follow any specific distribution.
When I use the change score in percent as an output variable in a linear mixed effect model (LMM), my residuals follow a normal distribution. I know there are some disadvantages of using percent change from baseline, as this might reduce statistical power, especially when the correlation between the baseline and post measures is low. I have not found any literature on the use of percent change from the baseline in LMM.
Considering we can account for the subject-specific intercepts in LMM, do the same results apply for this type of model?
My question is: in LMM, can I use percent change from baseline as an output variable to normalize my residuals? The correlation between my repeated observations is high (above 0.8). If anyone has any suggested literature, that would be highly welcome.
All the best
You may be interested in my reply to this question
https://www.researchgate.net/post/Is_there_a_difference_between_ANOVA_analysis_of_change_scores_and_repeated-measures_ANOVA
Thanks for replying - you may also be interested in this - full disclosure; I have very little experience in GEE.
https://www.researchgate.net/post/Where_can_I_find_good_material_on_the_difference_between_mixed_models_and_gee_models
Kelvyn Jones , agian, thanks a lot, I really appreciate it! All the best
Therese Nitter Moazami
Which software do you use? If you are using Stata I can tell you step by step.
Panel regression family is the best choice (GEE is population averaged effect model version of panel regression). Random effect model of panel regression is more similar to mixed effect models.
First, calculate as a percent change manually and then investigate the distribution of the obtained rates. Maybe they follow Gamma or Poisson distribution. Please upload its plot of distribution as histogram.
Seyyed Amir Yasin Ahmadi , thank you for your suggestions. I use both SPSS and STATA. When I calculate the percent change from baseline, the residuals of some of my variables become normally distributed. I am just not sure if using the percent change score is the correct/valid way. The uploaded histogram is from one of the variables where the assumption of normally distributed residuals was not met. I have never used panel regression, but that is an excellent suggestion; thank you so much!
Therese Nitter Moazami
Although rates and ratios have usually geometric distribution, in your case the distribution is symmetric and therefore you can use linear panel regression.
I have another suggestion. Change your raw variable as ratio. Consider the amount at time = 1 as the baseline (ratio = 1) and then divide each time to time 1.
The process in Stata:
1. Create your dataset as the form of panel data. The column names are "id", "time", "outcome" (i.e. the raw amount of your dependent variable), "covariate1", "covariate2", etc. For example, if you have 3 repeated measure for each id the table should be as below.
id ----- time ----- outcome
1 ----- 1
1 ----- 2
1 ----- 3
2 ----- 1
.....
2. Create the new variable named "outcome_ratio" with below code.
bysort id (time): generate outcome_ratio = outcome[_n]/outcome[1]
3. See your dataset to verify the above action.
4. Create the histogram of outcome_ratio and show me here. Use below code.
db histogram
5. Then I tell you which panel model should be used and how.
An outstanding set of Notes on all of these topics by Prof Marie Davidian can be found here: https://www4.stat.ncsu.edu/~davidian/st732/notes.html
Best, David Booth
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