Question

In the potential outcomes model (and in science), there is a principle called “intent to treat” (ITT) which says that you should evaluate people based on their assignment to a treated and untreated group and not based on whether or not they actually took a drug. For example, suppose we have a new diet we are trying to evaluate. Suppose we take a random sample of college students, and assign (randomly) half to a treatment group where they take the diet and half to an untreated group where they just eat normally. The researchers track what the people ate and whether or not they lost weight.

(a) (5 points) Suppose they compare those who followed the diet to those who did not; put this model in the potential outcomes model.

(b) (5 points) Suppose instead they followed the ITT principle and compared those who were assigned to the treated group to those who weren’t. Put this into the potential outcomes model; what’s the difference from (a)?

(c) (5 points) Which do you think it a more valid way to assess the efficacy of the diet? Relate your answer to our discussion of the ATET versus the ATE.

Answer 1

a)  The college students who were participating in this test are categorized in to two groups. Those who followed the diet(test) and those who didn't follow the diet(control).And we can identify the possible effects of both test and control.The casual effect or treatment effect is defined as the diifference between these two potential outcomes (effect).

We can represent this one in an equation,

Dt - those who are following the diet

Dc - those who are not following the diet

Dt - Dc is the potential effect of following the diet.

b) Instead of following ITT principle,  We can assign the group in to two , those who are treated group(following the diet properly) and those who aren't . In this ,we can identifiy what is the outcome of the treated and non treated. In this comaparison we are not only calculating the diifference of potential outcome but also tracking the result of the experiment. In this mode, we can track what is the potential effect of treated group compared to normal.This is the commom way of analysis of experiment.

c) I think principle A is the more valid way to assess the efficacy of the diet. Because the first model, we can compare the two groups and we can get the potential effect from the difference of each group. Test(treated) and control(untreated) groups are involved in this comaprison, so that we can easily identified the potential outcome of the study.In this, researchers can track what the people ate and whether or not they lost weight. And also we can identify what are the potential effects are happening those who are following the diet compared to those who are not following the diet.In this we can calculate  the average effect of treatment .