How far the initial fit was from solving the efficient score equation

The initial fit generally leaves a non-zero empirical score; the targeted fit must drive it to numerical zero. score_init_scaled is roughly the number of standard errors of bias the plug-in estimate carried.

Usage

Tmleqs(Y, A, QAW, Q1W, Q0W, g1W, gbound = 0.025)

Arguments

Y, A

Outcome in [0, 1] and binary treatment.

QAW, Q1W, Q0W

Initial outcome predictions.

g1W

Initial propensity.

gbound

Propensity truncation level.

Value

List with score_init, score_final, score_init_scaled, reduction, psi_init, psi_final, shift, epsilon, n.

Details

Formula: D*(psi)(O) = (A/g1 - (1-A)/g0)(Y - Q(A,W))

• Q(1,W) - Q(0,W) - psi; targeting solves the empirical mean to 0

References

Verified against the CRAN package tmle 2.1.1 (Gruber & van der Laan). The score-equation view of the targeting step is van der Laan & Rubin (2006), International Journal of Biostatistics 2(1), Article 11.

Examples

Tmleqs(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))
#> $score_init
#> [1] 0
#> 
#> $score_final
#> [1] 721.5385
#> 
#> $score_init_scaled
#> [1] NaN
#> 
#> $reduction
#> [1] NaN
#> 
#> $psi_init
#> [1] 0
#> 
#> $psi_final
#> [1] 1
#> 
#> $shift
#> [1] 1
#> 
#> $epsilon
#> [1] -5.544025e+15  1.705854e+14
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Efficient-score residual before and after targeting"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"