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 categorical time-varying exposure of three or more categories.
gestmultcat(
data,
idvar,
timevar,
Yn,
An,
Ybin,
Lny,
Lnp,
type = 1,
Cn = NA,
LnC = NA,
cutoff = NA,
...
)A data frame in long format containing the data to be analysed. See description for details.
Character string specifying the name of the ID variable in data.
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).
Character string specifying the name of the time-varying outcome variable.
Character string specifying the name of the time-varying exposure variable.
TRUE or FALSE indicator of whether the outcome is binary.
Vector of character strings specifying the names of the confounders to be included in the outcome model in quotations.
Vector of character strings specifying the names of the confounders to be included in the model calculating the propensity scores.
Value from 1-4 specifying SNMM type to fit. See details.
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.
Vector of character strings specifying the names of the covariates to be used in the censoring score model to calculate
the censoring weights. Note that any variable in LnC should also be in Lnp for the validity of the censoring and propensity weights.
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 cutoff time periods prior to
outcomes. See details.
Additional arguments, currently not in use.
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, j is the category level, and Lny[1] is set to the name of the first confounder in Lny.
type=1 Anj: The effect of exposure at category j, at any time t on all subsequent outcome times.
type=2 Anj: The effect of exposure at category j on outcome at any time t, when Ln[1] is set to zero, on all subsequent outcome times. Anj:Ln[1]: The effect modification by Lny[1], the additional effect of A at category j on all subsequent Y for each unit increase in Lny[1].
type=3 c=i.Anj: The effect of exposure at any time t on outcome c=i time periods later.
type=4 c=i.Anj: The effect of exposure at any time t on outcome c=i time periods later, when Ln[1] is set to zero.
c=i.Anj:Ln[1]: The effect modification by Lny[1], the additional effect of exposure at category j, on outcome c=i time periods later for each unit increase in Lny[1].
Suppose a series of time periods \(1,\ldots,T+1\) whereby a time-varying exposure and confounder (\(A_t\) and \(L_t\)) are measured over times \(t=1,\ldots,T\) and
a time varying outcome \(Y_s\) is measured over times \(s=2,\ldots,T+1\). Define \(c=s-t\) as the step length, that is the number of time periods separating an exposure measurement, and subsequent outcome measurement. Also suppose that \(A_t=a_t\) is a categorical variable consisting of \(k>2\) categories.
These categories may take any arbitrary list of names, but we assume for theory purposes they are labeled as \(j=0,1\ldots,k\)
where \(j=0\) denotes no exposure, or some reference category. Define binary variables \(A_t^j\) \(j=0,1,\ldots,k\) where \(A_t^j=1\) if \(A_t=j\) and 0 otherwise.
By using the transform \(t=s-c\), gestmultcat estimates the causal parameters \(\psi\) of a SNMM of the form
$$E\{Y_s(\bar{a}_{s-c},a^0)-Y_s(\bar{a}_{s-c-1},a^0)|\bar{a}_{s-c-1},\bar{l}_{s-c}\}=\sum_{j=1}^{k}\psi^j z_{sc}a^j_{s-c} \; \forall c=1,\ldots,T\; and\; \forall s>c$$
if Y is continuous or
$$\frac{E(Y_s(\bar{a}_{s-c},a^0)|\bar{a}_{s-c-1},\bar{l}_{s-c})}{E(Y_s(\bar{a}_{s-c-1},a^0)|\bar{a}_{s-c-1},\bar{l}_{s-c})}=exp(\sum_{j=1}^{k}\psi^j z_{sc}a^j_{s-c}) \; \forall c=1,\ldots,T\; and \; \forall s>c $$
if Y is binary. The SNNM fits a separate set of causal parameters \(\psi^j\), for the effect of exposure at category \(j\) on outcome,
compared to exposure at the reference category 0, for each non-reference category. The models form is defined by the parameter \(z_{sc}\), which can be controlled by the input type as follows
type=1 sets \(z_{sc}=1\). This implies that \(\psi^j\) is now the effect of exposure when set to category \(j\), compared to when set to the reference category, at any time t on all subsequent outcome periods.
type=2 sets \(z_{sc}=c(1,l_{s-c})\) and adds affect modification by the first named variable in Lny, which we denote \(L_t\). Now \(\psi^j=c(\psi^j_0,\psi^j_1)\) where \(\psi^j_0\) is the effect of exposure when set to category \(j\), compared to when set to the reference category, at any time t on all subsequent outcome periods when \(l_{s-c}=0\) for all t, modified by
\(\psi^j_1\) for each unit increase in \(l_{s-c}\) 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 \(c\), that is the causal effect for the exposure on outcome \(c\) time periods later.
We set \(z_{sc}\) to a vector of zeros of length T with a 1 in the \(c=s-t\)'th position. Now \(\psi^j=c(\psi^j_{1},\ldots,\psi^j_{T})\)
where \(\psi^j_c\) is the effect of exposure, when set to category \(j\), on outcome \(c\) time periods later for all \(s>c\) that is \(A^j_{s-c}\) on \(Y_s\) for all \(s>c\).
type=4 allows for a time-varying causal effect that can be modified by the first named variable in Lny, that is it allows for both time-varying effects and effect modification. It sets \(z_{sc}\) to a vector of zeros of length T with \(c(1,l_{s-c})\) in the \(c=s-t\)'th position.
Now \(\psi^j=(\underline{\psi^j_1},\ldots,\underline{\psi^j_T})\) where \(\underline{\psi^j_c}=c(\psi^j_{0c},\psi^j_{1c})\). Here \(\psi^j_{0c}\) is the effect of exposure when set to category \(j\) on outcome \(c\) time periods later, given \(l_{s-c}=0\), for all \(s>c\), modified by
\(\psi^j_{1c}\) for each unit increase in \(l_{s-c}\) for all \(s>c\). 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 \(A_t,L_t\) and \(C_{t+1},Y_{t+1}\). That is the censoring indicator for each row
should indicate that a user is censored AFTER time t, and the outcome the first outcome that occurs AFTER \(A_t\) and \(L_t\) are measured.
For example, data at time 1, should contain \(A_1\), \(L_1\), \(Y_{2}\), and optionally \(C_2\). If Y is binary, it must be written as a numeric vector 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.
By default the censoring, propensity and outcome models include the exposure history at the previous time as a variable. One may consider also including all previous exposure and confounder history as variables in Lny,Lnp, and LnC if necessary.
Censoring weights are handled as described in Sjolander and Vansteelandt (2016). Note that it is necessary that any variable included in LnC must also be in Lnp. Missing data not due to censoring are automatically handled by removing rows with missing data prior to fitting the model. If outcome models fail to fit, consider removing covariates from Lny but keeping
them in Lnp to reduce collinearity issues, or consider the sparseness of the data.
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<U+2013>1084. <doi:10.1093/aje/kwx347>.
# NOT RUN {
datas<-dataexamples(n=1000,seed=123,Censoring=FALSE)
data=datas$datagestmultcat
#A is a categorical variable with categories labeled 1,2 and 3, with 1 the
#reference category
idvar="id"
timevar="time"
Yn="Y"
An="A"
Ybin=FALSE
#Remove U from Y to avoid collinearity
Lny=c("L","U")
Lnp=c("L","U")
Cn<-NA
LnC<-NA
type=NA
gestmultcat(data,idvar,timevar,Yn,An,Ybin,Lny,Lnp,type=1)
#Example with censoring
datas<-dataexamples(n=1000,seed=123,Censoring=TRUE)
data=datas$datagestmultcat
Cn="C"
LnC=c("L","U")
gestmultcat(data,idvar,timevar,Yn,An,Ybin,Lny,Lnp,type=3,Cn,LnC,
cutoff=2)
# }
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