Binary regression models with right censored outcomes

```
riskreg_cens(
response,
censoring,
treatment = NULL,
prediction = NULL,
data,
newdata,
tau,
type = "risk",
M = 1,
call.response = "phreg",
args.response = list(),
call.censoring = "phreg",
args.censoring = list(),
preprocess = NULL,
efficient = TRUE,
control = list(),
...
)
```

## Arguments

- response
Response formula (e.g., Surv(time, event) ~ D + W).

- censoring
Censoring formula (e.g., Surv(time, event == 0) ~ D + A +
W)).

- treatment
Optional treatment model (ml_model)

- prediction
Optional prediction model (ml_model)

- data
data.frame.

- newdata
Optional data.frame. In this case the uncentered influence
function evalued in 'newdata' is returned with nuisance parameters
obtained from 'data'.

- tau
Time-point of interest, see Details.

- type
"risk", "treatment", "rmst", "brier"

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

- call.response
Model call for the response model (e.g. "mets::phreg").

- args.response
Additional arguments to the response model.

- call.censoring
Similar to call.response.

- args.censoring
Similar to args.response.

- preprocess
(optional) Data pre-processing function.

- efficient
If FALSE an IPCW estimator is returned

- control
See details

- ...
Additional arguments to lower level data pre-processing
functions.

## Details

The one-step estimator depends on the calculation of an integral
wrt. the martingale process corresponding to the counting process N(t) =
I(C>min(T,tau)). This can be decomposed into an integral wrt the counting
process, \(dN_c(t)\) and the compensator \(d\Lambda_c(t)\) where the
latter term can be computational intensive to calculate. Rather than
calculating this integral in all observed time points, we can make a
coarser evaluation which can be controlled by setting
`control=(sample=N)`

. With `N=0`

the (computational intensive)
standard evaluation is used.##'

## Author

Klaus K. Holst, Andreas Nordland