tmle {tmleLite}R Documentation

Targeted Maximum Likelihood Estimation of Additive Treatment Effect (Lite)

Description

Carries out a simplified version of targeted maximum likelihood estimation of marginal additive treatment effect of a binary point treatment on an outcome. This parameter is defined as E(E(Y|A=1,W) - E(Y|A=0,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 tmle function is minimally called with arguments (Y,A,W). Missingness in the outcome is accounted for in the estimation procedure, if optional missingness indicator Delta is supplied.

Usage

tmle(Y, A, W, Delta = rep(1, length(Y)), id = 1:length(Y),
Q = NULL, g_A = NULL, g_M = NULL, wts = rep(1, length(Y)), 
DSAargs = NULL, family = "gaussian", epsilon = NULL)

Arguments

Y continuous or binary outcome variable
A binary treatment indicator, 1 - treatment, 0 - control
W vector, matrix, or dataframe containing baseline covariates
Delta indicator of missing outcome or treatment assignment. 1 - observed, 0 - missing
id id identifying repeated measures
Q E(Y|A,W), the Q portion of the likelihood, specified in one of three ways:
NULL specifies DSA estimation of E(Y|A=a, W), with A forced into the model (default).
matrix of values, one row per observation, three columns: E(Y|A=a,W), E(Y|A=1,W), E(Y|A=0,W).
formula for estimation of E(Y|A, W), suitable for call to glm
g_A binary treatment mechanism, specified in one of three ways:
NULL defaults to DSA estimation of P(A=1|W)
vector of values P(A=1|W), one entry per observation
formula for estimation of P(A=1,W), suitable for call to glm
g_M missingness mechanism, specified in one of three ways:
NULL defaults to DSA estimation of P(Delta=1|W)
vector of values P(Delta=1|W), one entry per observation
formula for estimation of P(Delta=1,W), suitable for call to glm
wts optional weights on observations. Defaults to unweighted
DSAargs optional settings for DSA estimation. See DSA help files for further information. Default settings are: maxsumofpow = 2, maxorderint = 2, maxsize=15, vfold = 5, nsplits=1, Dmove=FALSE, Smove=FALSE.
family family specification for working regression models, generally ‘gaussian’ for continuous outcomes (default), ‘binomial’ for binary outcomes.
epsilon advanced option. Ordinarily this argument should not be specified, but can optionally be set to 0 to circumvent the targeting step.

Value

psi additive treatment effect estimate
var variance of estimate, based on the influence curve
pvalue two-sided p-value
CI 95% confidence interval
epsilon MLE for coefficient used in targeting step
Q initial estimate of Q portion of the likelihood. Q$coefficients are the coefficients for the model for Q selected by DSA or specified by the user. Q$Q is an nx3 matrix, where n is the number of observations. Columns contain targeted predicted values for Q(A,W),Q(1,W),Q(0,W), respectively. Q$type is method for estimating Q, NULL- user supplied, ‘DSA’, or ‘glm’
g_A treatment mechanism estimate. A list with two items: g_A$coefficients the coefficients for the model for g_A selected by DSA or specified by the user. g_A$g1W contains values of P(A=1|W) for each observation
g_M missingness mechanism estimate. A list with two items: g_M$coefficients the coefficients for the model for g_M selected by DSA or specified by the user. g_M$g1W contains values of P(Delta=1|A,W) for each observation
Qcounterfactual targeted estimate of counterfactual outcomes Q(1,W),Q(0,W)

Author(s)

Susan Gruber sgruber@berkeley.edu, in collaboration with Mark van der Laan.

References

1. Mark J. van der Laan and Daniel Rubin (2006), “Targeted Maximum Likelihood Learning”. The International Journal of Biostatistics, 2(1). http://www.bepress.com/ijb/vol2/iss1/11/

2. Susan Gruber and Mark J. van der Laan (2009), “Targeted Maximum Likelihood Estimation: A Gentle Introduction”. U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 252. http://www.bepress.com/ucbbiostat/paper252

3. Mark J. van der Laan, Sherri Rose, Susan Gruber editors, (2009) “Readings in Targeted Maximum Likelihood Estimation” . U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper xxx. http://www.bepress.com/ucbbiostat

4. Sandra E. Sinisi and Mark J. van der Laan, (2004). “Loss-Based Cross-Validated Deletion/Substitution/Addition Algorithms in Estimation”. U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 143. http://www.bepress.com/ucbbiostat/paper143

See Also

summary.tmle, estimate_Q, estimate_g, DSA

Examples

library(tmleLite)

# generate data
  n <- 500
  W <- matrix(rnorm(n*3), ncol=3)
  A <- rbinom(n,1, 1/(1+exp(-(.1*W[,1] - .1*W[,2] + .5*W[,3]))))
  Y <- A + 2*W[,1] + W[,3] + W[,2]^2 + rnorm(n)
  colnames(W) <- paste("W",1:3, sep="")

# Example 1. Simplest function invocation 
# DSA called to estimate Q, g_A.
# Because Delta is not supplied, all outcomes are known to be measured.
#   
  result1 <- tmle(Y,A,W)
  summary(result1)

# Example 2: Binary outcome 
# DSA called to estimate Q
# known treatment mechanism, g_A, is user supplied 
# 
  A.ex2 <- rbinom(n,1,.5)
  Y.ex2 <- A.ex2 + 2*W[,1] + W[,3] + W[,2]^2 + rnorm(n)
  result2 <- tmle(Y=Y.ex2,A=A.ex2,W, g_A =rep(.5, length(Y)))
  summary(result2)

# Example 3: 
# User-supplied (misspecified) model for Q, 
# DSA called to estimate g_A, g_M
# approx. 20

  Delta <- rbinom(n, 1, 1/(1+exp(-(1.7-1*W[,1]))))
  result3 <- tmle(Y,A,W, Delta=Delta, Q=Y~A+W1+W2+W3)
  summary(result3)

[Package tmleLite version 1.0-1 Index]