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-$n$ 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

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

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

Simulating Visual Attention Allocation of Pilots in an Advanced Cockpit Environment

This paper describes the results of experiments conducted with human line pilots and a cognitive pilot model during interaction with a new 40 Flight Management System (FMS). The aim of these experiments was to gather human pilot behavior data in order to calibrate the behavior of the model. Human behavior is mainly triggered by visual perception. Thus, the main aspect was to setup a profile of human pilots' visual attention allocation in a cockpit environment containing the new FMS. We first performed statistical analyses of eye tracker data and then compared our results to common results of familiar analyses in standard cockpit environments. The comparison has shown a significant influence of the new system on the visual performance of human pilots. Further on, analyses of the pilot models' visual performance have been performed. A comparison to human pilots' visual performance revealed important improvement potentials

Targeted Learning of an Optimal Dynamic Treatment, and Statistical Inference for its Mean Outcome

Suppose we observe n independent and identically distributed observations of a time-dependent random variable consisting of baseline covariates, initial treatment and censoring indicator, intermediate covariates, subsequent treatment and censoring indicator, and a final outcome. For example, this could be data generated by a sequentially randomized controlled trial, where subjects are sequentially randomized to a first line and second line treatment, possibly assigned in response to an intermediate biomarker, and are subject to right-censoring. In this article we consider estimation of an optimal dynamic multiple time-point treatment rule defined as the rule that maximizes the mean outcome under the dynamic treatment, where the candidate rules are restricted to only respond to a user-supplied subset of the baseline and intermediate covariates. This estimation problem is addressed in a statistical model for the data distribution that is nonparametric beyond possible knowledge about the treatment and censoring mechanism, while still providing statistical inference for the mean outcome under the optimal rule. This contrasts from the current literature that relies on parametric assumptions. For the sake of presentation, we first consider the case that the treatment/censoring is only assigned at a single time-point, and subsequently, we cover the multiple time-point case. We characterize the optimal dynamic treatment as a statistical target parameter in the nonparametric statistical model, and we propose highly data adaptive estimators of this optimal dynamic regimen, utilizing sequential loss-based super-learning of sequentially defined (so called) blip-functions, based on newly proposed loss-functions. We also propose a cross-validation selector (among candidate estimators of the optimal dynamic regimens) based on a cross-validated targeted minimum loss-based estimator of the mean outcome under the candidate regimen, thereby aiming directly to select the candidate estimator that maximizes the mean outcome. We also establish that the mean of the counterfactual outcome under the optimal dynamic treatment is a pathwise differentiable parameter under assumptions, and develop a targeted minimum loss-based estimator (TMLE) of this target parameter. We establish asymptotic linearity and statistical inference based on this targeted minimum loss-based estimator under specified conditions. In a sequentially randomized trial the statistical inference essentially only relies upon a second order difference between the estimator of the optimal dynamic treatment and the optimal dynamic treatment to be asymptotically negligible, which may be a problematic condition when the rule is based on multivariate time-dependent covariates. To avoid this condition, we also develop targeted minimum loss based estimators and statistical inference for data adaptive target parameters that are defined in terms of the mean outcome under the {\em estimate} of the optimal dynamic treatment. In particular, we develop a novel cross-validated TMLE approach that provides asymptotic inference under minimal conditions, avoiding the need for any empirical process conditions. For the sake of presentation, in the main part of the article we focus on two-time point interventions, but the results are generalized to general multiple time point interventions in the appendix