Pre-Post data with exposure-varying intervals

[LucyB]

I have some pre-post intervention data with a continuous outcome measurement and a very small sample size.

The measurements at pre and post were taken across varying levels of a certain trigger. So at pre intervention, each patient was exposed to greater and greater levels of an energy drink and heart beat was measured in response. Same was done post intervention. Each patient drank variable amounts of the energy drink, so they are not on the same scale. What statistical test would I use to assess whether if the treatment was effective in lowering the heart beat in response to increasing concentrations of the energy drink?

[peter9]

Dear Lucy,

I would suggest the following model:

proc mixed ...;

  class trial;  * 1=pre, 2=post ;

  model heartbeat = drinklevel * trial ;

  random drinklevel / subject = patient_id;

  repeated / subject = patient_id type=cs;

  estimate 'drinklevel*trial' drinklevel * trial;

run;

Modelling a random effect is necessary, when the response is heterogenous between patients (maybe because of some other unknown factors). It might be also necessary to model a different covariance of data within each trial and between different trials (i.e. before and after intervention). So you could try different covariance types in the "repeated"-statement (option type), or add the option "Group", which enables to model heterogeneity in the covariance matrix (see SAS-documentation of proc mixed).

Regards,

Peter

Regards,

Peter

[sld]

To address your research question, I think that you would want to compare the slope of the regression of HeartBeat on DrinkLevel for the pre level of Trial to the regression of HeartRate on DrinkLevel for the post level of Trial, keeping in mind that these two regressions exist for (and are paired by) each patient. Do you agree? If so, then this is a form of random coefficients model, and I would consider this code (which, of course, I have not tested and cannot guarantee) using variables as defined by  @peter9 :

proc glimmix data=have;
  class Trial Patient_ID;
  model HeartBeat = Trial | DrinkLevel / solution;
  random intercept / subject=Patient_ID;
  random intercept DrinkLevel / subject=Patient_ID*Trial;
  run;

You'd want a fair number of different DrinkLevels within each Trial for this model to work well and/or "well-behaved" data.

[LucyB]

thank you both!

[LucyB]

Hello again!

What if we were interested in whether there is significant differences between the regressions and not necessarily the slopes themselves? We want to be able to conclude that increased heartbeat is more suppressed post as compared to pre, but we do not necessarily want to make a conclusion about differences in slope (the varying levels of "drink" are actually not important).

THank you!

[sld]

In your original post, you said that

" at pre intervention, each patient was exposed to greater and greater levels of an energy drink and heart beat was measured in response. Same was done post intervention."

which led me to believe that heart rate was a consequence of the quantity or concentration (say, of caffeine) in the energy drink, that you had multiple observations of heart rate on each subject at different levels of some energy drink metric, and that you were interested in the regression of heart rate on that energy drink metric. 

Do you have multiple observations on each subject at different levels of some energy drink metric, or do you have only one observation (e.g., heart rate associated with the total quantity of energy drink consumed)? Is "trigger" the same as energy drink, or is it something else, like "treatment"?

We need a better description of the study protocol.

With respect to wanting to compare regressions but not necessarily wanting to compare slopes: Are you implying that you only want to compare intercepts or some other statistic that represents overall level? What if, for example, the regressions are linear and the slopes are not equal? What would you compare then? I'm perplexed.