I have a small pre/post study w/ a continuous outcome measure. A paired t-test is planned. Is it possible to adjust for potential confounders when using a paired t-test? If not, could I do a linear regression analysis instead, and adjust for potential confounders that way?
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$\begingroup$ Ideally, you would know for sure whether certain variables are confounders or not. You can biased results if you adjust for a variable that's not a confounder. The "when in doubt, adjust" strategy is simply incorrect. There are many ways to adjust for actual confounders (a confounder is a variable that sets up a backdoor path, by the way): backdoor adjustment, frontdoor adjustment, stratified, and intrumental variables. Some are more useful in some scenarios than others. Do you have a causal graph? $\endgroup$– Adrian KeisterCommented Sep 1, 2021 at 21:39
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$\begingroup$ Did you randomize people into two groups? What exactly are you going to t test? $\endgroup$– Demetri PananosCommented Sep 1, 2021 at 21:57
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$\begingroup$ @AdrianKeister Only those variables that meet the definition of a potential confounder would be adjusted for. Thanks for your response. $\endgroup$– MaldiniCommented Sep 1, 2021 at 23:58
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$\begingroup$ @DemetriPananos No randomization. One group w/ data collected at baseline and then 1 week later. Thanks for your response. $\endgroup$– MaldiniCommented Sep 1, 2021 at 23:59
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I'm not sure of all aspects of design, but I can respond to what I do know.
It sounds like you have a single sample which can be stratified by a binary variable. Even in the case where you do not want to adjust for covariates, it would be a good idea to perform an ANCOVA (essentially, a linear regression in which the post scores are regressed onto pre scores and the binary indicator). Let $y$ be the post score, let $x$ be the pre score, and let $z$ be the binary indicator (1 for presence, 0 for absence).
The model would then be $y = \beta_0 + \beta_1x + \beta_2z$. This approach is suggested by Bland & Altman in their paper found here. That paper specifically talks about randomized experiments, but it should also apply here.
Note, adjusting for covariates is now natural, just add them to the regression equation (assuming you don't want a causal interpretation, in which case things become a little harder). The test you seek is the test associated with $\beta_2$. This coefficient will tell you if estimated means are different conditional on having the same pre-test score (or other covariates, should you choose to adjust for them)
answered Sep 2, 2021 at 1:03
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$\begingroup$ This is great. Thank you. I'll read that paper. Quick clarification: Are you saying that I should be looking at the magnitude of the change in 𝛽2 after adding a covariate (i.e., potential confounder) to determine whether it is, in fact, a confounder? $\endgroup$– MaldiniCommented Sep 2, 2021 at 22:30
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$\begingroup$ @Maldini No. Confounders are determined a priori. What I am saying is that the test associated with $\beta_2$ will tell you if there is a difference between groups indicated by the $z$ variable. $\endgroup$ Commented Sep 2, 2021 at 23:01
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$\begingroup$ You say that confounders are determined a priori. My understanding is that variables that meet the definition of confounding (i.e., covariates that are risk factors for the dependent variable and associated with the independent variable) are included/retained in “the model” ONLY if their impact on the measure of association (e.g., beta, OR, etc.) is 10% or greater. I realize this may not be a universal definition...Am I wrong? Do you define a covariate as a confounder if it meets the definition, regardless of the change in the measure of association when added or removed from the model? $\endgroup$– MaldiniCommented Sep 8, 2021 at 15:28
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$\begingroup$ Also...If there was a third timepoint in this study (i.e., Baseline, TP1 and TP2), what would the regression equation look like? If you are regression the post score onto the pre score in the first equation you offered, how would this change when a third timepoints was involved? $\endgroup$– MaldiniCommented Sep 8, 2021 at 15:28
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$\begingroup$ As to your point about confounding, the 10% change rule is a working definition but is flawed in my opinion. Its better to think about our problem rather than "let the data speak for itself", hence confounders should be identified from domain expertise about the problem. As per your second question, I would assume we would regress TP2 on TP1 and Baseline. Alternatively, a mixed effect model could be used if we are interested in the evolution of the measure over time. $\endgroup$ Commented Sep 8, 2021 at 16:29