Toward a More Disproportionate Epidemiology

Abstract

Iwas lured into epidemiology by a friend in environmental engineering. “But don’t worry,” he assured me. “You don’t have to take any classes or anything. It’s not a real science like chemistry or physics.” Years later, a fictional department chair heard this story and was intrigued by the idea that teaching epidemiology might offer no benefit whatsoever for a large number of graduate students. He decided to save scarce funds by paying me for teaching only those students who would pass my course because they attended the class. There are 3 kinds of students, he reasoned: the type (A) who would pass the examination with or without attending the lectures, the type (B) who would pass the examination if they attended but fail if they did not, and the type (C) who were doomed to fail the examination regardless. He told me to figure out the number of type Bs in the student population, because this is the only group worth teaching. Fortunately, I had myself studied epidemiology, so I knew to partition my incoming class at random, which assured that the expected representation of each of these latent types would be the same in the 2 groups. Then I taught one group of 30 students my usual course and assigned the other group of 30 to stay away. Everyone was compliant with their assignments and there was no communication about epidemiology among the students (needless to say). At the end of the term, I gave my examination. Only 6 of 30 students passed the examination without the class, but 18 of 30 passed with instruction. I reasoned that the number who passed in the group with instruction was AB, whereas the number who passed in the group without instruction was simply A. The ratio of these numbers would be the causal effect of teaching, which was 18/6 3.0. It seemed that my teaching had tripled the pass rate, which made me happy, but did not please my fictional department chair. He wanted to pay me on the basis of the number of people who were Type B, whereas I had only identified the quantities A, AB, and their ratio (AB)/A. Again fortune came to my rescue, as my research assistant K. had been assigned to the group without epidemiologic instruction. Free from the strictures of epidemiologic habit that I had learned and passed on to my other students, K. advised me to simply take the difference between the 2 numbers instead of their ratio. The difference of (AB) in the treated group minus A in the untreated group would yield B. A total of 18 6 12 students passed the examination because of the instruction, a number completely obscured by the relative contrast that I had made without K.’s assistance. K.’s radical analytic insight proved even handier the following year, as the worsening economy drove many highly qualified applicants back to graduate school, and so the overall failure rate on exams decreased dramatically. There were again 60 students, with 30 assigned to each group. This time, 8 of 30 students passed the examination without the class, but 24 of 30 passed with instruction. The ratio (AB)/A showed that once again my instruction had tripled the pass rate, since 24/8 3.0. Without K.’s help, I might have claimed to have had the same effect on my students as in the previous year,