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Suppose I have five vitamins VA VB VC VD VE, and wish to study the effects of each drug on the weight of patients with data measured at daily frequency.

The typical data look like this Patient 1 take 1000mg of VA at day 15 ; take 1000mg of VD at day 19. Patient 2 take 1000mg of VE at day 35 ; take 1000mg of VB at day 87 ; then take 1000mg of VE at day 99 ....etc

In other words, if I measure the weight of patient 1 at day 25 for example, it includes the consequence of taking both VA at day 15, and taking VD at day 19.

This is the type of data I have, is there any treatment effect methodology that allow me to study the treatment effect of the drugs? So I can make the conclusion like the following : taking a one-time 1000mg VA would decrease weight by 2.9% , 60 days post taking the drug, something like that hypothetically taking a one-time 1000mg VD would increase weight by 1.3%, 60 days post taking the drug

Zwingli Tannenbaum
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2 Answers2

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It seems possible to sort this out (at least somewhat) if you create a dataset with variables Patient, Day, Cum.VA, Cum.VB, ..., Cum.VE, Weight, where you include data from each day you measure the patient's weight. By Cum.VA, etc., I mean the cumulative dose of VA up to that point (0 if none so far). Patient should be modeled as a random effect in a mixed-model analysis with Weight as the response variable and the others as predictors.

Russ Lenth
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at least the way you describe it, resolving this problem is logically impossible: you can only test for the effect of VA and VD together if the weight is only taken on D25. And test against what is not clear, as the control is not described. However, you may have higher level crossed design that you are not describing - are other patients taking the supplements in a different order (hopefully randomized).

katya
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