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Confidence Intervals for Discrete Data in Clinical Research

Ashis K. GangopadhyayVivek PradhanSandeep M. MenonCynthia BasuTathagata Banerjee

出版	Taylor & Francis Limited (Sales), 2024
主題	Mathematics / Probability & Statistics / GeneralMedical / GeneralMedical / PharmacologyMedical / Biostatistics
ISBN	10321286319781032128634
URL	http://books.google.com.hk/books?id=WiZX0AEACAAJ&hl=&source=gbs_api

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1.A Brief Review of Statistical Inference Introduction The frequentist approach: Confidence interval methods Hypothesis testing methods The Bayesian approach to inference Discussions and conclusions2. Are we slaves to the p-value: The ASA's Statement on P- value Introduction ASA statement on statistical significance and p-values Discussion and recommendation3.One Binomial Proportion Introduction Testing of a hypothesis Asymptotic Confidence interval methods Wald Confidence interval Wald with continuity corrected Confidence interval Score interval due to Wilson (1927) Continuity corrected Wilson interval Agresti and Coull interval Second-order corrected interval Bayesian intervals Non-informative prior - Jeffreys interval Non-informative priors - general MCMC approach Informative prior: Power prior Exact methods Clopper and Pearson Confidence interval Mid-p corrected Clopper-Pearson method Confidence interval due to Casella (1986) Confidence interval due to Blaker (2000) Discussion and recommendation4.Two Independent Binomials: Difference of Proportions Introduction Difference of two proportions: p1-p2 Hypotheses testing problems related to the Difference of proportions Asymptotic methods Using Wald Interval Using Agresti and Caffo Interval Newcombe's method (score) Profile likelihood based interval Farrington and Manning (score) interval Miettinen and Nurminen (score) interval MOVER Interval Exact methods Chan and Zhang interval Agresti and Min interval Coe and Tamhane interval Bayesian Intervals Discussion and recommendation5. Two Independent Binomials: Ratio of Proportions Introduction Hypotheses about the ratio of proportions Asymptotic methods Katz et al (KZ) interval Asymptotic score interval: Koopman Asymptotic score interval: Farrington and Manning Asymptotic score interval: Miettinen and Nurminen Profile likelihood interval Exact Intervals Chan and Zhang interval Agresti and Min interval Bayesian Intervals Discussion and recommendation6.Paired binomials: Difference of Proportions Introduction Difference of two paired binomial proportions Hypotheses testing formulation Asymptotic Intervals Wald interval Agresti and Min Interval MOVER Interval MOVER Wilson Interval MOVER Agresti-Coull Interval MOVER Jeffreys' Interval Asymptotic score interval Weighted profile likelihood method Confidence interval based on bivariate Copula Bayesian credible intervals Exact Confidence Intervals Exact Method by Sidik (2003) Paired binomials with missing data Confidence interval due to Chang (2011) Likelihood-based Confidence intervals Likelihood based Wald type intervals Profile likelihood-based Confidence interval Discussion and recommendation7.One Sample Rates for Count Data Introduction Poisson Distribution Confidence interval of Rate ParameterExact Intervals Garwood Interval Blaker's Interval Mid-P interval Asymptotic Intervals Wald-Interval Score-Interval The likelihood ratio Interval Bayesian Interval The Jeffreys' interval Remarks on the exact, asymptotic and Bayesian intervals Confidence interval for Mean: Other Count Data Models Negative Binomial distribution Generalized Poisson distribution Zero-Inflated Models Confidence Intervals for Zero-Inflated Poisson Distribution (ZIPD) Zero-Inflated Generalized Poisson Distribution (ZIGPD) Zero-Inflated Negative Binomial (ZINB) Bayesian Credible intervals for Poisson Distribution Discussion and recommendation.