1,678 research outputs found
Statistical inference for the mean outcome under a possibly non-unique optimal treatment strategy
We consider challenges that arise in the estimation of the mean outcome under
an optimal individualized treatment strategy defined as the treatment rule that
maximizes the population mean outcome, where the candidate treatment rules are
restricted to depend on baseline covariates. We prove a necessary and
sufficient condition for the pathwise differentiability of the optimal value, a
key condition needed to develop a regular and asymptotically linear (RAL)
estimator of the optimal value. The stated condition is slightly more general
than the previous condition implied in the literature. We then describe an
approach to obtain root- rate confidence intervals for the optimal value
even when the parameter is not pathwise differentiable. We provide conditions
under which our estimator is RAL and asymptotically efficient when the mean
outcome is pathwise differentiable. We also outline an extension of our
approach to a multiple time point problem. All of our results are supported by
simulations.Comment: Published at http://dx.doi.org/10.1214/15-AOS1384 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Evaluating the Impact of Treating the Optimal Subgroup
Suppose we have a binary treatment used to influence an outcome. Given data
from an observational or controlled study, we wish to determine whether or not
there exists some subset of observed covariates in which the treatment is more
effective than the standard practice of no treatment. Furthermore, we wish to
quantify the improvement in population mean outcome that will be seen if this
subgroup receives treatment and the rest of the population remains untreated.
We show that this problem is surprisingly challenging given how often it is an
(at least implicit) study objective. Blindly applying standard techniques fails
to yield any apparent asymptotic results, while using existing techniques to
confront the non-regularity does not necessarily help at distributions where
there is no treatment effect. Here we describe an approach to estimate the
impact of treating the subgroup which benefits from treatment that is valid in
a nonparametric model and is able to deal with the case where there is no
treatment effect. The approach is a slight modification of an approach that
recently appeared in the individualized medicine literature
Noise at a Fermi-edge singularity
We present noise measurements of self-assembled InAs quantum dots at high
magnetic fields. In comparison to I-V characteristics at zero magnetic field we
notice a strong current overshoot which is due to a Fermi-edge singularity. We
observe an enhanced suppression in the shot noise power simultaneous to the
current overshoot which is attributed to the electron-electron interaction in
the Fermi-edge singularity
Tunable graphene system with two decoupled monolayers
The use of two truly two-dimensional gapless semiconductors, monolayer and bilayer graphene, as current-carrying components in field-effect transistors (FET) gives access to new types of nanoelectronic devices. Here, we report on the development of graphene-based FETs containing two decoupled graphene monolayers manufactured from a single one folded during the exfoliation process. The transport characteristics of these newly-developed devices differ markedly from those manufactured from a single-crystal bilayer. By analyzing Shubnikov-de Haas oscillations, we demonstrate the possibility to independently control the carrier densities in both layers using top and bottom gates, despite there being only a nanometer scale separation between them
Statistical Inference for the Mean Outcome Under a Possibly Non-Unique Optimal Treatment Strategy
We consider challenges that arise in the estimation of the value of an optimal individualized treatment strategy defined as the treatment rule that maximizes the population mean outcome, where the candidate treatment rules are restricted to depend on baseline covariates. We prove a necessary and sufficient condition for the pathwise differentiability of the optimal value, a key condition needed to develop a regular asymptotically linear (RAL) estimator of this parameter. The stated condition is slightly more general than the previous condition implied in the literature. We then describe an approach to obtain root-n rate confidence intervals for the optimal value even when the parameter is not pathwise differentiable. In particular, we develop an estimator that, when properly standardized, converges to a normal limiting distribution. We provide conditions under which our estimator is RAL and asymptotically efficient when the mean outcome is pathwise differentiable. We outline an extension of our approach to a multiple time point problem in the appendix. All of our results are supported by simulations
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