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依赖删失下两个失效时间分布的比较AI 解读

In a randomised clinical trial to compare two groups of patients, suppose that the time to disease occurrence, the major response variable, may be subject to dependent censoring by death or selective patient withdrawal, while the patients who have reached the disease endpoint are followed for their secondary endpoints or survival information. To adjust for the dependent censoring in assessing the group difference in disease occurrence, we assume that, on a logarithmic scale,…

长度偏倚数据的风险率回归分析AI 解读

Length-biased sampling is frequently a convenient technique for the collection of positive-valued or lifetime data. Estimation porocedures based on pseudo-likelihood are developed under the proportional hazards model for length-biased data. Bias-adjusted risk set sampling is used for the construction of the pseudo-likelihood and the risk set sampling is rephcated to improve estimation performance. The average of the resulting likelihood estimators is taken as the estimator…

非参数密度估计的经验似然置信区间AI 解读

We suggest using empirical likelihood in conjunction with the kernel method to construct confidence intervals for the value of a probability density f at a point x. This suggestion arises from a simulation study which shows that confidence intervals produced by the kernel-based percentle-t bootstrap do not have the coverage claimed by the theory. This coverage discrepancy is due to a conflict between the prescribed undersmoothing and the explicit variance estimate needed by…

使多个参数函数的贝叶斯推断具有频率学有效性的先验AI 解读

We characterise priors which match, up to O(n−1), the posterior joint cumulative distribution function of multiple parametric functions with the corresponding frequentist cumulative distribution function. This work extends and unifies the work of Ghosh & Mukerjee (1993) and Datta & Ghosh (1995a) on the topic of probability-matching priors. A set of necessary and sufficient conditions is obtained for the above characterisation. Some of these conditions depend only on the…

随机区组设计的半参数贝叶斯模型AI 解读

A model is proposed for a Bayesian semiparametric analysis of randomised block experiments. The model is a hierarchical model in which a Dirichlet process is inserted at the middle stage for the distribution of the block effects. This model allows an arbitrary distribution of block effects, and it results in effective estimates of treatment contrasts, block effects and the distribution of block effects. An effective computational strategy is presented for describing the…

变量选择中模型先验概率的预测式设定AI 解读

We examine the problem of specifying prior probabilities for all possible subset models in the context of variable selection in normal linear models. A solution is proposed that uses a prior prediction for the observable, an associated weight, and prior opinion regarding error precision as the only required input. Numerical examples are given to illustrate the method.

多维 Hastings 与 Metropolis 算法的几何收敛和中心极限定理AI 解读

We develop results on geometric ergodicity of Markov chains and apply these and other recent results in Markov chain theory to multidimensional Hastings and Metropolis algorithms. For those based on random walk candidate distributions, we find sufficient conditions for moments and moment generating functions to converge at a geometric rate to a prescribed distribution π. By phrasing the conditions in terms of the curvature of the densities we show that the results apply to…

二参数指数族中后验分位数的频率学有效性AI 解读

Berger & Bernardo's (1989) reference priors and Tibshirani (1989) priors are derived for distributions in Bar-Lev & Reiser's (1982) two-parameter exponential family when either the location or the scale parameter is of interest. The reference prior is shown to be a Tibshirani prior. Furthermore, conditions under which a Tibshirani prior is a higher-order matching prior are investigated. When both the parameters are of interest, it is also shown that the reference prior…

用预测最小拟偏差准则选择广义线性模型AI 解读

We consider the problem of selecting a model with the best predictive ability in a class of generalised linear models. A predictive least quasi-deviance criterion is proposed to measure the predictive ability of a model. This criterion is obtained by applying the idea of the predictive minimum description length principle and the theory of quasi-likelihood functions. The resulting predictive quasi-deviance function is an extension of the predictive stochastic complexity of…

多层聚类数据中失效时间关联的建模AI 解读

In recent years substantial research has been devoted to developing failure-time methodology which accounts for possible dependency between observations. An example is the univariate frailty model (Vaupel, Manton & Stallard, 1979), which incorporates an exchangeable dependence structure by the inclusion of cluster-specific random effects. In some studies it may be reasonable to expect more than one level of within-cluster association: for instance, association between a…

相关响应临床试验的序贯监测AI 解读

This paper demonstrates how the alpha-spending method of Lan & DeMets (1983) can be applied to the generalised estimating equations regression model for correlated data proposed by Liang & Zeger (1986). Under large-sample conditions, the sequential regression parameters are shown to have an independent increments structure, conditional on the amount of Type I error allocated at each interim analysis. We propose and evaluate surrogates for the information fraction, which…

多元分类响应的一类回归模型AI 解读

When data composed of several categorical responses together with categorical or continuous predictors are observed, it is often useful to relate the response probabilities to the predictors via a generalised linear model with a composite link function. This paper discusses a class of link functions that lie between the two extremes of the multivariate logistic transform of McCullagh & Nelder (1989) and the log-linear decomposition of contingency table analysis. The models…

贝叶斯设计问题的预测方法及其在正态回归模型中的应用AI 解读

A predictive decision-theoretic approach is developed for the Bayesian design problem. The loss functions used are fair Bayes, or proper scoring rules, and are quadratic measures of distance between probability measures. Optimal Bayesian designs are those which minimise the preposterior risk for the decision problem. Such designs typically depend on both the prior distribution and the loss function. The results are applied to certain normal regression models where explicit…

抽样方案的 Rao–Blackwell 化AI 解读

This paper proposes a post-simulation improvement for two common Monte Carlo methods, the Accept-Reject and Metropolis algorithms. The improvement is based on a Rao-Blackwellisation method that integrates over the uniform random variables involved in the algorithms, and thus post-processes the standard estimators. We show how the Rao-Blackwellised versions of these algorithms can be implemented and, through examples, illustrate the improvement in variance brought by these…

利用多元正态混合进行贝叶斯曲线拟合AI 解读

Problems of regression smoothing and curve fitting are addressed via predictive inference in a flexible class of mixture models. Multidimensional density estimation using Dirichlet mixture models provides the theoretical basis for semi-parametric regression methods in which fitted regression functions may be deduced as means of conditional predictive distributions. These Bayesian regression functions have features similar to generalised kernel regression estimates, but the…

通过两个剩余寿命分布的区分度刻画比例风险模型AI 解读

A time-dependent Kullback-Leibler discrimination function is defined by comparing residual life distributions at each age t. It is proved that the resulting Kullback-Leibler discrimination function is constant in t if and only if the two survival distributions satisfy a proportional hazards model.

长期生存率的回归分析AI 解读

A method of regression analysis for long-term survival rate, when the survival times are subject to right censoring, is proposed. Under some mild conditions, the regression estimate is consistent and has an asymptotically normal distribution. The procedures are illustrated with the data from a clinical trial. Results from Monte Carlo studies show that the new procedures are reliable for practical use.

非线性动力系统的条件密度与敏感度度量估计AI 解读

Using locally polynomial regression, we develop nonparametric estimators for the conditional density function and its square root, and their partial derivatives. Two measures of sensitivity to initial conditions in nonlinear stochastic dynamic systems are proposed, one of which relates Fisher information with initial-value sensitivity in dynamical systems. We propose estimators for these, and show asymptotic normality for one of them. We further propose a simple method for…

多元极值中近独立性的统计分析AI 解读

We propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence. We examine inference under the model and develop tests for independence of extremes of the marginal variables, both when the thresholds are fixed, and when they increase with the sample size. Motivated by results obtained from this model, we give a new and widely applicable…

比例超额风险模型AI 解读

Assume that the excess risk of an individual over a known background rate can be well approximated by the proportional hazards model. Such might be the case for a cohort at risk of dying from causes that are independent of those that affect the general population. We propose estimators for both the regression parameters and the nonparametric baseline hazard function. The estimators are shown to be consistent, asymptotically normal and efficient. Analogues of the Wald, score…

两条生存曲线的变换模型：经验过程方法AI 解读

A new transformation model for two survival curves with possibly nonproportional hazards is presented. The model assumes the existence of an unknown transformation of the survival curves into Weibull distributions with different shape parameters. The partial likelihood approach fails in the model. A new method of estimation called the empirical process approach is proposed. This approach is based on the strong approximation of the Kaplan-Meier product-limit estimators and…

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多元二元响应的边际回归分析AI 解读

We propose the use of the mean parameter for regression analysis of a multivariate binary response. We model the association using dependence ratios defined in terms of the mean parameter, the components of which are the joint success probabilities of all orders. This permits flexible modelling of higher-order associations, using maximum likelihood estimation. We reanalyse two data sets, one with variable cluster size and the other a longitudinal data set with constant…