In the large Swedish study on the effectiveness of mammograms the researchers couldn't force people to get mammograms but they could force them to receive letters. Swedish women in two counties were randomized into two groups. One group received an invitation to get a mammogram and the other group did not. The EMILIA study of the effectiveness of Kadcyla on advanced breast cancer suffered from biased attrition. In both studies, the researchers resorted to "intent-to-treat" to save their study, get published and claim a causal relationship.
Intent-to-treat refers to the idea that while the patients were not randomly assigned to the treatment groups they were randomly assigned an observed characteristic (they received a letter or not) and that observed characteristic MAY be associated with the treatment assignment. It is like doing one stage of a two-stage instrumental variables analysis.
The problem with relying on intent-to-treat is that it may not provide evidence of causality.
To see this, think about what happens if we just observed two groups, one group received regular mammography and the other group did not. We also observe their breast cancer rates and survival rates. In fact, assume that we observe higher survival rates among the women who received regular mammography. From this information, and only this information, can we determine the causal effect of mammography on survival from breast cancer?
The problem is that we don't know anything about how the two groups were selected. Even if we are able to account for differences in the observable characteristics like age, there still may be differences in unobserved characteristics such as the women's genetic profile.
Now what if I told you that the group who received a mammogram was much more likely to have received an invitation to get the mammography than the group who did not receive a mammography? Moreover, the invitation was randomly assigned. Can this information determine the causal effect of mammography on survival from breast cancer?
The problem is the same. Despite the random assignment of the invitation we still do not know the make up of the two groups. In particular, we do not know things about the unobserved characteristics of the women such as genetics or a family history of breast cancer that would make them more likely to get a mammography (with or without the invitation).
The same problem occurs in the EMILIA trial. Women left the trial at different rates depending on the treatment arm that they were assigned. Because they left we do not know when or if they passed away. The women that remained in the trial may be different across the two arms, so we can no longer assign the difference in the treatment outcomes to the different treatments. We can no longer remove the possibility that the different outcomes were due to other differences between the women in the two trial arms. We cannot use the trial to determine the causal effect of Kadcyla on breast cancer survival even though the women were randomly assigned to treatments.