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A bayesian hierarchical model for classification with selection of functional predictors.

ABSTRACT: In functional data classification, functional observations are often contaminated by various systematic effects, such as random batch effects caused by device artifacts, or fixed effects caused by sample-related factors. These effects may lead to classification bias and thus should not be neglected. Another issue of concern is the selection of functions when predictors consist of multiple functions, some of which may be redundant. The above issues arise in a real data application where we use fluorescence spectroscopy to detect cervical precancer. In this article, we propose a Bayesian hierarchical model that takes into account random batch effects and selects effective functions among multiple functional predictors. Fixed effects or predictors in nonfunctional form are also included in the model. The dimension of the functional data is reduced through orthonormal basis expansion or functional principal components. For posterior sampling, we use a hybrid Metropolis-Hastings/Gibbs sampler, which suffers slow mixing. An evolutionary Monte Carlo algorithm is applied to improve the mixing. Simulation and real data application show that the proposed model provides accurate selection of functional predictors as well as good classification.

SUBMITTER: Zhu H

PROVIDER: S-EPMC3042776 | biostudies-literature | 2010 Jun

REPOSITORIES: biostudies-literature

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A bayesian hierarchical model for classification with selection of functional predictors.

Zhu Hongxiao H Vannucci Marina M Cox Dennis D DD

Biometrics 20090609 2

In functional data classification, functional observations are often contaminated by various systematic effects, such as random batch effects caused by device artifacts, or fixed effects caused by sample-related factors. These effects may lead to classification bias and thus should not be neglected. Another issue of concern is the selection of functions when predictors consist of multiple functions, some of which may be redundant. The above issues arise in a real data application where we use fl ...[more]

PMID: 19508236

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Project description:BackgroundGlobal estimates of unsafe abortions have been produced for 1995, 2003, and 2008. However, reconceptualisation of the framework and methods for estimating abortion safety is needed owing to the increased availability of simple methods for safe abortion (eg, medical abortion), the increasingly widespread use of misoprostol outside formal health systems in contexts where abortion is legally restricted, and the need to account for the multiple factors that affect abortion safety.MethodsWe used all available empirical data on abortion methods, providers, and settings, and factors affecting safety as covariates within a Bayesian hierarchical model to estimate the global, regional, and subregional distributions of abortion by safety categories. We used a three-tiered categorisation based on the WHO definition of unsafe abortion and WHO guidelines on safe abortion to categorise abortions as safe or unsafe and to further divide unsafe abortions into two categories of less safe and least safe.FindingsOf the 55· 7 million abortions that occurred worldwide each year between 2010-14, we estimated that 30·6 million (54·9%, 90% uncertainty interval 49·9-59·4) were safe, 17·1 million (30·7%, 25·5-35·6) were less safe, and 8·0 million (14·4%, 11·5-18·1) were least safe. Thus, 25·1 million (45·1%, 40·6-50·1) abortions each year between 2010 and 2014 were unsafe, with 24·3 million (97%) of these in developing countries. The proportion of unsafe abortions was significantly higher in developing countries than developed countries (49·5% vs 12·5%). When grouped by the legal status of abortion, the proportion of unsafe abortions was significantly higher in countries with highly restrictive abortion laws than in those with less restrictive laws.InterpretationIncreased efforts are needed, especially in developing countries, to ensure access to safe abortion. The paucity of empirical data is a limitation of these findings. Improved in-country data for health services and innovative research to address these gaps are needed to improve future estimates.FundingUNDP/UNFPA/UNICEF/WHO/World Bank Special Programme of Research, Development and Research Training in Human Reproduction; David and Lucile Packard Foundation; UK Aid from the UK Government; Dutch Ministry of Foreign Affairs; Norwegian Agency for Development Cooperation.

Project description:BACKGROUND:The basket trial evaluates the treatment effect of a targeted therapy in patients with the same genetic or molecular aberration, regardless of their cancer types. Bayesian hierarchical modeling has been proposed to adaptively borrow information across cancer types to improve the statistical power of basket trials. Although conceptually attractive, research has shown that Bayesian hierarchical models cannot appropriately determine the degree of information borrowing and may lead to substantially inflated type I error rates. METHODS:We propose a novel calibrated Bayesian hierarchical model approach to evaluate the treatment effect in basket trials. In our approach, the shrinkage parameter that controls information borrowing is not regarded as an unknown parameter. Instead, it is defined as a function of a similarity measure of the treatment effect across tumor subgroups. The key is that the function is calibrated using simulation such that information is strongly borrowed across subgroups if their treatment effects are similar and barely borrowed if the treatment effects are heterogeneous. RESULTS:The simulation study shows that our method has substantially better controlled type I error rates than the Bayesian hierarchical model. In some scenarios, for example, when the true response rate is between the null and alternative, the type I error rate of the proposed method can be inflated from 10% up to 20%, but is still better than that of the Bayesian hierarchical model. LIMITATION:The proposed design assumes a binary endpoint. Extension of the proposed design to ordinal and time-to-event endpoints is worthy of further investigation. CONCLUSION:The calibrated Bayesian hierarchical model provides a practical approach to design basket trials with more flexibility and better controlled type I error rates than the Bayesian hierarchical model. The software for implementing the proposed design is available at http://odin.mdacc.tmc.edu/~yyuan/index_code.html.

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A bayesian hierarchical model for classification with selection of functional predictors.

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A bayesian hierarchical model for classification with selection of functional predictors.

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