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平滑Cox回归AI 解读

Nonparametric regression was shown by Beran and McKeague and Utikal to provide a flexible method for analysis of censored failure times and more general counting processes models in the presence of covariates. We discuss application of kernel smoothing towards estimation in a generalized Cox regression model with baseline intensity dependent on a covariate. Under regularity conditions we show that estimates of the regression parameters are asymptotically normal at rate…

马尔可夫更新模型中的 Cox 回归：骨髓移植数据分析AI 解读

We discuss estimation and prediction in a Markov renewal model where intensities of the one-step transitions follow a Cox regression model with baseline hazards and covariates depending on the backward recurrence time. A modification of the Andersen and Gill results is given to extend the asymptotic properties of the partial likelihood estimates to this setting. We further consider prediction of the realization of the process in a single individual based on the follow-up…

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…

删失匹配对数据的符号秩检验AI 解读

I consider the problem of testing bivariate symmetry in matched-pair experiments where the observations are subject to univariate censoring. Thus the observable random variables are given by (Y 1, Y 2) and (δ1, δ2), where Y j = min(X j , C) and δ j = I(X j ≤ C) (j = 1, 2). Here (X 1, X 2) is a random pair of partially observable lifetimes and C is a fixed or random censoring variable. The hypothesis to be tested is that (X 1, X 2) and (X 2, X 1) have the same distribution.…

两个总体累积风险的图形比较AI 解读

We consider graphs, confidence procedures and tests that can be used with censored survival data to compare the hazard experience of a treatment group with that of a control group. In particular, we consider the relative change Δ(t) in a cumulative rate function which is used to define a generalized proportional hazard model. This model is equivalent to the model obtained by introducing a gamma distributed frailty term in the proportional hazard model. We introduce an…

核条件 Kaplan–Meier 估计的一致收敛性AI 解读

We consider a class of nonparametric regression estimates introduced by Beran to estimate conditional survival functions in the presence of right censoring. An exponential probability bound for the tails of distributions of kernel estimates of conditional survival functions is derived. This inequality is next used to prove weak and strong uniform consistency results. The developments rest on sharp exponential bounds for the oscillation modulus of multivariate empirical…

两样本广义优势率模型的估计与检验AI 解读

The generalized odds ratio for a survival variable T is defined as Λ T (t | c) = c -1[1 - Sc (t)]/Sc (t) for c > 0 and -log S(t) for c = 0, where S(t) = Pr(T > t). This ratio coincides with the integrated hazard for c = 0 and the odds ratio for c = 1. When the distribution of T depends on a covariate vector, we assume that conditionally on the covariates, log Λ T (t | c) is linear in the covariates. This model is a generalization of the proportional hazard model (PHM), which…

比例风险模型中中位与平均生存时间的估计及置信区间AI 解读

Estimation procedures and confidence intervals are given for the median and mean survival time in the proportional hazard regression model. For median survival, the methods apply to censored data. The procedures are based on Cox's partial likelihood estimates of the linear model parameters in the log linear proportional hazard model and on Breslow's estimate of the baseline hazard function. The asymptotic properties of these semiparametric estimates are developed and they…

比例风险模型中生存时间中位数与均值的估计及置信区间AI 解读

Estimation procedures and confidence intervals are given for the median and mean survival time in the proportional hazard regression model. For median survival, the methods apply to censored data. The procedures are based on Cox's partial likelihood estimates of the linear model parameters in the log linear proportional hazard model and on Breslow's estimate of the baseline hazard function. The asymptotic properties of these semiparametric estimates are developed and they…

双变量删失数据的独立性秩检验AI 解读

The paper discusses statistics that can be used to test whether two failure times, say $X_1$ and $X_2$, are independent. The two variables are subject to right censoring so that what is observed is $Y_i = \min(X_i, Z_i)$ and $\delta_i = I(X_i = Y_i)$, where $(Z_1, Z_2)$ are censoring times independent of $(X_1, X_2)$. Statistics that generalize the Spearman rank correlation and the log-rank correlation are considered, as well as general linear rank statistics. The…