1,809 research outputs found
Targeted Maximum Likelihood Estimation using Exponential Families
Targeted maximum likelihood estimation (TMLE) is a general method for
estimating parameters in semiparametric and nonparametric models. Each
iteration of TMLE involves fitting a parametric submodel that targets the
parameter of interest. We investigate the use of exponential families to define
the parametric submodel. This implementation of TMLE gives a general approach
for estimating any smooth parameter in the nonparametric model. A computational
advantage of this approach is that each iteration of TMLE involves estimation
of a parameter in an exponential family, which is a convex optimization problem
for which software implementing reliable and computationally efficient methods
exists. We illustrate the method in three estimation problems, involving the
mean of an outcome missing at random, the parameter of a median regression
model, and the causal effect of a continuous exposure, respectively. We conduct
a simulation study comparing different choices for the parametric submodel,
focusing on the first of these problems. To the best of our knowledge, this is
the first study investigating robustness of TMLE to different specifications of
the parametric submodel. We find that the choice of submodel can have an
important impact on the behavior of the estimator in finite samples
Non-agency interventions for causal mediation in the presence of intermediate confounding
Recent approaches to causal inference have focused on causal effects defined
as contrasts between the distribution of counterfactual outcomes under
hypothetical interventions on the nodes of a graphical model. In this article
we develop theory for causal effects defined with respect to a different type
of intervention, one which alters the information propagated through the edges
of the graph. These information transfer interventions may be more useful than
node interventions in settings in which causes are non-manipulable, for example
when considering race or genetics as a causal agent. Furthermore, information
transfer interventions allow us to define path-specific decompositions which
are identified in the presence of treatment-induced mediator-outcome
confounding, a practical problem whose general solution remains elusive. We
prove that the proposed effects provide valid statistical tests of mechanisms,
unlike popular methods based on randomized interventions on the mediator. We
propose efficient non-parametric estimators for a covariance version of the
proposed effects, using data-adaptive regression coupled with semi-parametric
efficiency theory to address model misspecification bias while retaining
-consistency and asymptotic normality. We illustrate the use of our
methods in two examples using publicly available data
Second-Order Inference for the Mean of a Variable Missing at Random
We present a second-order estimator of the mean of a variable subject to
missingness, under the missing at random assumption. The estimator improves
upon existing methods by using an approximate second-order expansion of the
parameter functional, in addition to the first-order expansion employed by
standard doubly robust methods. This results in weaker assumptions about the
convergence rates necessary to establish consistency, local efficiency, and
asymptotic linearity. The general estimation strategy is developed under the
targeted minimum loss-based estimation (TMLE) framework. We present a
simulation comparing the sensitivity of the first and second order estimators
to the convergence rate of the initial estimators of the outcome regression and
missingness score. In our simulation, the second-order TMLE improved the
coverage probability of a confidence interval by up to 85%. In addition, we
present a first-order estimator inspired by a second-order expansion of the
parameter functional. This estimator only requires one-dimensional smoothing,
whereas implementation of the second-order TMLE generally requires kernel
smoothing on the covariate space. The first-order estimator proposed is
expected to have improved finite sample performance compared to existing
first-order estimators. In our simulations, the proposed first-order estimator
improved the coverage probability by up to 90%. We provide an illustration of
our methods using a publicly available dataset to determine the effect of an
anticoagulant on health outcomes of patients undergoing percutaneous coronary
intervention. We provide R code implementing the proposed estimator
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