Hello,
I want to perform a research study on the effect of a procedure on the echographic parameters (continuous outcome) of a population on different time points (two, at baseline (A) , and post-procedure (B))
For that I am going to use a paired t-test, given that the variables are not independent.
However, a paired t-test will not allow me to adjust for co-variates/study interactions (for instance to see if age played a role in the effectivenes/lack of effectiveness of the procedure in my outcome)
Normaly I would use some sort of regression (by creating a variable consisting of the difference between measurement A and B), but given that these variables are NOT independent, I would not be able to use a linear regression model (I think, but I am unsure).
Does anyone have any ideas?
Thank you
In its simplest form there is no point doing this is you have a covariate like age. Each pair will have the same age and so the covariate in confounded with individual differences which are not part of the error term in the paired t test.
However, if you have a time-varying covariate then this might be worth doing (in which case you'd need something like a multilevel model). Finally its possible that there might be a covariate by time interaction. In that case you could set this up as a repeated measures ANOVA model and include the covariate and covariate by time interaction. Depending on software its sensible to centre the covariate before computing the interaction term (as some software may not handle uncensored variables in this sort of model well).
Thom thanks for the super answer. I might have not given the best example, or I may not be understanding the answer correctly due to statistical innapetence!
Let me rephrase - imagine that I have a measurement at point A, then a procedure happens, and then I have a new measurement at point B of the same individual.
If I use the paired t test I will have an average effect of all the diferences of all individuals, and of course, intra-individual difference is null, however we will have an average crude effect size (an average difference with a confidence interval).
But let's imagine that in females the difference between A and B was great, and in males it was null (so gender affected the result).
Also let's imagine that in older patients the difference was smaller than in newer patients.
In an indipendent variables model I would simply use a multiple linear regression and adjust for sex and age.
Here, how can I do that?
Hello Miguel,
It sounds as if you should construct a regression model using: (a) Time A score; (b) covariate 1; (c) covariate 2; (d) interaction of covariate 1 & Time A score; (e) interaction of covariate 2 & Time A score and Time B score as the DV.
This would allow you to draw inferences about what additional explanatory power your covariates had, and whether they moderate the relationship of Time A/Time B.
Good luck with your work.
David Morse suggests a solid way to handle what you want to do. However, a word of caution. Statistical correction using a covariate will not fully adjust for preexisting group differences.
Thank you David Morse and James E. McLean it's trully a privilege to share knowledge with such distinguished scientists.
James E. McLean - I think that given that A and B would be the same participant, just evaluated in different timeframes , preexisting differences would not be an issua.
David Morse - And given than A and B are not independent, can I still use them in a linear regression model? If so that would be life-saving :)
Hello again Miguel,
All of the measures in a model are "dependent" in the sense that they come from the same cases!
The issue arises when outcomes/DVs are dependent...there are a variety of ways to handle this. Recasting the problem with Time A as a covariate/IV leaves you with just one DV. So, no issue.
Good luck with your work.
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