5: ESTIMATION
After a little hiatus, back to discussing Robins 1986 (with a new keyboard)! Robins starts by reminding us (me) that we are assuming the super-population model for inference
If we had a infinite n in our study, we could use NPMLE. However, time-varying exposures have a particular large number of possible intervention plans. We probably don't have anywhere near enough obs to consider all the possible plans
Instead we use a parametric projection of the time-varying variables. We hope that the parametric projection is sufficiently flexible to approx the true density function (it is why it is best to include as many splines and interaction terms as feasible)
We now move to the arsenic example to connect the method discussed in the previous section
To estimate the parameters for the equations for the g-formula. Robins uses conditional logit for the parameters
With those estimated parameters, we can then use the Monte Carlo procedure previously described to estimate potential outcomes under the treatment plans of interest
Further mention of our models being correctly specified, and the recommendation to use bootstrapping for inference
Section 5 closes with further discussion of the issue of parametric model specification. The upside (and teaser for the next section) ius that nonparam null hypothesis testing is possible
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