ctSFTM {contTimeCausal} R Documentation

## Continuous-time Structural Failure Time Model

### Description

The function estimates the regime (in terms of time to treatment initiation) of treatment effect for a survival outcome under a Structural Failure Time Model (SFTM) with time-varying confounding in the presence of dependent censoring. Studying the effect of time to treatment discontinuation is applicable by redefining "treatment initiation" in the current description to "treatment discontinuation".

### Usage

ctSFTM(data, base = NULL, td = NULL)


### Arguments

 data A data.frame object. A data.frame containing all observed data. At a minimum, this data.frame must contain columns with headers "id", "U", "V", "deltaU", and "deltaV". If time-dependent covariates are included, additional columns include "stop" and "start". See Details for further information base A character or integer vector or NULL. The columns of data to be included in the time-independent component of the model. If NULL, time-independent covariates are excluded from the Cox model for treatment discontinuation. td A character or integer vector or NULL. The columns of data to be included in the time-dependent component of the model. If NULL, time-dependent covariates are excluded from the Cox model for treatment discontinuation.

### Details

The SFTM assumes that the potential failure time U had the individual never received treatment and the observed failure time T follow

U \sim \int_0^T e^{\psi A_u}d u,

where ~ means "has the same distribution as", and A_u is the treatment indicator at time u. We assume that the individual continuously received treatment until time V. The observed failure time can be censored assuming the censoring time is independent of the failure time given the treatment and covariate history (the so-called ignorable censoring). The current function allows for multi-dimensional baseline covariates and/or multi-dimensional time-dependent covariate. Variance estimates should be implemented by delete-one-group jackknifing and recalling ctSFTM.

If only time-independent covariates are included, the data.frame must contain the following columns:

id:

A unique participant identifier.

U:

The time to the clinical event or censoring.

deltaU:

The clinical event indicator (1 if U is the event time; 0 otherwise.

V:

The time to optional treatment discontinuation, a clinical event, censoring, or a treatment-terminating event.

deltaV:

The indicator of optional treatment discontinuation (1 if treatment discontinuation was optional; 0 if treatment discontinuation was due to a clinical event, censoring or a treatment-terminating event.

If time-dependent covariates are to be included, the data.frame must be a time-dependent dataset as described by package survival. Specifically, the time-dependent data must be specified for an interval (lower,upper] and the data must include the following additional columns:

start:

The lower boundary of the time interval to which the data pertain.

stop:

The upper boundary of the time interval to which the data pertain.

### Value

An S3 object of class ctc. Object contains element ‘psi’, the estimate of the SFTM parameter(s) and ‘coxPH’, the Cox regression for V.

### References

Yang, S., K. Pieper, and F. Cools. (2019) Semiparametric estimation of structural failure time model in continuous-time processes. Biometrika, 107(1), 123-136.

ctCoxMSM

### Examples


data(ctcData)

# sample data to reduce computation time of example
smp <- ctcData\$id %in% sample(1:1000, 200, FALSE)
ctcData <- ctcData[smp,]

# analysis with both time-dependent and time-independent components
res <- ctSFTM(data = ctcData, base = "x", td = "xt")

# analysis with only the time-independent component
res <- ctSFTM(data = ctcData, base = "x")

# analysis with only the time-dependent component
res <- ctSFTM(data = ctcData, td = "xt")



[Package contTimeCausal version 1.0 Index]