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协变量存在测量误差的匹配病例对照研究中优势比回归参数的估计AI 解读

This article studies estimators of the odds ratio and odds ratio regression parameters in finely matched case-control studies containing a binary exposure of primary interest and subject-specific covariates that are subject to measurement error. A retrospective logistic regression model for the binary exposure variable is used. The effect of measurement errors on the conditional maximum likelihood estimator is determined. Three alternatives are considered: bias-corrected,…

协变量存在测量误差时匹配病例对照研究的优势比回归估计AI 解读

This article studies estimators of the odds ratio and odds ratio regression parameters in finely matched case-control studies containing a binary exposure of primary interest and subject-specific covariates that are subject to measurement error. A retrospective logistic regression model for the binary exposure variable is used. The effect of measurement errors on the conditional maximum likelihood estimator is determined. Three alternatives are considered: bias-corrected,…

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关于逻辑回归最大似然估计存在条件的补充说明AI 解读

This note expands the paper by Albert & Anderson (1984) on the existence and uniqueness of maximum likelihood estimates in logistic regression models. Their three possible mutually exclusive data patterns: (i) overlap, (ii) complete separation, and (iii) quasiseparation are considered. The maximum likelihood estimate exists only in (i). Modifications of the statement and proofs of Albert & Anderson's results are given for (ii) and (iii) The identifiability for a more general…

二乘二列联表中成功概率差与比值的小样本置信区间AI 解读

Consider two binomial populations II1 and II2 having “success” probabilities p 1 in (0, 1) and p 2 in (0, 1), respectively. This article studies the problem of constructing small-sample confidence intervals for the difference of the success probabilities, Δ = p 1 – p 2 and their ratio (the “relative risk”), ρ = p 1/p 2 based on independent random samples of sizes n 1 and n 2 from II1 and II2, respectively. These are nuisance parameter problems; hence the proposed intervals…

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多元正态概率不等式及其设计问题应用AI 解读

Some results from the theory of total positivity and Schur convexity are applied in deriving inequalities for multivariate normal probabilities having a certain convariance matrix. The result is applied to determine an optimal experimental design in an analysis of covariance model when selection of the best treatment is desired.

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排序与选择问题中的受限子集选择方法AI 解读

Let $\pi_1,\cdots, \pi_k$ be $k$ populations with $\pi_i$ characterized by a scalar $\lambda_i \in \Lambda$, a specified interval on the real line. The object of the problem is to make some inference about $\pi_{(k)}$, the population with largest $\lambda_i$. The present work studies rules which select a random number of populations between one and $m$ where the upper bound, $m$, is imposed by inherent setup restrictions of the subset selection and indifference zone…