est_dcar

DCAR Projection of the Efficient Influence Function

internal

An algorithm for flexible conditional density estimation based on
application of pooled hazard regression to an artificial repeated measures
dataset constructed by discretizing the support of the outcome variable. To
facilitate flexible estimation of the conditional density, the highly
adaptive lasso, a non-parametric regression function shown to estimate
cadlag (RCLL) functions at a suitably fast convergence rate, is used. The
use of pooled hazards regression for conditional density estimation as
implemented here was first described for by Díaz and van der Laan (2011)
<doi:10.2202/1557-4679.1356>. Building on the conditional density estimation
utilities, non-parametric inverse probability weighted (IPW) estimators of
the causal effects of additive modified treatment policies are implemented,
using conditional density estimation to estimate the generalized propensity
score. Non-parametric IPW estimators based on this can be coupled with
undersmoothing of the generalized propensity score estimator to attain the
semi-parametric efficiency bound (per Hejazi, Díaz, and van der Laan
<doi:10.48550/arXiv.2205.05777>).

Nima Hejazi

haldensify

Highly Adaptive Lasso Conditional Density Estimation

David Benkeser

Mark van der Laan

Rachael Phillips

est_dcar function

<dl><dt>psi_ipw</dt>
<dd>A <code>numeric</code> vector of IPW point estimates corresponding
to the conditional density estimates of the exposure mechanism provided in
the arguments <code>gn_pred_natural</code> and <code>gn_pred_shifted</code>.</dd>
<dt>gn_pred_natural</dt>
<dd>A <code>matrix</code> of conditional density estimates of
the exposure mechanism g(A|W) along a grid of the regularization parameter,
at the natural (i.e., observed) values of the exposure.</dd>
<dt>gn_pred_shifted</dt>
<dd>A <code>matrix</code> of conditional density estimates of
the exposure mechanism g(A+delta|W) along a grid of the regularization
parameter, at the shifted (i.e., counterfactual) values of the exposure.</dd>
<dt>Qn_pred_natural</dt>
<dd>A <code>numeric</code> of the outcome mechanism estimate at
the natural (i.e., observed) values of the exposure. HAL regression is used
for the estimate, with the regularization term chosen by cross-validation.</dd>
<dt>Qn_pred_shifted</dt>
<dd>A <code>numeric</code> of the outcome mechanism estimate at
the shifted (i.e., counterfactual) values of the exposure. HAL regression
is used for the estimate, with the regularization term chosen by
cross-validation.</dd></dl>

Arguments

DCAR Projection of the Efficient Influence Function — est_dcar

<dl>

<dt>psi_ipw</dt>
<dd>A <code>numeric</code> vector of IPW point estimates corresponding
to the conditional density estimates of the exposure mechanism provided in
the arguments <code>gn_pred_natural</code> and <code>gn_pred_shifted</code>.</dd>


<dt>gn_pred_natural</dt>
<dd>A <code>matrix</code> of conditional density estimates of
the exposure mechanism g(A|W) along a grid of the regularization parameter,
at the natural (i.e., observed) values of the exposure.</dd>


<dt>gn_pred_shifted</dt>
<dd>A <code>matrix</code> of conditional density estimates of
the exposure mechanism g(A+delta|W) along a grid of the regularization
parameter, at the shifted (i.e., counterfactual) values of the exposure.</dd>


<dt>Qn_pred_natural</dt>
<dd>A <code>numeric</code> of the outcome mechanism estimate at
the natural (i.e., observed) values of the exposure. HAL regression is used
for the estimate, with the regularization term chosen by cross-validation.</dd>


<dt>Qn_pred_shifted</dt>
<dd>A <code>numeric</code> of the outcome mechanism estimate at
the shifted (i.e., counterfactual) values of the exposure. HAL regression
is used for the estimate, with the regularization term chosen by
cross-validation.</dd>

</dl>

est_dcar: DCAR Projection of the Efficient Influence Function

Description

Usage

Arguments