tmle  R Documentation 
Targeted maximum likelihood estimation of parameters of a marginal structural model, and of marginal treatment effects of a binary point treatment on an outcome. In addition to the additive treatment effect, risk ratio and odds ratio estimates are reported for binary outcomes. The tmle
function is generally called with arguments (Y,A,W)
, where Y
is a continuous or binary outcome variable, A
is a binary treatment variable, (A=1
for treatment, A=0
for control), and W
is a matrix or dataframe of baseline covariates. The population mean outcome is calculated when there is no variation in A
. If values of binary mediating variable Z
are supplied, estimates are returned at each level of Z
. Missingness in the outcome is accounted for in the estimation procedure if missingness indicator Delta
is 0 for some observations. Repeated measures can be identified using the id
argument. Option to adjust for biased sampling using the obsWeights
argument. Targeted bootstrap inference can be obtained in addition to ICbased inference by setting B
to a value greater than 1 (10,000 recommended for analyses requiring high precision).
tmle(Y, A, W, Z=NULL, Delta = rep(1,length(Y)), Q = NULL, Q.Z1 = NULL, Qform = NULL,
Qbounds = NULL, Q.SL.library = c("SL.glm", "tmle.SL.dbarts2", "SL.glmnet"),
cvQinit = TRUE, g1W = NULL, gform = NULL,
gbound = NULL, pZ1=NULL,
g.Zform = NULL, pDelta1 = NULL, g.Deltaform = NULL,
g.SL.library = c("SL.glm", "tmle.SL.dbarts.k.5", "SL.gam"),
g.Delta.SL.library = c("SL.glm", "tmle.SL.dbarts.k.5", "SL.gam"),
family = "gaussian", fluctuation = "logistic", alpha = 0.9995, id=1:length(Y),
V.Q = 10, V.g=10, V.Delta=10, V.Z = 10,
verbose = FALSE, Q.discreteSL=FALSE, g.discreteSL=FALSE, g.Delta.discreteSL=FALSE,
prescreenW.g=TRUE, min.retain = 5, target.gwt = TRUE, automate=FALSE,
obsWeights = NULL, alpha.sig = 0.05, B = 1)
Y 
continuous or binary outcome variable 
A 
binary treatment indicator, 
W 
vector, matrix, or dataframe containing baseline covariates 
Z 
optional binary indicator for intermediate covariate for controlled direct effect estimation 
Delta 
indicator of missing outcome or treatment assignment. 
Q 
optional 
Q.Z1 
optional 
Qform 
optional regression formula for estimation of 
Qbounds 
vector of upper and lower bounds on 
Q.SL.library 
optional vector of prediction algorithms to use for 
cvQinit 
logical, if 
g1W 
optional vector of conditional treatment assingment probabilities, 
gform 
optional regression formula of the form 
gbound 
value between (0,1) for truncation of predicted probabilities. See 
pZ1 
optional 
g.Zform 
optional regression formula of the form 
pDelta1 
optional matrix of conditional probabilities for missingness mechanism, 
g.Deltaform 
optional regression formula of the form 
g.SL.library 
optional vector of prediction algorithms to use for 
g.Delta.SL.library 
optional vector of prediction algorithms to use for 
family 
family specification for working regression models, generally ‘gaussian’ for continuous outcomes (default), ‘binomial’ for binary outcomes 
fluctuation 
‘logistic’ (default), or ‘linear’ 
alpha 
used to keep predicted initial values bounded away from (0,1) for logistic fluctuation 
id 
optional subject identifier 
V.Q 
Number of crossvalidation folds for super learner estimation of Q 
V.g 
Number of crossvalidation folds for super learner estimation of g 
V.Delta 
Number of crossvalidation folds for super learner estimation of missingness mechanism 
V.Z 
Number of crossvalidation folds for super learner estimation of intermediate variable 
verbose 
status messages printed if set to 
Q.discreteSL 
if TRUE, discreteSL is used instead of ensemble SL. Ignored when SL not used to estimate Q 
g.discreteSL 
if TRUE, discreteSL is used instead of ensemble SL. Ignored when SL not used to estimate g1W 
g.Delta.discreteSL 
if TRUE, discreteSL is used instead of ensemble SL. Ignored when SL not used to estimate P(Delta = 1  A,W) 
prescreenW.g 
Option to screen covariates before estimating g in order to retain only those associated with the outcome (Recommend FALSE in low dimensional datasets) 
min.retain 
Minimum number of covariates to retain when prescreening covariates for g. Ignored when prescreenW.g=FALSE 
target.gwt 
When TRUE, move g from denominator of clever covariate to the weight when fitting epsilon 
automate 
When TRUE, all tuning parameters are set to their default values. Number of cross validation folds, truncation level for g, and decision to prescreen covariates for modeling g are set dataadaptively based on sample size (see details). 
obsWeights 
Optional observation weights to account for biased sampling 
alpha.sig 
significance level for constructing 
B 
Number of boostrap iterations. Set 
gbounds
Lower bound defaults to lb = 5/sqrt(n)/log(n)
. For treatment effect estimates and population mean outcome the upper bound defaults to 1. For ATT and ATC, the upper bound defaults to 1 lb.
W
may contain factors. These are converted to indicators via a call to model.matrix
.
Controlled direct effects are estimated when binary covariate Z
is nonnull. The tmle function returns an object of class tmle.list
, a list of two items of class tmle
. The first corresponds to estimates obtained when Z
is fixed at 0
, the second corresponds to estimates obtained when Z
is fixed at 1
.
When automate = TRUE the sample size determines the number of cross validation folds, V based on the effective sample size. When Y is continuous n.effective = n. When Y is binary n.effective = 5 * size of minority class. When n.effective <= 30 V= n.effective; When n.effective <= 500 V= 20; When 500 < n <=1000 V=10; When 1000 < n <= 10000 V=5; Otherwise V=2. Bounds on g
set to (5/sqrt(n)/log(n), 1)
, except for ATT and ATE, where upper bound is 1lower bound. Wretain.g
set to TRUE when number of covariates >= n.effective / 5
.
Set B
= 10,000 to obtain high precision targeted bootstrap quantilebased confidence intervals and variance of bootstrap point estimates. Set B
= 1,000 for rough approximation, and B
= 1 for ICbased inference only.
estimates 
list with elements EY1 (population mean), ATE (additive treatment effect), ATT (additive treatment effect among the treated), ATC (additive treatment effect among the controls), RR (relative risk), OR (odds ratio). Each element in the estimates of these is itself a list containing

Qinit 
initial estimate of 
Qstar 
targeted estimate of 
g 
treatment mechanism estimate. A list with four items: 
g.Z 
intermediate covariate assignment estimate (when applicable). A list with four items: 
g.Delta 
missingness mechanism estimate. A list with four items: 
gbound 
bounds used to truncate g 
gbound.ATT 
bounds used to truncated g for ATT and ATC estimation 
W.retained 
names of covariates used to model the components of g 
Susan Gruber sgruber@cal.berkeley.edu, in collaboration with Mark van der Laan.
1. Gruber, S. and van der Laan, M.J. (2012), tmle: An R Package for Targeted Maximum Likelihood Estimation. Journal of Statistical Software, 51(13), 135. https://www.jstatsoft.org/v51/i13/
2. Gruber, S. and van der Laan, M.J. (2009), Targeted Maximum Likelihood Estimation: A Gentle Introduction. U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 252. https://biostats.bepress.com/ucbbiostat/paper252/
3. Gruber, S. and van der Laan, M.J. (2010), A Targeted Maximum Likelihood Estimator of a Causal Effect on a Bounded Continuous Outcome. The International Journal of Biostatistics, 6(1), 2010.
4. Rosenblum, M. and van der Laan, M.J. (2010).Targeted Maximum Likelihood Estimation of the Parameter of a Marginal Structural Model. The International Journal of Biostatistics, 6(2), 2010.
5. van der Laan, M.J. and Rubin, D. (2006), Targeted Maximum Likelihood Learning. The International Journal of Biostatistics, 2(1). https://biostats.bepress.com/ucbbiostat/paper252/
6. van der Laan, M.J., Rose, S., and Gruber,S., editors, (2009) Readings in Targeted Maximum Likelihood Estimation . U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 254. https://biostats.bepress.com/ucbbiostat/paper254/
7. van der Laan, M.J. and Gruber S. (2016), OneStep Targeted Minimum Lossbased Estimation Based on Universal Least Favorable OneDimensional Submodels. The International Journal of Biostatistics, 12 (1), 351378.
8. Gruber, S., Phillips, R.V., Lee, H., van der Laan, M.J. DataAdaptive Selection of the Propensity Score Truncation Level for Inverse Probability Weighted and Targeted Maximum Likelihood Estimators of Marginal Point Treatment Effects. American Journal of Epidemiology 2022; 191(9), 16401651.
summary.tmle
,
estimateQ
,
estimateG
,
calcParameters
,
oneStepATT
,
tmleMSM
,
calcSigma
library(tmle)
set.seed(1)
n < 250
W < matrix(rnorm(n*3), ncol=3)
A < rbinom(n,1, 1/(1+exp((.2*W[,1]  .1*W[,2] + .4*W[,3]))))
Y < A + 2*W[,1] + W[,3] + W[,2]^2 + rnorm(n)
# Example 1. Simplest function invocation
# SuperLearner called to estimate Q, g
# Delta defaults to 1 for all observations
## Not run:
result1 < tmle(Y,A,W)
summary(result1)
## End(Not run)
# Example 2:
# Usersupplied regression formulas to estimate Q and g
# binary outcome
n < 250
W < matrix(rnorm(n*3), ncol=3)
colnames(W) < paste("W",1:3, sep="")
A < rbinom(n,1, plogis(0.6*W[,1] +0.4*W[,2] + 0.5*W[,3]))
Y < rbinom(n,1, plogis(A + 0.2*W[,1] + 0.1*W[,2] + 0.2*W[,3]^2 ))
result2 < tmle(Y,A,W, family="binomial", Qform="Y~A+W1+W2+W3", gform="A~W1+W2+W3")
summary(result2)
## Not run:
# Example 3:
# Incorporate sampling weights and
# request targeted bootstrapbased inference along with ICbased results
pi < .25 + .5*W[,1] > 0
enroll < sample(1:n, size = n/2, p = pi)
result3 < tmle(Y[enroll],A[enroll],W[enroll,], family="binomial", Qform="Y~A+W1+W2+W3",
gform="A~W1+W2+W3", obsWeights = 1/pi[enroll],B=1000)
summary(result3)
# Example 4: Population mean outcome
# Usersupplied (misspecified) model for Q,
# Super learner called to estimate g, g.Delta
# V set to 2 for demo, not recommended at this sample size
# approx. 20
Y < W[,1] + W[,2]^2 + rnorm(n)
Delta < rbinom(n, 1, 1/(1+exp((1.71*W[,1]))))
result4 < tmle(Y,A=NULL,W, Delta=Delta, Qform="Y~A+W1+W2+W3", V.g=2, V.Delta=2)
print(result4)
# Example 5: Controlled direct effect
# Usersupplied models for g, g.Z
# V set to 2 for demo, not recommended at this sample size
A < rbinom(n,1,.5)
Z < rbinom(n, 1, plogis(.5*A + .1*W[,1]))
Y < 1 + A + 10*Z + W[,1]+ rnorm(n)
CDE < tmle(Y,A,W, Z, gform="A~1", g.Zform = "Z ~ A + W1", V.Q=2, V.g=2)
print(CDE)
total.effect < tmle(Y,A, W, gform="A~1")
print(total.effect)
## End(Not run)
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