Get standard error, p-value, and confidence interval for one ltmle object Summarizing results from Longitudinal Targeted Maximum Likelihood Estimation (ltmle)

These functions are methods for class ltmle or summary.ltmle objects.

Usage

# S3 method for ltmle
summary(object, estimator = ifelse(object$gcomp, "gcomp", "tmle"), ...)

# S3 method for ltmleEffectMeasures
summary(object, estimator = ifelse(object$gcomp, "gcomp", "tmle"), ...)

# S3 method for ltmleMSM
summary(object, estimator = ifelse(object$gcomp, "gcomp", "tmle"), ...)

# S3 method for summary.ltmleMSM
print(
  x,
  digits = max(3, getOption("digits") - 3),
  signif.stars = getOption("show.signif.stars"),
  ...
)

# S3 method for summary.ltmle
print(x, ...)

# S3 method for ltmleEffectMeasures
print(x, ...)

# S3 method for summary.ltmleEffectMeasures
print(x, ...)

# S3 method for ltmleMSM
print(x, ...)

# S3 method for ltmle
print(x, ...)

Arguments

object: an object of class "ltmle" or "ltmleMSM" or "ltmleEffectMeasures", usually a result of a call to ltmle or ltmleMSM.
estimator: character; one of "tmle", "iptw", "gcomp". The estimator for which to get effect measures. "tmle" is valid iff the original ltmle/ltmleMSM call used gcomp=FALSE. "gcomp" is valid iff the original ltmle/ltmleMSM call used gcomp=TRUE
...: further arguments passed to or from other methods.
x: an object of class "summary.ltmle" or "summary.ltmleMSM" or "ltmleEffectMeasures", usually a result of a call to summary.ltmle or summary.ltmleMSM.
digits: the number of significant digits to use when printing.
signif.stars: logical. If TRUE, significance stars are printed for each coefficient.

Value

summary.ltmle returns an object of class "summary.ltmle", a list with components

treatment

a list with components summarizing the estimate of object

estimate - the parameter estimate of \(E[Y_d]\)
std.dev - estimated standard deviation of parameter
p.value - two-sided p-value
CI - vector of length 2 with 95 percent confidence interval

call

the matched call to ltmle for object

estimator

the estimator input argument

variance.estimate.ratio

ratio of the TMLE based variance estimate to the influence curve based variance estimate

summary.ltmleEffectMeasures returns an object of class "summary.ltmleEffectMeasures", a list with same components as summary.ltmle above, but also includes:

effect.measures

a list with components, each with the same components as treatment in summary.ltmle above

treatment - corresponds to the first in the list abar (or rule) passed to ltmle
control - corresponds to the second in the list abar (or rule) passed to ltmle
ATE - average treatment effect
RR - relative risk
OR - odds ratio

summary.ltmleMSM returns an object of class "summary.ltmleMSM", a matrix with rows for each MSM parameter and columns for the point estimate, standard error, 2.5percent confidence interval, 97.5percent confidence interval, and p-value.

Details

summary.ltmle returns the parameter value of the estimator, the estimated variance, a 95 percent confidence interval, and a p-value.

summary.ltmleEffectMeasures returns the additive treatment effect for each of the two objects in the abar list passed to ltmle. Relative risk, and odds ratio are also returned, along with the variance, confidence interval, and p-value for each.

summary.ltmleMSM returns a matrix of MSM parameter estimates.

Examples


rexpit <- function(x) rbinom(n = length(x), size = 1, prob = plogis(x))

# Compare the expected outcomes under two counterfactual plans: Treatment plan:
# set A1 to 1 if W > 0, set A2 to 1 if W > 1.5, always set A3 to 1 Control plan:
# always set A1, A2, and A3 to 0
W <- rnorm(1000)
A1 <- rexpit(W)
A2 <- rexpit(W + 2 * A1)
A3 <- rexpit(2 * A1 - A2)
Y <- rexpit(W - A1 + 0.5 * A2 + 2 * A3)
data <- data.frame(W, A1, A2, A3, Y)
treatment <- cbind(W > 0, W > 1.5, 1)
control <- matrix(0, nrow = 1000, ncol = 3)
result <- ltmle(data, Anodes = c("A1", "A2", "A3"), Ynodes = "Y", abar = list(treatment,
    control))
#> Qform not specified, using defaults:
#> formula for Y:
#> Q.kplus1 ~ W + A1 + A2 + A3
#> 
#> gform not specified, using defaults:
#> formula for A1:
#> A1 ~ W
#> formula for A2:
#> A2 ~ W + A1
#> formula for A3:
#> A3 ~ W + A1 + A2
#> 
#> Estimate of time to completion: < 1 minute
print(summary(result))
#> Estimator:  tmle 
#> Call:
#> ltmle(data = data, Anodes = c("A1", "A2", "A3"), Ynodes = "Y", 
#>     abar = list(treatment, control))
#> 
#> Treatment Estimate:
#>    Parameter Estimate:  0.76323 
#>     Estimated Std Err:  0.054433 
#>               p-value:  <2e-16 
#>     95% Conf Interval: (0.65654, 0.86991) 
#> 
#> Control Estimate:
#>    Parameter Estimate:  0.46619 
#>     Estimated Std Err:  0.064218 
#>               p-value:  3.8871e-13 
#>     95% Conf Interval: (0.34032, 0.59205) 
#> 
#> Additive Treatment Effect:
#>    Parameter Estimate:  0.29704 
#>     Estimated Std Err:  0.082759 
#>               p-value:  0.00033163 
#>     95% Conf Interval: (0.13484, 0.45925) 
#> 
#> Relative Risk:
#>    Parameter Estimate:  1.6372 
#>   Est Std Err log(RR):  0.15373 
#>               p-value:  0.0013429 
#>     95% Conf Interval: (1.2113, 2.2129) 
#> 
#> Odds Ratio:
#>    Parameter Estimate:  3.6911 
#>   Est Std Err log(OR):  0.38754 
#>               p-value:  0.00075227 
#>     95% Conf Interval: (1.727, 7.8891) 
#> 

## For examples of summary.ltmle and summary.ltmleMSM, see example(ltmle)