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计数过程与生存分析AI 解读

Preface. 0. The Applied Setting. 1. The Counting Process and Martingale Framework. 2. Local Square Integrable Martingales. 3. Finite Sample Moments and Large Sample Consistency of Tests and Estimators. 4. Censored Data Regression Models and Their Application. 5. Martingale Central Limit Theorem. 6. Large Sample results of the Kaplan-Meier Estimator. 7. Weighted Logrank Statistics. 8. Distribution Theory for Proportional Hazards Regression. Appendix A: Some Results from…

Cox 模型中的回归样条：肝病协变量效应应用AI 解读

The Cox proportional hazards model restricts the log hazard ratio to be linear in the covariates. A smooth nonlinear covariate effect may go undetected in this model but can be well approximated by a spline function. A survival model based on data from a clinical trial of primary biliary cirrhosis is developed using regression splines, and the resulting log hazard ratio estimates are compared with those from nonparametric methods. We remove the linear restriction on the log…

边际齐性模型设计矩阵的构造AI 解读

Suppose that a homogeneous group of n subjects is observed on T occasions. Each subject has one of K levels of response at each of the T occasions. The cross-classification of the recorded responses over time forms a KT contingency table. This paper discusses the design matrix for the marginal homogeneity model, which assumes that the first-order marginal probabilities at each time are equal. The marginal homogeneity model is a linear model for the vector of cell…

边际齐性模型设计矩阵的构造AI 解读

Suppose that a homogeneous group of n subjects is observed on T occasions. Each subject has one of K levels of response at each of the T occasions. The cross-classification of the recorded responses over time forms a KT contingency table. This paper discusses the design matrix for the marginal homogeneity model, which assumes that the first-order marginal probabilities at each time are equal. The marginal homogeneity model is a linear model for the vector of cell…

对数秩与广义 Wilcoxon 统计量的上确界版本AI 解读

Considerable progress has been made in generalizing to censored data hypothesis tests based on rank statistics. The most commonly used generalizations are the log-rank test statistic, which extends the Savage exponential scores statistic (Cox 1972; Mantel 1966) and the generalized Wilcoxon statistics (Gehan 1965; Peto and Peto 1972). Gill (1980) showed that in the two-sample problem the asymptotic efficiency properties of the Savage and Wilcoxon statistics are maintained in…

右删失生存数据的一类秩检验程序AI 解读

SUMMARY A class of linear rank statistics is proposed for the k-sample problem with rightcensored survival data. The class contains as special cases the log rank test (Mantel, 1966; Cox, 1972) and a test essentially equivalent to Peto & Peto's (1972) generalization of the Wilcoxon test. Martingale theory is used to establish asymptotic normality of test statistics under the null hypotheses considered, and to derive expressions for asymptotic relative efficiencies under…