Stabilize a targeted estimate by truncating the propensity score

Truncation caps the clever-covariate weight at the price of bias; the whole trade-off curve is returned rather than one point. max_weight far above sqrt(n) means the estimate rests on a handful of observations.

Usage

Tmlestab(Y, A, QAW, Q1W, Q0W, g1W, gbounds = NULL)

Arguments

Y, A

Outcome in [0, 1] and binary treatment.

QAW, Q1W, Q0W

Initial outcome predictions.

g1W

Initial propensity.

gbounds

Truncation levels to try.

Value

List with gbounds, estimate, se, max_weight, n_truncated, spread, n.

Details

Formula: g_trunc = min(max(g, delta), 1 - delta); re-target at each delta and report psi, se and max weight

References

Verified against the CRAN package tmle 2.1.1 (Gruber & van der Laan), which bounds the propensity before forming the clever covariates. The stabilizing role of that bound is the subject of Gruber & van der Laan (2010), International Journal of Biostatistics 6(1), Article 26, which this row cites.

Examples

Tmlestab(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))
#> $gbounds
#> [1] 0.001 0.010 0.025 0.050 0.100
#> 
#> $estimate
#> [1] 1 1 1 1 1
#> 
#> $se
#> [1] 6311.90472  637.68562  259.51100  133.60856   70.97861
#> 
#> $max_weight
#> [1] 8.008008 8.080808 8.205128 8.421053 8.888889
#> 
#> $n_truncated
#> [1] 8 8 8 8 8
#> 
#> $spread
#> [1] 0
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Propensity truncation trade-off for a targeted estimate"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"