An individual measure of relative survival

Summary.  Relative survival techniques are used to compare survival experience in a study cohort with that expected if background population rates apply. The techniques are especially useful when cause-specific death information is not accurate or not available as they provide a measure of excess mortality in a group of patients with a certain disease. Whereas these methods are based on group comparisons, we present here a transformation approach which instead gives for each individual an outcome measure relative to the appropriate background population. The new outcome measure is easily interpreted and can be analysed by using standard survival analysis techniques. It provides additional information on relative survival and gives new options in regression analysis. For example, one can estimate the proportion of patients who survived longer than a given percentile of the respective general population or compare survival experience of individuals while accounting for the population differences. The regression models for the new outcome measure are different from existing models, thus providing new possibilities in analysing relative survival data. One distinctive feature of our approach is that we adjust for expected survival before modelling. The paper is motivated by a study into the survival of patients after acute myocardial infarction.     

新世纪档案继续教育浅论

档案继续教育的主要特点是全方位性。针对目前档案继续教育存在的缺乏宏观指导、统筹规划以及没有对继续教育资格的认定、继续教育还未制度化等问题,笔者提出了如下对策:健全我国档案继续教育的保障体系;引入竞争和激励机制;完善教育体系,改进教学方法;建立考核评估体系,制定档案继续教育证书制度。     

A likelihood ratio test to discriminate exponential–Poisson and gamma distributions

The exponential–Poisson (EP) distribution with scale and shape parameters β>0 and λ∈?, respectively, is a lifetime distribution obtained by mixing exponential and zero-truncated Poisson models. The EP distribution has been a good alternative to the gamma distribution for modelling lifetime, reliability and time intervals of successive natural disasters. Both EP and gamma distributions have some similarities and properties in common, for example, their densities may be strictly decreasing or unimodal, and their hazard rate functions may be decreasing, increasing or constant depending on their shape parameters. On the other hand, the EP distribution has several interesting applications based on stochastic representations involving maximum and minimum of iid exponential variables (with random sample size) which make it of distinguishable scientific importance from the gamma distribution. Given the similarities and different scientific relevance between these models, one question of interest is how to discriminate them. With this in mind, we propose a likelihood ratio test based on Cox's statistic to discriminate the EP and gamma distributions. The asymptotic distribution of the normalized logarithm of the ratio of the maximized likelihoods under two null hypotheses – data come from EP or gamma distributions – is provided. With this, we obtain the probabilities of correct selection. Hence, we propose to choose the model that maximizes the probability of correct selection (PCS). We also determinate the minimum sample size required to discriminate the EP and gamma distributions when the PCS and a given tolerance level based on some distance are before stated. A simulation study to evaluate the accuracy of the asymptotic probabilities of correct selection is also presented. The paper is motivated by two applications to real data sets.     

Testing dominance of biometric functions

The hazard rate (HR) and mean residual lifetime are two of the most practical and best-known functions in biometry, reliability, statistics and life testing. Recently, the reversed HR function is found to have interesting properties useful in additional areas such as censored data and forensic science. For these three biometric functions, we propose testing methods that they take on a known functional form against that they dominate or are dominated by this known form. This goodness-of-fit-type testing is wider in applications and more interesting than the long-standing testing procedures for exponentiality against the monotonicity of these functions or even the change point problems. This is so since we can test against any choice of the survival distribution and not just exponentiality. For this general testing, we present easy to implement tests and generalize them into classes of statistics that could lead to more powerful and efficient testing.     

Basu–Dhar bivariate geometric distribution in the presence of covariates and censored data: a Bayesian approach

In this paper, we introduce classical and Bayesian approaches for the Basu–Dhar bivariate geometric distribution in the presence of covariates and censored data. This distribution is considered for the analysis of bivariate lifetime as an alternative to some existing bivariate lifetime distributions assuming continuous lifetimes as the Block and Basu or Marshall and Olkin bivariate distributions. Maximum likelihood and Bayesian estimators are presented. Two examples are considered to illustrate the proposed methodology: an example with simulated data and an example with medical bivariate lifetime data.     

Aging and ordering properties of multivariate lifetimes with Archimedean dependence structures

This paper further studies monotone aging properties of the multivariate random lifetime. We revise the sufficient condition for the negative monotone aging property in terms of the multivariate usual stochastic order in Theorem 3.3 of Rezapour et al. (2013) Rezapour, M., Alamatsaz, M.H., Pellerey, F. (2013). Multivariate aging with Archimedean dependence structures in high dimensions. Commun. Stat. - Theory Methods 42:2056–2070.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar] and derive the condition sufficient to the multivariate monotone aging properties in terms of the upper orthant order. Also we study the upper orthant order of multivariate residual lifetimes and inactivity times from populations sharing a common Archimedean survival copula and Archimedean survival copula, respectively. Two simple applications in multivariate stress-strength and frailty models are presented as well.     

Optimal design of repetitive group sampling plans for Weibull and gamma distributions with applications and comparison to the Birnbaum–Saunders distribution

In this paper, we propose a multiple deferred state repetitive group sampling plan which is a new sampling plan developed by incorporating the features of both multiple deferred state sampling plan and repetitive group sampling plan, for assuring Weibull or gamma distributed mean life of the products. The quality of the product is represented by the ratio of true mean life and specified mean life of the products. Two points on the operating characteristic curve approach is used to determine the optimal parameters of the proposed plan. The plan parameters are determined by formulating an optimization problem for various combinations of producer's risk and consumer's risk for both distributions. The sensitivity analysis of the proposed plan is discussed. The implementation of the proposed plan is explained using real-life data and simulated data. The proposed plan under Weibull distribution is compared with the existing sampling plans. The average sample number (ASN) of the proposed plan and failure probability of the product are obtained under Weibull, gamma and Birnbaum–Saunders distributions for a specified value of shape parameter and compared with each other. In addition, a comparative study is made between the ASN of the proposed plan under Weibull and gamma distributions.     

Some properties of Lin–Wong divergence on the past lifetime data

Measures of statistical divergence are used to assess mutual similarities between distributions of multiple variables through a variety of methodologies including Shannon entropy and Csiszar divergence. Modified measures of statistical divergence are introduced throughout the present article. Those modified measures are related to the Lin–Wong (LW) divergence applied on the past lifetime data. Accordingly, the relationship between Fisher information and the LW divergence measure was explored when applied on the past lifetime data. Throughout this study, a number of relations are proposed between various assessment methods which implement the Jensen–Shannon, Jeffreys, and Hellinger divergence measures. Also, relations between the LW measure and the Kullback–Leibler (KL) measures for past lifetime data were examined. Furthermore, the present study discusses the relationship between the proposed ordering scheme and the distance interval between LW and KL measures under certain conditions.     

Estimation of Benchmark Dose of Lifetime Cadmium Intake for Adverse Renal Effects Using Hybrid Approach in Inhabitants of an Environmentally Exposed River Basin in Japan

The aim of this study is to estimate the reference level of lifetime cadmium intake (LCd) as the benchmark doses (BMDs) and their 95% lower confidence limits (BMDLs) for various renal effects by applying a hybrid approach. The participants comprised 3,013 (1,362 men and 1,651 women) and 278 (129 men and 149 women) inhabitants of the Cd‐polluted and nonpolluted areas, respectively, in the environmentally exposed Kakehashi River basin. Glucose, protein, aminonitrogen, metallothionein, and β₂‐microglobulin in urine were measured as indicators of renal dysfunction. The BMD and BMDL that corresponded to an additional risk of 5% were calculated with background risk at zero exposure set at 5%. The obtained BMDLs of LCd were 3.7 g (glucose), 3.2 g (protein), 3.7 g (aminonitrogen), 1.7 g (metallothionein), and 1.8 g (β₂‐microglobulin) in men and 2.9 g (glucose), 2.5 g (protein), 2.0 g (aminonitrogen), 1.6 g (metallothionein), and 1.3 g (β₂‐microglobulin) in women. The lowest BMDL was 1.7 g (metallothionein) and 1.3 g (β₂‐microglobulin) in men and women, respectively. The lowest BMDL of LCd (1.3 g) was somewhat lower than the representative threshold LCd (2.0 g) calculated in the previous studies. The obtained BMDLs may contribute to further discussion on the health risk assessment of cadmium exposure.