Estimators for stochastic direct and indirect effects.
Consider observed data O=(W,A,Z,M,Y) for each of n individuals, where we assume O1, ..., On, are i.i.d. for the true, unknown data distribution, P0, on O. The subscript 0 denotes values under this true, unknown distribution P0. P is any probability distribution in statistical model, which is the set of distributions for which our estimand is identifiable.
- W is a vector of exogenous baseline covariates, W=f(UW), where UW is unobserved exogenous error on W.
- A is a binary treatment, which may be an instrumental variable for several of the functions A=f(W, UA).
- Z is an intermediate variable, Z=f(W, A, UZ).
- M is a mediator. Depending on the function, M=f(W, Z, UM) or M=f(W, A, Z, UM), see details in each of the functions.
- Y is an outcome. Depending on the function, Y=f(W,Z,M,UY) or Y=f(W,A,Z,M,UY), see details in each of the functions.
ivmedtmle.R estimates the 1) stochastic direct effect of A on Y not through M and the 2) indirect effect of A to Z to M to Y in the scenario where A is an instrumental variable which adheres to exclusion restriction M=f(W, Z, UM) and Y=f(W,Z,M,UY).
medtmle_intermedvar.R estimates the 1) stochastic direct effect of A on Y not through M and the 2) indirect effect of A to Z to M to Y in the scenario where A is not an instrumental variable, so there is no exclusion restriction: M=f(W, A, Z, UM) and Y=f(W,A,Z,M,UY).
medtmle_nointermedvar.R estimates the 1) stochastic direct effect of A on Y not through M and the 2) indirect effect of A to M to Y in the scenario where A is not an instrumental variable and there is no intermediate variable, Z, so there is no exclusion restriction: M=f(W, A, UM) and Y=f(W,A,M,UY).
CSDE_*.R functions estimate the complier stochastic direct effect of Z on Y not through M, using A as an instrument to address observed and unobserved confounding in the scenario where A is an A is an instrumental variable which adheres to exclusion restriction M=f(W, Z, UM) and Y=f(W,Z,M,UY).