Parameters estimation and application of generalized exponential distribution under grouped and right-censored data

Generalized exponential distribution is a class of important distribution in lifedata analysis,especially in some skewed lifedata.The Parameter estimation problem for generalized exponential distribution model with grouped and right-censored data is considered.The maximum likelihood estimators are obtained using the EM algorithm.Some simulations are carried out to illustrate that the proposed algorithm is effective for the model.Finally,a set of medicine data is analyzed by generalized exponential distribution.

Semiparametric quantile-difference estimation for length-biased and right-censored data

Prevalent cohort studies frequently involve length-biased and right-censored data, a fact that has drawn considerable attention in survival analysis. In this article, we consider survival data arising from lengthbiased sampling, and propose a new semiparametric-model-based approach to estimate quantile differences of failure time. We establish the asymptotic properties of our new estimators theoretically under mild technical conditions, and propose a resampling method for estimating their asymptotic variance. We then conduct simulations to evaluate the empirical performance and efficiency of the proposed estimators, and demonstrate their application by a real data analysis.

Analyzing Left-truncated and Right-censored Data under Cox Models with Long-term Survivors

We analyze left-truncated and right-censored data using Cox proportional hazard models with long-term survivors. The estimators of covariate coefficients and the long-term survivor proportion are obtained by the partial likelihood method, and their asymptotic properties are also established. Simulation studies demonstrate the performance of the proposed estimators, and an application to a real dataset is provided.

New Tests for Assessing Non-Inferiority and Equivalence from Survival Data

We propose a new nonparametric method for assessing non-inferiority of an experimental therapy compared to a standard of care. The ratio μE/μR of true median survival times is the parameter of interest. This is of considerable interest in clinical trials of generic drugs. We think of the ratio mE/mR of the sample medians as a point estimate of the ratioμE/μR. We use the Fieller-Hinkley distribution of the ratio of two normally distributed random variables to derive an unbiased level-α test of inferiority null hypothesis, which is stated in terms of the ratio μE/μR and a pre-specified fixed non-inferiority margin δ. We also explain how to assess equivalence and non-inferiority using bootstrap equivalent confidence intervals on the ratioμE/μR. The proposed new test does not require the censoring distributions for the two arms to be equal and it does not require the hazard rates to be proportional. If the proportional hazards assumption holds good, the proposed new test is more attractive. We also discuss sample size determination. We claim that our test procedure is simple and attains adequate power for moderate sample sizes. We extend the proposed test procedure to stratified analysis. We propose a “two one-sided tests” approach for assessing equivalence.

Asymptotic Normality of the Nelson-Aalen and the Kaplan-Meier Estimators in Competing Risks

This paper studies the asymptotic normality of the Nelson-Aalen and the Kaplan-Meier estimators in a competing risks context in presence of independent right-censorship. To prove our results, we use Robelledo’s theorem which makes it possible to apply the central limit theorem to certain types of particular martingales. From the results obtained, confidence bounds for the hazard and the survival functions are provided.

Equivalence between the Dependent Right Censorship Model and the Independent Right Censorship Model

Yu et al. (2012) considered a certain dependent right censorship model. We show that this model is equivalent to the independent right censorship model, extending a result with continuity restriction in Williams and Lagakos (1977). Then the asymptotic normality of the product limit estimator under the dependent right censorship model follows from the existing results in the literature under the independent right censorship model, and thus partially solves an open problem in the literature.

Integrated Square Error of Hazard Rate Estimation for Survival Data with Missing Censoring Indicators

The problem of hazard rate estimation under right-censored assumption has been investigated extensively.Integrated square error(ISE)of estimation is one of the most widely accepted measurements of the global performance for nonparametric kernel estimation.But there are no results available for ISE of hazard rate estimation under right-censored model with censoring indicators missing at random(MAR)so far.This paper constructs an imputation estimator of the hazard rate function and establish asymptotic normality of the ISE for the kernel hazard rate estimator with censoring indicators MAR.At the same time,an asymptotic representation of the mean integrated square error(MISE)is also presented.The finite sample behavior of the estimator is investigated via one simple simulation.