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条件 Logistic 回归的高效蒙特卡洛方法AI 解读

Exact inference for the logistic regression model is based on generating the permutation distribution of the sufficient statistics for the regression parameters of interest conditional on the sufficient statistics for the remaining (nuisance) parameters. Despite the availability of fast numerical algorithms for the exact computations, there are numerous instances where a data set is too large to be analyzed by the exact methods, yet too sparse or unbalanced for the maximum…

通过控制变量法估计精确 p 值：蒙特卡洛救援AI 解读

Despite algorithmic advances in exact nonparametric inference, problems often occur that are too large for exact p value computations but too sparse for reliable asymptotic results. In these situations Monte Carlo methods are a good compromise. They bound the true p value within a confidence interval. But a factor discouraging the use of Monte Carlo p values is their sensitivity to the random number sequence. One can overcome this drawback by computing a 99% C.I. confidence…

有序类别列联表的精确推断AI 解读

This article proposes an efficient numerical algorithm for small-sample exact inferences in contingency tables having ordinal classifications. The inferences, which apply conditional on the observed marginal totals, also provide an exact analysis for the log-linear model of linear-by-linear association for cell probabilities. An exact test of independence has a one-sided P value equal to the null probability that model-based maximum likelihood estimates of odds ratios are at…

用于估计置换推断精确概率的重要性抽样AI 解读

This article discusses importance sampling as an alternative to conventional Monte Carlo sampling for estimating exact significance levels in a broad class of two-sample tests, including all of the linear rank tests (with or without censoring), homogeneity tests based on the chi-squared, hypergeometric, and likelihood ratio statistics, the Mantel—Haenszel trend test, and Zelen's test for a common odds ratio in several 2 × 2 contingency tables. Inference is based on randomly…

精确 Logistic 回归所需分布的计算AI 解读

Logistic regression is a commonly used technique for the analysis of retrospective and prospective epidemiological and clinical studies with binary response variables. Usually this analysis is performed using large sample approximations. When the sample size is small or the data structure sparse, the accuracy of the asymptotic approximations is in question. On other occasions, singularity of the covariance matrix of parameter estimates precludes asymptotic analysis. Under…

多个 2×2 列联表共同优势比精确置信区间的计算AI 解读

A quadratic time network algorithm is provided for computing an exact confidence interval for the common odds ratio in several 2×2 independent contingency tables. The algorithm is shown to be a considerable improvement on an existing algorithm developed by Thomas (1975), which relies on exhaustive enumeration. Problems that would formerly have consumed several CPU hours can now be solved in a few CPU seconds. The algorithm can easily handle sparse data sets where asymptotic…

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用于多行多列列联表 Fisher 精确检验的网络算法AI 解读

An exact test of significance of the hypothesis that the row and column effects are independent in an r × c contingency table can be executed in principle by generalizing Fisher's exact treatment of the 2 × 2 contingency table. Each table in a conditional reference set of r × c tables with fixed marginal sums is assigned a generalized hypergeometric probability. The significance level is then computed by summing the probabilities of all tables that are no larger (on the…