tmle_exposed: Targeted minimum-loss based estimator for stochastic and...

In amalielykkemark/tmleExposed: Targeted minimum-loss based estimator for stochastic and deterministic interventions among the exposed

Targeted minimum-loss based estimator for stochastic and deterministic interventions among the exposed

Description

The tmle_exposed is a Targeted Minumum-loss based estimator (TMLE) that can be used to estimate effects of interventions targeting an intermediate factor among the exposed. The intermediate factor (Z) is an effect of the exposure (A) and a cause of the outcome (Y), A -> Z -> Y. According to the intervention of interest, different parameters and estimators can be chosen using intervention. If intervention='unexposed', which is the default, then the estimated parameter is the expected change in outcome risk among the exposed (A=1) if hypothetically the exposed had the same probability of the intermediate (Z) variable as the unexposed (A=0). Other parameteres can be estimated by setting intervention to a number between 0 and 1. If intervention=1, then the estimated parameter is the expected outcome risk among the exposed (A=1) if all exposed received the intermediate variable (Z). intervention can be fixed to any probability of interest, for example if intervention=0.6, then the estimated parameter would be the expected outcome risk among the exposed (A=1) if all exposed had 60 intermediate variable (Z). Regardless of which intervention is chosen, the expected outcome risk under intervention is compared to the outcome risk among the exposed when the distribution of the intermediate variable was set to the observed level among the exposed. Importantly, for this estimator the exposure, intermediate variable, and outcome must all be binary. The underlying model for the exposure, intermediate, and outcome, which are needed to estimate any of the parameters, can be modelled using Super learning. Super learning can be used to produce a weighted combination of candidate algorithms that optimize the cross-validated loss-function or to select the single best perfoming algorithm among the candidate algorithms, also known as the discrete Super learner. One must define a library of candidate algortihms which should be considered by the Super learner. If the Super learner library contains only one algorithm, results will be estimated based on this algorithm alone, and thus, not using Super Learning.

Usage

tmle_exposed(data, intervention='unexposed', discrete.SL=TRUE,
 exposure.A=NA, intermediate.Z=NA, outcome.Y=NA, cov.A, cov.Z, cov.Y,
 SL.lib.A=FALSE, SL.lib.Z=FALSE, SL.lib.Y=FALSE, iterations=10)

Arguments

data	A data frame/data table with a binary exposure, a binary intermediate variable, a binary outcome, and covariates.
intervention	Either the character string unexposed for a stochastic intervention or or a value, X, between 0 and 1 for a deterministic intervention. If unexposed then the distribution of the intermediate (Z) among the exposed (A=1) is set to the distribution of (Z) observed among the unexposed (A=0). Under the deterministic intervention the chance of the intermediate among the exposed is set to the fixed value X, i.e. if X=1 then all exposed observations received the intermediate.
discrete.SL	If FALSE TMLE will use the weighted combination of the algorithms in the super learner library that minimizes the loss function. Defaults to TRUE, in which case the discrete super learner i used, i.e. the best performing algorithm.
exposure.A	Name of the binary exposure.
intermediate.Z	Name of the binary intermediate variable, which is the target of the hypothetical intervention.
outcome.Y	Name of the binary outcome.
cov.A	A vector containing names of possible confounders which should be included in models of the exposure.
cov.Z	A vector of confounders which should be included in models of the intermediate. Do not include the exposure as the function does this.
cov.Y	A vector of confounders which should be included in models of the outcome. Do not include the exposure and the intermediate as the function does this.
SL.lib.A	A vector of algorithms that should be considered by the super learner when modelling the exposure. All algorithms must be specified as Super Learner objects.
SL.lib.Z	A vector of algorithms for modelling the intermediate. All algorithms must be specified as Super Learner objects.
SL.lib.Y	A vector of algorithms for modelling the outcome. All algorithms must be specified as Super Learner objects.
iterations	Number of iterations for the updating step in TMLE. Defaults to 10.

Details

The structure of the data should be as follows: \item For the binary exposure (exposure.A) 1 = exposed and 0 = unexposed. \item For the binary intermediate variable (intermediate.Z) 1 = treatment and 0 = no treatment. \item For the binary outcome (outcome.Y) 1 = event and 0 = no event.

Value

The function outputs the absolute outcome risk among the exposed under a hypothetical intervention ('unexposed' or fixed chance of intermediate) (psi0 or psi0star), the absolute outcome risk among the exposed under no intervention, where the probability of the intermediate variable is as observed (psi1), and the absolute risk difference between the two (psi or psistar) along with the standard errors for psi0/psi0star, psi1, and psi/psistar.

Author(s)

Amalie Lykkemark Moller [e-mail] Helene Charlotte Wiese Rytgaard, Thomas Alexander Gerds, and Christian Torp-Pedersen

Examples

library(data.table)
require(tmleExposed)
n=5000
set.seed(1)
sex <- rbinom(n,1,0.4)
age <- rnorm(n,65,sd=5)
disease <- rbinom(n,1,0.6)

A <- rbinom(n, 1, plogis(-3+0.05*age+1*sex))
Z <- rbinom(n, 1, plogis(5-0.08*age+1*sex-1.2*disease-0.8*A+0.01*A*disease))
Y <- rbinom(n, 1, plogis(-9+0.09*age+0.5*sex+0.8*disease-1.2*Z+0.7*A))

d <- data.table(id=1:n, exposure=as.integer(A), intermediate=as.integer(Z),
               outcome=as.integer(Y), age, sex, disease)

##### Define algorithms for the Super Learner library #####
lib = c('SL.glm','SL.step.interaction')

#intervention: changing probability of the intermediate (Z=1) among the exposed (A=1)
#to what it would have been had they been unexposed (A=0).
#target parameter: the change in outcome among the exposed (A=1) had their chance of
#the intermediate (Z=1) been as among the unexposed (A=0).

res<-tmle_exposed(data=d,
                 intervention = 'unexposed',
                 exposure.A='exposure',
                 intermediate.Z='intermediate',
                 outcome.Y='outcome',
                 cov.A=c('sex','age'),
                 cov.Z =c('sex','age','disease'),
                 cov.Y=c('sex','age','disease'),
                 SL.lib.A = lib,
                 SL.lib.Z = lib,
                 SL.lib.Y = lib,
                 discrete.SL = FALSE)

summary(res)

#intervention: all exposed (A=1) receives the intermediate (Z=1).
#target parameter: the change in outcome among the exposed had all
#exposed received the intermediate (Z=1).
tmle_exposed(data=d,
            intervention = 1,
            exposure.A='exposure',
            intermediate.Z='intermediate',
            outcome.Y='outcome',
            cov.A=c('sex','age'),
            cov.Z =c('sex','age','disease'),
            cov.Y=c('sex','age','disease'),
            SL.lib.A = lib,
            SL.lib.Z = lib,
            SL.lib.Y = lib,
            discrete.SL = FALSE)

#intervention: all exposed (A=1) had 60% chance of reciving
#the intermediate (Z=1).
#target parameter: the change in outcome among the exposed had
#60% exposed received the intermediate (Z=1).
tmle_exposed(data=d,
            intervention = 0.6,
            exposure.A='exposure',
            intermediate.Z='intermediate',
            outcome.Y='outcome',
            cov.A=c('sex','age'),
            cov.Z =c('sex','age','disease'),
            cov.Y=c('sex','age','disease'),
            SL.lib.A = lib,
            SL.lib.Z = lib,
            SL.lib.Y = lib,
            discrete.SL = FALSE)

amalielykkemark/tmleExposed documentation built on May 6, 2023, 1:26 a.m.