tmleMSM: Targeted Maximum Likelihood Estimation of Parameter of MSM

In tmle: Targeted Maximum Likelihood Estimation

Targeted Maximum Likelihood Estimation of Parameter of MSM

Description

Targeted maximum likelihood estimation of the parameter of a marginal structural model (MSM) for binary point treatment effects. The tmleMSM function is minimally called with arguments (Y,A,W, MSM), 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. MSM is a valid regression formula for regressing Y on any combination of A, V, W, T, where V defines strata and T represents the time at which repeated measures on subjects are made. 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. Observation weigths (sampling weights) may optionally be provided

Usage

tmleMSM(Y, A, W, V, T = rep(1,length(Y)), Delta = rep(1, length(Y)), MSM, 
        v = NULL, Q = NULL, Qform = NULL, Qbounds = c(-Inf, Inf), 
        Q.SL.library = c("SL.glm", "tmle.SL.dbarts2", "SL.glmnet"), 
        cvQinit = TRUE, hAV = NULL, hAVform = NULL, g1W = NULL, 
        gform = 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"),
	ub = sqrt(sum(Delta))* log(sum(Delta)) / 5, family = "gaussian", 
	fluctuation = "logistic", alpha  = 0.995, id = 1:length(Y), 
	V.Q = 10, V.g = 10, V.Delta = 10, inference = TRUE, verbose = FALSE, 
	Q.discreteSL = FALSE, g.discreteSL = FALSE, alpha.sig = 0.05, obsWeights = NULL)

Arguments

Y	continuous or binary outcome variable
A	binary treatment indicator, 1 - treatment, 0 - control
W	vector, matrix, or dataframe containing baseline covariates. Factors are not currently allowed.
V	vector, matrix, or dataframe of covariates used to define strata
T	optional time for repeated measures data
Delta	indicator of missing outcome or treatment assignment. 1 - observed, 0 - missing
MSM	MSM of interest, specified as valid right hand side of a regression formula (see examples)
v	optional value defining the strata of interest (V=v) for stratified estimation of MSM parameter
Q	optional n \times 2 matrix of initial values for Q portion of the likelihood, (E(Y|A=0,W), E(Y|A=1,W))
Qform	optional regression formula for estimation of E(Y|A, W), suitable for call to glm
Qbounds	vector of upper and lower bounds on Y and predicted values for initial Q
Q.SL.library	optional vector of prediction algorithms to use for SuperLearner estimation of initial Q
cvQinit	logical, if TRUE, estimates cross-validated predicted values using discrete super learning, default=TRUE
hAV	optional n \times 2 matrix used in numerator of weights for updating covariate and the influence curve. If unspecified, defaults to conditional probabilities P(A=1|V) or P(A=1|T), for repeated measures data. For unstabilized weights, pass in an n \times 2 matrix of all 1s
hAVform	optionalregression formula of the form A~V+T, if specified this overrides the call to SuperLearner
g1W	optional vector of conditional treatment assingment probabilities, P(A=1|W)
gform	optional regression formula of the form A~W, if specified this overrides the call to SuperLearner
pDelta1	optional n \times 2 matrix of conditional probabilities for missingness mechanism,P(Delta=1|A=0,V,W,T), P(Delta=1|A=1,V,W,T).
g.Deltaform	optional regression formula of the form Delta~A+W, if specified this overrides the call to SuperLearner
g.SL.library	optional vector of prediction algorithms to use for SuperLearner estimation of g1W
g.Delta.SL.library	optional vector of prediction algorithms to use for SuperLearner estimation ofpDelta1
ub	upper bound on inverse probability weights. See Details section for more information
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 cross-validation folds for Super Learner estimation of Q
V.g	number of cross-validation folds for Super Learner estimation of g
V.Delta	number of cross-validation folds for Super Learner estimation of g_Delta
inference	if TRUE, variance-covariance matrix, standard errors, pvalues, and 95% confidence intervals are calculated. Setting to FALSE saves a little time when bootstrapping.
verbose	status messages printed if set to TRUE (default=FALSE)
Q.discreteSL	If true, use discrete SL to estimate Q, otherwise ensembleSL by default. Ignored when SL is not used.
g.discreteSL	If true, use discrete SL to estimate each component of g, otherwise ensembleSL by default. Ignored when SL is not used.
alpha.sig	significance level for constructing 1-alpha.sig confidence intervals
obsWeights	optional weights for biased sampling and two-stage designs.

Details

ub bounds the IC by bounding the factor h(A,V)/[g(A,V,W)P(Delta=1|A,V,W)] between 0 and ub, default value based on sample size.

Value

psi	MSM parameter estimate
sigma	variance covariance matrix
se	standard errors extracted from sigma
pvalue	two-sided p-value
lb	lower bound on 95% confidence interval
ub	upper bound on 95% confidence interval
epsilon	fitted value of epsilon used to target initial Q
psi.Qinit	MSM parameter estimate based on untargeted initial Q
Qstar	targeted estimate of Q, an n \times 2 matrix with predicted values for Q(0,W), Q(1,W) using the updated fit
Qinit	initial estimate of Q. Qinit$coef are the coefficients for a glm model for Q, if applicable. Qinit$Q is an n \times 2 matrix, where n is the number of observations. Columns contain predicted values for Q(0,W),Q(1,W) using the initial fit. Qinit$type is method for estimating Q
g	treatment mechanism estimate. A list with three items: g$g1W contains estimates of P(A=1|W) for each observation, g$coef the coefficients for the model for g when glm used, g$type estimation procedure
g.AV	estimate for h(A,V) or h(A,T). A list with three items: g.AV$g1W an n \times 2 matrix containing values of P(A=0|V,T), P(A=1|V,T) for each observation, g.AV$coef the coefficients for the model for g when glm used, g.AV$type estimation procedure
g_Delta	missingness mechanism estimate. A list with three items: g_Delta$g1W an n \times 2 matrix containing values of P(Delta=1|A,V,W,T) for each observation, g_Delta$coef the coefficients for the model for g when glm used, g_Delta$type estimation procedure

Author(s)

Susan Gruber [e-mail], in collaboration with Mark van der Laan.

References

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), 1-35. https://www.jstatsoft.org/v51/i13/

2. 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.

3. Gruber, S., Phillips, R.V., Lee, H., van der Laan, M.J. Data-Adaptive 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), 1640-1651.

See Also

summary.tmleMSM, estimateQ, estimateG, calcSigma, tmle

Examples

library(tmle)
# Example 1. Estimating MSM parameter with correctly specified regression formulas
# MSM: psi0 + psi1*A + psi2*V + psi3*A*V  (saturated)
# true parameter value: psi = (0, 1, -2, 0.5) 
# generate data
  set.seed(100)
  n <- 1000
  W <- matrix(rnorm(n*3), ncol = 3)
  colnames(W) <- c("W1", "W2", "W3")
  V <- rbinom(n, 1, 0.5)
  A <- rbinom(n, 1, 0.5)
  Y <- rbinom(n, 1, plogis(A - 2*V + 0.5*A*V))
  result.ex1 <- tmleMSM(Y, A, W, V, MSM = "A*V", Qform = "Y~.", gform = "A~1", 
                        hAVform = "A~1", family = "binomial")
  print(result.ex1)
## Not run: 

# Example 2. Biased sampling from example 1 population
# (observations having V = 1 twice as likely to be included in the dataset
  retain.ex2 <- sample(1:n, size = n/2, p = c(1/3 + 1/3*V))
  wt.ex2 <- 1/(1/3 + 1/3*V)
  result.ex2 <- tmleMSM(Y[retain.ex2], A[retain.ex2], W[retain.ex2,], 
			V[retain.ex2], MSM = "A*V", Qform = "Y~.", gform = "A~1", 
                        hAVform = "A~1", family = "binomial",
			obsWeight = wt.ex2[retain.ex2])
  print(result.ex2)

# Example 3. Repeated measures data, two observations per id
# (e.g., crossover study design)
# MSM: psi0 + psi1*A + psi2*V + psi3*V^2 + psi4*T
# true parameter value: psi = (-2, 1, 0, -2, 0 )
# generate data in wide format (id,  W1, Y(t),  W2(t), V(t), A(t)) 
   set.seed(10)
   n <- 250
   id <- rep(1:n)
   W1   <- rbinom(n, 1, 0.5)
   W2.1 <- rnorm(n)
   W2.2 <- rnorm(n)  
   V.1   <- rnorm(n)  
   V.2   <- rnorm(n)
   A.1 <- rbinom(n, 1, plogis(0.5 + 0.3 * W2.1))
   A.2 <- 1-A.1
   Y.1  <- -2 + A.1 - 2*V.1^2 + W2.1 + rnorm(n)
   Y.2  <- -2 + A.2 - 2*V.2^2 + W2.2 + rnorm(n)
   d <- data.frame(id, W1, W2=W2.1, W2.2, V=V.1, V.2, A=A.1, A.2, Y=Y.1, Y.2)

# change dataset from wide to long format
   longd <- reshape(d, 
          varying = cbind(c(3, 5, 7, 9), c(4, 6, 8, 10)),
          idvar = "id",
          direction = "long",
          timevar = "T",
          new.row.names = NULL,
          sep = "")
# misspecified model for initial Q, partial misspecification for g. 
# V set to 2 for Q and g to save time, not recommended at this sample size
   result.ex3 <- tmleMSM(Y = longd$Y, A = longd$A, W = longd[,c("W1", "W2")], V = longd$V, 
          T = longd$T, MSM = "A + V + I(V^2) + T", Qform = "Y ~ A + V", gform = "A ~ W2", 
	id = longd$id, V.Q=2, V.g=2)
   print(result.ex3)


# Example 4:  Introduce 20
# V set to 2 for Q and g to save time, not recommended at this sample size
  Delta <- rbinom(nrow(longd), 1, 0.8)
  result.ex4 <- tmleMSM(Y = longd$Y, A = longd$A, W = longd[,c("W1", "W2")], V = longd$V, T=longd$T,
          Delta = Delta, MSM = "A + V + I(V^2) + T", Qform = "Y ~ A + V", gform = "A ~ W2",
	  g.Deltaform = "Delta ~ 1", id=longd$id, verbose = TRUE, V.Q=2, V.g=2)
  print(result.ex4)


## End(Not run)

tmle documentation built on May 29, 2024, 6:38 a.m.