Nonparametric bootstrap interval for the targeted risk difference

The INITIAL FITS are carried along as fixed columns, so this bootstraps the targeting step and the empirical means, not the machine learning that produced Q and g; it therefore understates uncertainty when those fits are themselves adaptive. The influence-curve interval is returned beside it.

Usage

Tmleboot(
  Y,
  A,
  QAW,
  Q1W,
  Q0W,
  g1W,
  B = 200,
  seed = 1,
  gbound = 0.025,
  level = 0.95
)

Arguments

Y, A

Outcome in [0, 1] and binary treatment.

QAW, Q1W, Q0W

Initial outcome predictions.

g1W

Initial propensity.

B

Fixed number of bootstrap replicates.

seed

Seed for the pinned generator.

gbound

Propensity truncation level.

level

Confidence level.

Value

List with estimate, boot_se, ci_lower, ci_upper, ic_se, ic_lower, ic_upper, boot_mean, B, n.

Details

Formula: resample indices with replacement, re-target each replicate, take the empirical percentiles of psi*

References

Verified against the CRAN package tmle 2.1.1 (Gruber & van der Laan) for the targeting step and the influence-curve interval. The bootstrap is Efron (1979), Annals of Statistics 7(1), 1-26; van der Laan & Rose (2011), Targeted Learning, recommend the influence-curve interval as the default and the bootstrap as a check.

Examples

Tmleboot(Y = c(1, 2, 3, 4, 5, 6, 7, 8), A = c(1, 2, 3, 4, 5, 6, 7, 8),
  QAW = c(1, 2, 3, 4, 5, 6, 7, 8), Q1W = c(1, 2, 3, 4, 5, 6, 7, 8),
  Q0W = c(1, 2, 3, 4, 5, 6, 7, 8), g1W = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $estimate
#> [1] 1
#> 
#> $boot_se
#> [1] 0
#> 
#> $ci_lower
#> [1] 1
#> 
#> $ci_upper
#> [1] 1
#> 
#> $ic_se
#> [1] 259.511
#> 
#> $ic_lower
#> [1] -507.6322
#> 
#> $ic_upper
#> [1] 509.6322
#> 
#> $boot_mean
#> [1] 1
#> 
#> $B
#> [1] 200
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Bootstrap and influence-curve intervals for a TMLE"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"