ctCoxMSM {contTimeCausal}

Continuous-time Cox Marginal Structural Model

Description

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

Usage

ctCoxMSM(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 Cox marginal structural model (MSM) assumes that the potential failure time T^{\overline{a}} under the treatment \overline{a} follows a proportional hazards model with \psi*a_u. We assume that the participant 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 function allows for multi-dimensional baseline covariates and/or multi-dimensional time-dependent covariates. Variance estimates can be implemented by delete-one-group jackknifing and recalling ctCoxMSM.

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 Cox MSM parameter(s) and ‘coxPH’, the Cox regression for V.

References

Yang, S., A. A. Tsiatis, and M. Blazing (2018). Modeling survival distribution as a function of time to treatment discontinuation: A dynamic treatment regime approach, Biometrics, 74, 900–909.

See Also

ctSFTM

Examples

 data(ctcData)

 # sample data to reduce computation time of example
 smp <- ctcData$id %in% sample(1:1000, 150, FALSE)
 ctcData <- ctcData[smp,]

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

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

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