gestMultiple {gesttools} | R Documentation |
G-Estimation for a Time-Varying Outcome
Description
Performs g-estimation of a structural nested mean model (SNMM), based on the outcome regression methods described in Sjolander and Vansteelandt (2016) and Dukes and Vansteelandt (2018). We assume a dataset with a time-varying outcome that is either binary or continuous, time-varying and/or baseline confounders, and a time-varying exposure that is either binary, continuous or categorical.
Usage
gestMultiple(
data,
idvar,
timevar,
Yn,
An,
Cn = NA,
outcomemodels,
propensitymodel,
censoringmodel = NULL,
type,
EfmVar = NA,
cutoff = NA,
...
)
Arguments
data |
A data frame in long format containing the data to be analysed. See description for details. |
idvar |
Character string specifying the name of the ID variable in data. |
timevar |
Character string specifying the name of the time variable in the data. Note that timevar must specify time periods as integer values starting from 1 (must not begin at 0). |
Yn |
Character string specifying the name of the time-varying outcome variable. |
An |
Character string specifying the name of the time-varying exposure variable. |
Cn |
Optional character string specifying the name of the censoring indicator variable. The variable specified in Cn should be a numeric vector taking values 0 or 1, with 1 indicating censored. |
outcomemodels |
a list of formulas or formula objects specifying the outcome models for Yn prior to adjustment by propensity score. The i'th entry of the list specifies the outcome model for the i step counterfactuals. See description for details. |
propensitymodel |
A formula or formula object specifying the propensity score model for An. |
censoringmodel |
A formula or formula object specifying the censoring model for Cn. |
type |
Value from 1-4 specifying SNMM type to fit. See details. |
EfmVar |
Character string specifying the name of the effect modifying variable for types 2 or 4. |
cutoff |
An integer taking value from 1 up to T, where T is the maximum value of timevar.
Instructs the function to estimate causal effects based only on exposures up to |
... |
Additional arguments, currently not in use. |
Details
Suppose a series of time periods whereby a time-varying exposure and confounder (
and
) are measured over times
and
a time varying outcome
is measured over times
. Define
as the step length, that is the number of time periods separating an exposure measurement, and subsequent outcome measurement.
By using the transform
,
gestmult
estimates the causal parameters of a SNMM of the form
if Y is continuous or
if Y is binary. The SNMMs form is defined by the parameter , which can be controlled by the input
type
as follows
type=1
sets. This implies that
is now the effect of exposure at any time t on all subsequent outcome periods.
type=2
setsand adds affect modification by the variable named in
EfmVar
, which we denote. Now
where
is the effect of exposure at any time t on all subsequent outcome periods, when
at all times t, modified by
for each unit increase in
at all times t. Note that effect modification is currently only supported for binary or continuous confounders.
type=3
can posit a time-varying causal effect for each value of, that is the causal effect for the exposure on outcome
time periods later. We set
to a vector of zeros of length T with a 1 in the
'th position. Now
where
is the effect of exposure on outcome
time periods later for all outcome periods
that is
on
.
type=4
allows for a time-varying causal effect that can be modified byEfmVar
, denoted, that is it allows for both time-varying effects and effect modification. It sets
to a vector of zeros of length T with
in the
'th position. Now
where
. Here
is the effect of exposure on outcome
time periods later, given
for all
, modified by
for each unit increase in
for all
. Note that effect modification is currently only supported for binary or continuous confounders.
The data must be in long format, where we assume the convention that each row with time=t
contains and
. That is the censoring indicator for each row
should indicate that a user is censored AFTER time t and the outcome indicates the first outcome that occurs AFTER
and
are measured.
For example, data at time 1, should contain
,
,
, and optionally
. If either A or Y are binary, they must be written as numeric vectors taking values either 0 or 1.
The same is true for any covariate that is used for effect modification.
The data must be rectangular with a row entry for every individual for each exposure time 1 up to T. Data rows after censoring should be empty apart from the ID and time variables. This can be done using the function FormatData
.
The input outcomemodels should be a list with T elements (the number of exposure times), where element i describes the outcome model for up to the i step counterfactual outcomes, that is the model is fitted to all counterfactuals up to Y_{s-i}
.
Value
List of the fitted causal parameters of the posited SNMM. These are labeled as follows for each SNMM type, where An is set to the name of the exposure variable, i is the current value of c, and EfmVar is the effect modifying variable.
type=1 |
An: The effect of exposure at any time t on outcome at all subsequent times. |
type=2 |
An: The effect of exposure on outcome at any time t, when EfmVar is set to zero, on all subsequent outcome times. |
type=3 |
c=i.An: The effect of exposure at any time t on outcome |
type=4 |
c=i.An: The effect of exposure at any time t on outcome |
The function also returns a summary of the propensity scores and censoring scores via PropensitySummary
and CensoringSummary
,
along with Data
, holding the original dataset with the propensity and censoring scores as a tibble dataset.
References
Vansteelandt, S., & Sjolander, A. (2016). Revisiting g-estimation of the Effect of a Time-varying Exposure Subject to Time-varying Confounding, Epidemiologic Methods, 5(1), 37-56. <doi:10.1515/em-2015-0005>.
Dukes, O., & Vansteelandt, S. (2018). A Note on g-Estimation of Causal Risk Ratios, American Journal of Epidemiology, 187(5), 1079–1084. <doi:10.1093/aje/kwx347>.
Examples
datas <- dataexamples(n = 1000, seed = 123, Censoring = FALSE)
data <- datas$datagestmult
data <- FormatData(
data = data, idvar = "id", timevar = "time", An = "A",
varying = c("Y", "A", "L"), GenerateHistory = TRUE, GenerateHistoryMax = 1
)
idvar <- "id"
timevar <- "time"
Yn <- "Y"
An <- "A"
Cn <- NA
outcomemodels <- list("Y~A+L+U+Lag1A", "Y~A+L+U+Lag1A", "Y~A+L+U")
propensitymodel <- c("A~L+U+as.factor(time)+Lag1A")
censoringmodel <- NULL
EfmVar <- NA
gestMultiple(data, idvar, timevar, Yn, An, Cn, outcomemodels, propensitymodel,
censoringmodel = NULL, type = 1, EfmVar,
cutoff = NA
)
# Example with censoring
datas <- dataexamples(n = 1000, seed = 123, Censoring = TRUE)
data <- datas$datagestmult
data <- FormatData(
data = data, idvar = "id", timevar = "time", An = "A", Cn = "C",
varying = c("Y", "A", "L"), GenerateHistory = TRUE, GenerateHistoryMax = 1
)
Cn <- "C"
EfmVar <- "L"
outcomemodels <- list("Y~A+L+U+A:L+Lag1A", "Y~A+L+U+A:L+Lag1A", "Y~A+L+U+A:L")
censoringmodel <- c("C~L+U+as.factor(time)")
gestMultiple(data, idvar, timevar, Yn, An, Cn, outcomemodels, propensitymodel,
censoringmodel = censoringmodel, type = 2, EfmVar,
cutoff = 2
)