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Getting started: one call, eight estimators

Source: vignettes/getting-started.Rmd
getting-started.Rmd

dr3 implements the average treatment effect (ATE) estimators reconciled in Three Routes to One Answer. The organizing idea is that AIPW, TMLE, and double machine learning all target the same efficient influence function

D(O)=[Ag(X)−1−A1−g(X)](Y−QA(X))+(Q1(X)−Q0(X))−ψ, D(O) = \Big[\tfrac{A}{g(X)} - \tfrac{1-A}{1-g(X)}\Big]\,\big(Y - Q_A(X)\big) + \big(Q_1(X) - Q_0(X)\big) - \psi,

and differ only in how they solve it (average the score vs. targeting) and how the nuisances g(X)=P(A=1∣X)g(X)=P(A=1\mid X) and Qa(X)=E[Y∣A=a,X]Q_a(X)=E[Y\mid A=a,X] are fit (full-sample, cross-fit, or double cross-fit). dr3 runs the whole family on one shared Super Learner library, so any difference you see is estimator-driven, not implementation-driven.

One call

We use the canonical Hernán–Robins NHEFS example (quitting smoking → 1971–1982 weight change), which ships in causaldata, so nothing needs downloading.

d <- dr_nhefs()

# A small library keeps the vignette fast; use default_dr_library for real work.
fit <- dr_panel(d$Y, d$A, d$X, SL.library = c("SL.mean", "SL.glm", "SL.glmnet"),
                seed = 1)
#> Loading required package: nnls
#> Loading required namespace: glmnet
fit
#> dr3 estimator panel  (n = 1566)
#>       estimator         nuisance estimate         95% CI
#>   g-computation             full    3.156               
#>            IPTW             full    3.200               
#>            AIPW             full    3.331 (2.396, 4.267)
#>            TMLE             full    3.340 (2.404, 4.275)
#>      AIPW = DML        cross-fit    3.407 (2.462, 4.352)
#>  TMLE (CV-TMLE)        cross-fit    3.413 (2.469, 4.356)
#>  AIPW (DC-AIPW) double-cross-fit    3.335 (2.397, 4.274)
#>  TMLE (DC-TMLE) double-cross-fit    3.348 (2.411, 4.285)

The six doubly-robust estimators (AIPW, TMLE, DML, CV-TMLE, DC-AIPW, DC-TMLE) land within about a tenth of a kilogram of one another and of the ~3.4–3.5 kg literature benchmark, while the singly-robust plug-ins (g-computation, IPTW) sit a little apart and carry no analytic interval — exactly the picture the paper draws.

Plot it 

plot(fit)

Look under the hood

dr_panel() is a thin wrapper. You can fit the shared nuisances yourself and hand them to any estimator — pairing dr_aipw() with cross-fit nuisances is double machine learning:

nu <- dr_nuisance(d$Y, d$A, d$X, strategy = "crossfit",
                  SL.library = c("SL.mean", "SL.glm", "SL.glmnet"))
dr_aipw(d$Y, d$A, nu)$estimate   # DML
#> [1] 3.406938
dr_tmle(d$Y, d$A, nu)$estimate   # CV-TMLE
#> [1] 3.412667

Where to next

  • Binary outcomes — right-heart catheterization (RHC), on the risk-difference scale.
  • Reconciling with tmle, AIPW, and DoubleML — the software bridge: what you must match for the packages to agree.