Estimation of the Average Treatment Effect among Responders

```
RATE(
response,
post.treatment,
treatment,
data,
family = gaussian(),
M = 5,
pr.treatment,
treatment.level,
SL.args.response = list(family = gaussian(), SL.library = c("SL.mean", "SL.glm")),
SL.args.post.treatment = list(family = binomial(), SL.library = c("SL.mean", "SL.glm")),
preprocess = NULL,
efficient = TRUE,
...
)
```

## Arguments

- response
Response formula (e.g, Y~D*A)

- post.treatment
Post treatment marker formula (e.g., D~W)

- treatment
Treatment formula (e.g, A~1)

- data
data.frame

- family
Exponential family for response (default gaussian)

- M
Number of folds in cross-fitting (M=1 is no cross-fitting)

- pr.treatment
(optional) Randomization probability of treatment.

- treatment.level
Treatment level in binary treatment (default 1)

- SL.args.response
Arguments to SuperLearner for the response model

- SL.args.post.treatment
Arguments to SuperLearner for the post treatment indicator

- preprocess
(optional) Data preprocessing function

- efficient
If TRUE, the estimate will be efficient. If FALSE, the estimate will be a simple plug-in estimate.

- ...
Additional arguments to lower level functions

## Author

Andreas Nordland, Klaus K. Holst