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A Markov chain representation of the multiple testing problem.

ABSTRACT: The problem of multiple hypothesis testing can be represented as a Markov process where a new alternative hypothesis is accepted in accordance with its relative evidence to the currently accepted one. This virtual and not formally observed process provides the most probable set of non null hypotheses given the data; it plays the same role as Markov Chain Monte Carlo in approximating a posterior distribution. To apply this representation and obtain the posterior probabilities over all alternative hypotheses, it is enough to have, for each test, barely defined Bayes Factors, e.g. Bayes Factors obtained up to an unknown constant. Such Bayes Factors may either arise from using default and improper priors or from calibrating p-values with respect to their corresponding Bayes Factor lower bound. Both sources of evidence are used to form a Markov transition kernel on the space of hypotheses. The approach leads to easy interpretable results and involves very simple formulas suitable to analyze large datasets as those arising from gene expression data (microarray or RNA-seq experiments).

SUBMITTER: Cabras S

PROVIDER: S-EPMC5808946 | biostudies-literature | 2018 Feb

REPOSITORIES: biostudies-literature

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A Markov chain representation of the multiple testing problem.

Cabras Stefano S

Statistical methods in medical research 20160316 2

The problem of multiple hypothesis testing can be represented as a Markov process where a new alternative hypothesis is accepted in accordance with its relative evidence to the currently accepted one. This virtual and not formally observed process provides the most probable set of non null hypotheses given the data; it plays the same role as Markov Chain Monte Carlo in approximating a posterior distribution. To apply this representation and obtain the posterior probabilities over all alternative ...[more]

PMID: 26984908

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Project description:Screening tests are widely recommended for the early detection of disease among asymptomatic individuals. While detecting disease at an earlier stage has the potential to improve outcomes, screening also has negative consequences, including false positive results which may lead to anxiety, unnecessary diagnostic procedures, and increased healthcare costs. In addition, multiple false positive results could discourage participating in subsequent screening rounds. Screening guidelines typically recommend repeated screening over a period of many years, but little prior research has investigated how often individuals receive multiple false positive test results. Estimating the cumulative risk of multiple false positive results over the course of multiple rounds of screening is challenging due to the presence of censoring and competing risks, which may depend on the false positive risk, screening round, and number of prior false positive results. To address the general challenge of estimating the cumulative risk of multiple false positive test results, we propose a nonhomogeneous multistate model to describe the screening process including competing events. We developed alternative approaches for estimating the cumulative risk of multiple false positive results using this multistate model based on existing estimators for the cumulative risk of a single false positive. We compared the performance of the newly proposed models through simulation studies and illustrate model performance using data on screening mammography from the Breast Cancer Surveillance Consortium. Across most simulation scenarios, the multistate extension of a censoring bias model demonstrated lower bias compared to other approaches. In the context of screening mammography, we found that the cumulative risk of multiple false positive results is high. For instance, based on the censoring bias model, for a high-risk individual, the cumulative probability of at least two false positive mammography results after 10 rounds of annual screening is 40.4.

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A Markov chain representation of the multiple testing problem.

Publications

A Markov chain representation of the multiple testing problem.

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