I conducted an experiment to investigate the effect of a physical therapy treatment on the signal intensities of the 5 lumbar discs (L1-2 to L5-S1) on MR images. I found that the signal intensity of the upper most lumbar disc (i.e. L1-2) was significantly higher than that of the lower 4 discs (i.e. L2-3, L3-4, L4-5 and L5-S1) at baseline. There was no significant difference in signal intensities among the lowest four discs although it was apparent that the signal intensities of lower lumbar discs tended to have lower signal intensities.
Interestingly, the post-treatment signal intensities of the upper two discs (i.e. L1-2 and L2-3) decreased, while the post-treatment signal intensities of the lower three discs (i.e. L3-4, L4-5, and L5-S1) increased. As such, I wondered this observation was related to the regression to the mean (i.e. a decrease in post-treatment signal intensities for the lumbar discs with higher baseline signal intensities, and positive changes in post-treatment signal intensities for those discs with lower baseline signal intensity). I used a linear regression model to test my hypothesis by treating pooled signal intensities of all discs at baseline as the independent factor, and treating the difference in pre- and post-tratment signal intensity as the dependent variable. However, a statistician told me that I should not use a linear regression model for this case because the dependent variable was closely related to the independent variable. She suggested me to use a generalized estimating equation in SPSS for this test. Since she is not in my geographical area, she cannot show me how to run the test on SPSS.
Can anyone explain to me how to run this test on SPSS? Any suggested articles for a dummy? Any other suggestions for testing regression to the mean for my data?
Your suggestions are much appreciated.
Hello Dr Wong, if you go to my website, then go to favourite links and look at the electronic statistical textbook, it is good for definitions. Thanks
Deborah Hilton Statistics Online
http://sites.google.com/site/deborahhilton/
Thanks for your help, Deborah! However, the textbook doesn't seem to have the definition or explanation of the generalized estimating equation. Would you mind to give me some more guidance?
I do not know how to use SPSS, but I would suggest that since you have pre-post result associate with other factors. The General Linear Model (regression) in Minitab is useful to determine the effect of each.
You open the SPSS and go to analyze. click on it and then go to Generalized linear model then you get GEE model. you keep the variables in the specific boxes.
I note that GEE and mixed linear model can serve similar purpose. However, GEE seems to work only with larger sample size. Can anyone pinpoint the differences between the two methods and give some general rules in choosing these models?
I can explain about GEE and Mixed modelling (but a warning that I will be biased as I favour the latter)
There are two types of models when dealing with a panel study where occasions are nested within individuals, subjects or clusters, that is there is dependency or autocorrelation over time in the response variable. THis has particular importance for discrete outcomes eg predicted probability having a disease (say) from an estimated model.
The two approaches to within subject variation:
1) Marginal i.e. Population average models: estimated by GEE estimation: the slope is the effect of change in the whole population if everyone’s predictor variable changed by one unit
2) Conditional: cluster specific, mixed or multilevel: the slope is the effect of change for a particular ‘individual’ or subject of a unit change in a predictor.
Marginal estimates should not be used to make inferences about individuals (committing ecological fallacy), while conditional estimates should not be used to inferences about populations (atomistic fallacy). Population average approach underestimates the individual risk & vice-versa .
GEE estimation is robust to assumptions about the higher level, between- subject distribution; gives correct SE for fixed part and gives the Population average value. But does not give the higher-level variance, it is not extendible to random slopes and 3 level models etc; and does not give & cannot derive the cluster-specific estimates. All things that you get with the mixed, multilevel random-effects approach.
Population-averaged values can be obtained from random effects model in the MLwiN software via simulating predicted probabilities, see below
In practice there has to be a lot of difference between individuals and therefore (equivalently) a lot of similarity over time within subjects for there to be a difference between the two estimates. Thus when a fixed estimate is -1.5 on the logit scale, and the between variance is 1.0 (ie some 23 percent of the variance lies at the occasion level), the cluster specific result is a probability of 0.18 while the population average value is 0.22 . However if the between variance on a logit scale is 3 (so that 48% of the total variance lies at the occasion level) , the cluster specific result remains a probability of 0.18 while the population average value is now 0.27.
The GEE approach treats this clustering as a nuisance and does not give an estimate of the higher-level variance. The mixed random effects model treats the clustering as of substantive interest and you do get an estimate of its size and nature – but this generally requires distributional assumptions about the higher-level random effects; although non-parametric random effects procedures are possible.
There is more on mixed modelling for longitudinal analysis here
Developing multilevel models for analysing contextuality, heterogeneity and change using MLwiN, Volume 2 Kelvyn Jones, VS Subramanian ; available from
https://www.researchgate.net/publication/260772180_Developing_multilevel_models_for_analysing_contextuality_heterogeneity_and_change_using_MLwiN_Volume_2?ev=prf_pub
And the MLwin procedure is documented here:
https://www.researchgate.net/publication/234015221_Manual_supplement_for_MLwiN_Version_2.14?ev=prf_pub
The following is a general reference dealing with approaches to regression to the mean:
Regression to the mean: what it is and how to deal with it http://ije.oxfordjournals.org/content/34/1/215.full.pdf+html?sid=082adbb7-c3f2-4604-b507-c82304113dee
And this too is useful
Healy MJR and Goldstein H. (1978). Regression to the Mean (PDF, 0.3 mb). Annals of Hum.Biol. 5 (3) 277-280.
and so is this
Stephen Senn (2011)Francis Galton and regression to the mean, Significance
Volume 8 Issue 3 (September 2011) Doi: 10.1111/j.1740-9713.2011.00509.x
I think you need to get your helpful statistician to explain why they think GEE will be especially useful here beyond being robust to within-subject variation.
Book Developing multilevel models for analysing contextuality, he...
Data Manual supplement for MLwiN Version 2.14
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