Cost-aware Generalized α\alpha-investing for Multiple Hypothesis Testing

We consider the problem of sequential multiple hypothesis testing with nontrivial data collection costs. This problem appears, for example, when conducting biological experiments to identify differentially expressed genes of a disease process. This work builds on the generalized $\alpha$-investing framework which enables control of the false discovery rate in a sequential testing setting. We make a theoretical analysis of the long term asymptotic behavior of $\alpha$-wealth which motivates a consideration of sample size in the $\alpha$-investing decision rule. Posing the testing process as a game with nature, we construct a decision rule that optimizes the expected $\alpha$-wealth reward (ERO) and provides an optimal sample size for each test. Empirical results show that a cost-aware ERO decision rule correctly rejects more false null hypotheses than other methods for $n=1$ where $n$ is the sample size. When the sample size is not fixed cost-aware ERO uses a prior on the null hypothesis to adaptively allocate of the sample budget to each test. We extend cost-aware ERO investing to finite-horizon testing which enables the decision rule to allocate samples in a non-myopic manner. Finally, empirical tests on real data sets from biological experiments show that cost-aware ERO balances the allocation of samples to an individual test against the allocation of samples across multiple tests.Comment: 26 pages, 5 figures, 8 table

Cost-Aware Generalized α-Investing for Multiple Hypothesis Testing

We consider the problem of sequential multiple hypothesis testing with nontrivial data collection cost. This problem appears, for example, when conducting biological experiments to identify differentially expressed genes in a disease process. This work builds on the generalized α-investing framework that enables control of the false discovery rate in a sequential testing setting. We make a theoretical analysis of the long term asymptotic behavior of α-wealth which motivates a consideration of sample size in the α-investing decision rule. Using the game theoretic principle of indifference, we construct a decision rule that optimizes the expected return (ERO) of α-wealth and provides an optimal sample size for the test. We show empirical results that a cost-aware ERO decision rule correctly rejects more false null hypotheses than other methods. We extend cost-aware ERO investing to finite-horizon testing which enables the decision rule to hedge against the risk of unproductive tests. Finally, empirical tests on a real data set from a biological experiment show that cost-aware ERO produces actionable decisions as to which tests to conduct and if so at what sample size

Prevalence of dental fluorosis among 12–15 years school children of Bharatpur city: A cross-sectional study

Introduction: Healthy teeth are important for any section of society. Dental caries, the product of man's progress toward civilization, has a very high morbidity potential. Fluoride has been recognized as one of the most influential factor responsible for the observed decline of caries among children as well as adults of these countries. While fluoride is accepted as an effective method to prevent caries, the excessive consumption of fluoride can put teeth at risk of developing dental fluorosis. Aims and Objectives: To assess the prevalence of dental fluorosis among 12–15 years old government and private school children of Bharatpur city, Rajasthan. Methodology: A cross-sectional study was carried out on total 1400 school children, out of which 700 school children were from government schools and 700 were from private schools. Simple random sampling methodology was used to select the sample. The subjects were examined for dental fluorosis according to WHO 1997 assessment form. Results: The prevalence of dental fluorosis was found higher among government school children, that is, 54.5% when compared to private school children, that is, 45.5% respectively, and this difference was found to be statistically significant (P ≤ 0.05). Conclusion: The study showed the increased prevalence of dental fluorosis among government school children as compared to private school children. Dental fluorosis was found to be the major public health problem among both government and private school children of Bharatpur city which needed immediate attention. Regular dental check-ups and routine oral hygiene practice will enable them to lead a healthier life