HW 3-8

HW 3-8

by Hyelee Kim -


Hi! 

I have a question about question 8 of hw 3.

"Considering the effect of MMR vaccine A on the risk of ASD diagnosis Y, provide a numerical example of the following table (again, each row represents 1 million subjects) under each of the 2 scenarios described below"

I am not sure what the highlighted part would mean. When I saw this question, I assumed that each ID is for one subject. However, this question specifies that each row represents 1 million subjects. Would it different from when we assume that each row represents 1 subject?

Thank you!

Hyelee

Re: HW 3-8

by Dan Kelly -
Hi Hyelee,

Thanks for your question.

By stating that each row represents 1 million subjects, we make the assumption that there is no random variability with our counterfactual outcomes.

Random variability occurs in the counterfactual world through two types of random error (sampling variability and/or nondeterministic counterfactuals). Sampling variability is something to consider when estimating the average causal effect. The Zeus example in Hernan Chapter 1.4 represents the whole population but usually we only have a proportion of the population. As the population becomes increasingly large, we are able to make a consistent estimate of the average causal effect.

On the individual level, or by each row, we need to consider that the counterfactual outcome itself can be probabilistic depending on the treatment. Instead of Zeus having a 100% chance of dying if treated and 0% chance of dying if untreated, maybe he only has a 90% chance of dying if treated and 10% chance of dying if untreated, which would be nondeterministic or stochastic. However, if we view each row as represented by 1 million subjects, we can ignore random error and assume the counterfactual outcomes are deterministic (Zeus has a 100% chance of dying if treated, etc...).

Hope that helps!
Dan