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泊松分布与二项分布的似然比检验AI 解读

The estimation of N in the binomial B(N, p) distribution is a considerably harder problem than the estimation of p. We approach it as a “boundary value” estimation and testing problem, where the boundary N = ∞ corresponds to a Poisson distribution for the data, whereas N < ∞ corresponds to a binomial distribution. The asymptotic distribution of the deviance statistic for testing the hypothesis that the true value of N is infinite is shown to be a 50–50 mixture between a…

泊松分布与二项分布的似然比检验AI 解读

The estimation of N in the binomial B(N, p) distribution is a considerably harder problem than the estimation of p. We approach it as a “boundary value” estimation and testing problem, where the boundary N = ∞ corresponds to a Poisson distribution for the data, whereas N < ∞ corresponds to a binomial distribution. The asymptotic distribution of the deviance statistic for testing the hypothesis that the true value of N is infinite is shown to be a 50–50 mixture between a…

生存数据中的充分随访与异常值检验AI 解读

A situation in which a sample of failure times with many of the largest times censored may be taken as evidence of a proportion of “immune” or “cured” individuals, who are not subject to failure, in the population. A plot of the Kaplan-Meier empirical distribution function for such data will tend to level off near its right extreme, provided that follow-up of individuals has been continued for long enough. This article develops a diagnostic test for sufficient follow-up in…

An estimator for the proportion of ‘immunes’ in a population is proposed, when a sample of censored failure times is available. Our suggestion is to use one minus the maximum observed value of the Kaplan-Meier empirical distribution function. This estimator is shown to be consistent and asymptotically normal, under modest conditions on the censoring mechanism. Simulations suggest that the estimator is approximately normal for quite small sample sizes, provided the immune…

删失样本中免疫个体比例的估计AI 解读

An estimator for the proportion of ‘immunes’ in a population is proposed, when a sample of censored failure times is available. Our suggestion is to use one minus the maximum observed value of the Kaplan-Meier empirical distribution function. This estimator is shown to be consistent and asymptotically normal, under modest conditions on the censoring mechanism. Simulations suggest that the estimator is approximately normal for quite small sample sizes, provided the immune…

关于生存分析的指数模型AI 解读

A simple sufficient condition for the existence, consistency and asymptotic normality of the regression coefficient in the exponential model for survial is given. The intuition that consistent estimation can only be guaranteed when censoring variable are not too small, depending on the values of the covariates, can be quantified in some examples with the use of this condition.

生存分析指数模型的估计条件AI 解读

A simple sufficient condition for the existence, consistency and asymptotic normality of the regression coefficient in the exponential model for survial is given. The intuition that consistent estimation can only be guaranteed when censoring variable are not too small, depending on the values of the covariates, can be quantified in some examples with the use of this condition.