This article deals with correlating two variables that have values that fall below the known limit of detection (LOD) of the measuring device;these values are known as non-detects (NDs). We use simulation to compare s...This article deals with correlating two variables that have values that fall below the known limit of detection (LOD) of the measuring device;these values are known as non-detects (NDs). We use simulation to compare several methods for estimating the association between two such variables. The most commonly used method, simple substitution, consists of replacing each ND with some representative value such as LOD/2. Spearman’s correlation, in which all NDs are assumed to be tied at some value just smaller than the LOD, is also used. We evaluate each method under several scenarios, including small to moderate sample size, moderate to large censoring proportions, extr</span><span style="font-family:Verdana;">eme imbalance in censoring proportions, and non-bivariate nor</span><span style="font-family:Verdana;">mal (BVN) data. In this article, we focus on the coverage probability of 95% confidence intervals obtained using each method. Confidence intervals using a maximum likelihood approach based on the assumption of BVN data have acceptable performance under most scenarios, even with non-BVN data. Intervals based on Spearman’s coefficient also perform well under many conditions. The methods are illustrated using real data taken from the biomarker literature.展开更多
Firstly, the maximum likelihood estimate and asymptotic confidence interval of the unkown parameter for the Topp-Leone distribution are obtained under Type-I left censored samples, furthermore, the asymptotic confiden...Firstly, the maximum likelihood estimate and asymptotic confidence interval of the unkown parameter for the Topp-Leone distribution are obtained under Type-I left censored samples, furthermore, the asymptotic confidence interval of reliability function is obtained based on monotonicity. Secondly, under different loss functions, the Bayesian estimates of the unkown parameter and reliability function are obtained, and the expected mean square errors of Bayesian estimates are calculated. Monte-Carlo method is used to calculate the mean values and relative errors of the estimates. Finally, an example of life data is analyzed by using the statistical method in this paper.展开更多
For left truncated and right censored model, letF n be the product-limit estimate and φ a nonnegative measurable function. The almost sure limits of the cumulative hazard function based onF n pd the integral ∫ ?dF n...For left truncated and right censored model, letF n be the product-limit estimate and φ a nonnegative measurable function. The almost sure limits of the cumulative hazard function based onF n pd the integral ∫ ?dF n are given. The results are useful in establishing strong consistent results of various estimates. For left truncated data, similar results were obtained in literature.展开更多
This paper presents a hierarchical Bayesian approach to the estimation of components’ reliability (survival) using a Weibull model for each of them. The proposed method can be used to estimation with general survival...This paper presents a hierarchical Bayesian approach to the estimation of components’ reliability (survival) using a Weibull model for each of them. The proposed method can be used to estimation with general survival censored data, because the estimation of a component’s reliability in a series (parallel) system is equivalent to the estimation of its survival function with right- (left-) censored data. Besides the Weibull parametric model for reliability data, independent gamma distributions are considered at the first hierarchical level for the Weibull parameters and independent uniform distributions over the real line as priors for the parameters of the gammas. In order to evaluate the model, an example and a simulation study are discussed.展开更多
For left censored response longitudinal data, we propose a composite quantile regression estimator（CQR） of regression parameter. Statistical properties such as consistency and asymptotic normality of CQR are studied...For left censored response longitudinal data, we propose a composite quantile regression estimator（CQR） of regression parameter. Statistical properties such as consistency and asymptotic normality of CQR are studied under relaxable assumptions of correlation structure of error terms. The performance of CQR is investigated via simulation studies and a real dataset analysis.展开更多
For the model with both left truncation and right censoring,suppose all the distributions are continuous. It is proved that the sampled cumulative hazard function Λ n and the product-limit estimate F n are stro...For the model with both left truncation and right censoring,suppose all the distributions are continuous. It is proved that the sampled cumulative hazard function Λ n and the product-limit estimate F n are strong consistent. For any nonnegative measurable , the almost sure convergences of ∫d Λ n and ∫dF n to the true values ∫d Λ and ∫dF respectively are obtained.The strong consistency of the estimator for the truncation probability is proved.展开更多
In this article the authors establish the Bahadur type representations for the kernel quantileestimator and the kernel estimator of the derivatives of the quantile function on the basis of lefttruncated and right cens...In this article the authors establish the Bahadur type representations for the kernel quantileestimator and the kernel estimator of the derivatives of the quantile function on the basis of lefttruncated and right censored data. Under suitable conditions, with probability one, the exactconvergence rate of the remainder term in the representations is obtained. As a by-product, theLIL, the asymptotic normality for those kernel estimators are derived.展开更多
文摘This article deals with correlating two variables that have values that fall below the known limit of detection (LOD) of the measuring device;these values are known as non-detects (NDs). We use simulation to compare several methods for estimating the association between two such variables. The most commonly used method, simple substitution, consists of replacing each ND with some representative value such as LOD/2. Spearman’s correlation, in which all NDs are assumed to be tied at some value just smaller than the LOD, is also used. We evaluate each method under several scenarios, including small to moderate sample size, moderate to large censoring proportions, extr</span><span style="font-family:Verdana;">eme imbalance in censoring proportions, and non-bivariate nor</span><span style="font-family:Verdana;">mal (BVN) data. In this article, we focus on the coverage probability of 95% confidence intervals obtained using each method. Confidence intervals using a maximum likelihood approach based on the assumption of BVN data have acceptable performance under most scenarios, even with non-BVN data. Intervals based on Spearman’s coefficient also perform well under many conditions. The methods are illustrated using real data taken from the biomarker literature.
基金Supported by National Natural Science Foundation of China(Grant No.11901058).
文摘Firstly, the maximum likelihood estimate and asymptotic confidence interval of the unkown parameter for the Topp-Leone distribution are obtained under Type-I left censored samples, furthermore, the asymptotic confidence interval of reliability function is obtained based on monotonicity. Secondly, under different loss functions, the Bayesian estimates of the unkown parameter and reliability function are obtained, and the expected mean square errors of Bayesian estimates are calculated. Monte-Carlo method is used to calculate the mean values and relative errors of the estimates. Finally, an example of life data is analyzed by using the statistical method in this paper.
基金the National Natural Science Foundation of China (Grant No. 19971006) .
文摘For left truncated and right censored model, letF n be the product-limit estimate and φ a nonnegative measurable function. The almost sure limits of the cumulative hazard function based onF n pd the integral ∫ ?dF n are given. The results are useful in establishing strong consistent results of various estimates. For left truncated data, similar results were obtained in literature.
文摘This paper presents a hierarchical Bayesian approach to the estimation of components’ reliability (survival) using a Weibull model for each of them. The proposed method can be used to estimation with general survival censored data, because the estimation of a component’s reliability in a series (parallel) system is equivalent to the estimation of its survival function with right- (left-) censored data. Besides the Weibull parametric model for reliability data, independent gamma distributions are considered at the first hierarchical level for the Weibull parameters and independent uniform distributions over the real line as priors for the parameters of the gammas. In order to evaluate the model, an example and a simulation study are discussed.
基金Supported in part by the National Natural Science Foundation of China under(Grant No.11601097 and 11471302)the State Key Program of National Natural Science of China(Grant No.11231010)
文摘For left censored response longitudinal data, we propose a composite quantile regression estimator（CQR） of regression parameter. Statistical properties such as consistency and asymptotic normality of CQR are studied under relaxable assumptions of correlation structure of error terms. The performance of CQR is investigated via simulation studies and a real dataset analysis.
文摘For the model with both left truncation and right censoring,suppose all the distributions are continuous. It is proved that the sampled cumulative hazard function Λ n and the product-limit estimate F n are strong consistent. For any nonnegative measurable , the almost sure convergences of ∫d Λ n and ∫dF n to the true values ∫d Λ and ∫dF respectively are obtained.The strong consistency of the estimator for the truncation probability is proved.
文摘In this article the authors establish the Bahadur type representations for the kernel quantileestimator and the kernel estimator of the derivatives of the quantile function on the basis of lefttruncated and right censored data. Under suitable conditions, with probability one, the exactconvergence rate of the remainder term in the representations is obtained. As a by-product, theLIL, the asymptotic normality for those kernel estimators are derived.
