ngreifer
commented
1 year ago The recommended approach is to estimate weights separately in each group of the effect modifier. You can do this using the by argument as you mentioned. This method is agnostic to how the weights are created, and so is compatible with energy balancing or any other method.
The expression you found is correct only when the propensity score model is correct. Notice that the denominator of the weights is identical to what it would be if $Q$ was just a covariate. There is no special formula for propensity scores in the context of effect modification. Using a stabilization factor in the numerator is optional as described in the paper, and is in accordance with the general advice given in Cole & Hernán (2008) that if you are adjusting for a covariate in the outcome model, you can include it in the stabilization factor at no cost, where it is also optional.
So, what I mean to communicate is that this is not a special formula for weights under effect modification; this is a general formula for propensity score weights, and the stabilization factor is optional and consistent with its use in standard analysis of weighted treatment effect estimates. I also want to say that the empirical application of this formula may not yield the least bias or most precise estimates of the subgroup treatment effects; a method that fully achieves balance within each subgroup will do that, and such a method typically involves estimating weights separately within each subgroup, which you can do using the by argument. Rather than thinking about the formula for a propensity score model, think about weights that achieve balance; energy balancing weights do not estimate propensity scores and don't involve a model (except in an abstract, implicit way), and so do not correspond to the formula you included.
lorenzoFabbri
I would like to explore the possibility of effect modification (between exposure and one or more covariates) in my models. VanderWeele provides the following formula for the weights of a Marginal Structural Model (for effect modification rather than interaction) [1]:
$$ w_i^E = \frac{P(E = e_i | Q = q_i)}{P(E = e_i | Q = q_i, X = x_i)}, $$
with $E$ being the treatment/exposure, $Q$ the effect modifier, and $X$ the confounders. In my case, the exposure $E$ is continuous, while $Q$ can be either continuous or categorical (up to 6 levels).
I would like to know whether this is possible with the
WeightItpackage (right now I am using theenergymethod). I thought about estimating the weights passing $Q$ to thebyargument.[1] On the Distinction Between Interaction and Effect Modification. DOI: 10.1097/EDE.0b013e3181ba333c.