There are two interesting features of this targeting problem. First, we see that the nuisance parameter Qbarbar_M1_times_M2_a can be viewed in two ways: (1) the conditional mean of Qbarbar_M1_a given C with respect to the marginal of M_2 given A = a, C; (2) the conditional mean of Qbarbar_M2_a given C with respect to the marginal of M_1 given A = a, C. The natural inclination then is to use a sum loss function, which it seems we can do here.
target_Qbarbar_M1_times_M2_a( Qbarbar, Y, A, a, a_star, gn, tol = 1/(sqrt(length(Y)) * log(length(Y))), max_iter = 25, iterative = FALSE, ... )
| Qbarbar | Iterated mean estimates |
|---|---|
| Y | A vector of continuous or binary outcomes. |
| A | A vector of binary treatment assignment (assumed to be equal to 0 or 1). |
| a | The label for the treatment. The effects estimates returned pertain
to estimation of interventional effects of |
| a_star | The label for the treatment. The effects estimates returned pertain
to estimation of interventional effects of |
| gn | Power users may wish to pass in their own properly formatted list of the
propensity score so that
nuisance parameters can be fitted outside of |
| tol | The tolerance for stopping the iterative targeting procedure. |
| max_iter | The maximum number of iterations for the TMLE |