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TARGETED SEQUENTIAL DESIGN FOR TARGETED LEARNING INFERENCE OF THE OPTIMAL TREATMENT RULE AND ITS MEAN REWARD.

ABSTRACT: This article studies the targeted sequential inference of an optimal treatment rule (TR) and its mean reward in the non-exceptional case, i.e., assuming that there is no stratum of the baseline covariates where treatment is neither beneficial nor harmful, and under a companion margin assumption. Our pivotal estimator, whose definition hinges on the targeted minimum loss estimation (TMLE) principle, actually infers the mean reward under the current estimate of the optimal TR. This data-adaptive statistical parameter is worthy of interest on its own. Our main result is a central limit theorem which enables the construction of confidence intervals on both mean rewards under the current estimate of the optimal TR and under the optimal TR itself. The asymptotic variance of the estimator takes the form of the variance of an efficient influence curve at a limiting distribution, allowing to discuss the efficiency of inference. As a by product, we also derive confidence intervals on two cumulated pseudo-regrets, a key notion in the study of bandits problems. A simulation study illustrates the procedure. One of the corner-stones of the theoretical study is a new maximal inequality for martingales with respect to the uniform entropy integral.

SUBMITTER: Chambaz A

PROVIDER: S-EPMC5794253 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature

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TARGETED SEQUENTIAL DESIGN FOR TARGETED LEARNING INFERENCE OF THE OPTIMAL TREATMENT RULE AND ITS MEAN REWARD.

Chambaz Antoine A Zheng Wenjing W van der Laan Mark J MJ

Annals of statistics 20171215 6

This article studies the targeted sequential inference of an optimal treatment rule (TR) and its mean reward in the non-exceptional case, <i>i.e.</i>, assuming that there is no stratum of the baseline covariates where treatment is neither beneficial nor harmful, and under a companion margin assumption. Our pivotal estimator, whose definition hinges on the targeted minimum loss estimation (TMLE) principle, actually infers the mean reward under the current estimate of the optimal TR. This data-ada ...[more]

PMID: 29398733

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Project description:Functional networks play an important role in the analysis of biological processes and systems. The inference of these networks from high-throughput (-omics) data is an area of intense research. So far, the similarity-based inference paradigm (e.g. gene co-expression) has been the most popular approach. It assumes a functional relationship between genes which are expressed at similar levels across different samples. An alternative to this paradigm is the inference of relationships from the structure of machine learning models. These models are able to capture complex relationships between variables, that often are different/complementary to the similarity-based methods.We propose a protocol to infer functional networks from machine learning models, called FuNeL. It assumes, that genes used together within a rule-based machine learning model to classify the samples, might also be functionally related at a biological level. The protocol is first tested on synthetic datasets and then evaluated on a test suite of 8 real-world datasets related to human cancer. The networks inferred from the real-world data are compared against gene co-expression networks of equal size, generated with 3 different methods. The comparison is performed from two different points of view. We analyse the enriched biological terms in the set of network nodes and the relationships between known disease-associated genes in a context of the network topology. The comparison confirms both the biological relevance and the complementary character of the knowledge captured by the FuNeL networks in relation to similarity-based methods and demonstrates its potential to identify known disease associations as core elements of the network. Finally, using a prostate cancer dataset as a case study, we confirm that the biological knowledge captured by our method is relevant to the disease and consistent with the specialised literature and with an independent dataset not used in the inference process.The implementation of our network inference protocol is available at: http://ico2s.org/software/funel.html.

Dataset Information

TARGETED SEQUENTIAL DESIGN FOR TARGETED LEARNING INFERENCE OF THE OPTIMAL TREATMENT RULE AND ITS MEAN REWARD.

Publications

TARGETED SEQUENTIAL DESIGN FOR TARGETED LEARNING INFERENCE OF THE OPTIMAL TREATMENT RULE AND ITS MEAN REWARD.

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