INFERENCES FOR THE CHANGE-POINT OF THE EXPONENTIATED WEIBULL HAZARD FUNCTION

In many applications of lifetime data analysis, it is important to perform inferences about the change-point of the hazard function. The change-point could be a maximum for unimodal hazard functions or a minimum for bathtub forms of hazard functions and is usually of great interest in medical or industrial applications. For lifetime distributions where this change-point of the hazard function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can also be obtained. Considering the exponentiated Weibull distribution for the lifetime data, we have different forms for the hazard function: constant, increasing, unimodal, decreasing or bathtub forms. This model gives great flexibility of fit, but we do not have analytic expressions for the change-point of the hazard function. In this way, we consider the use of Markov Chain Monte Carlo methods to get posterior summaries for the change-point of the hazard function considering the exponentiated Weibull distribution.

A new long-term lifetime distribution induced by a latent complementary risk framework

In this paper, we proposed a new three-parameter long-term lifetime distribution induced by a latent complementary risk framework with decreasing, increasing and unimodal hazard function, the long-term complementary exponential geometric distribution. The new distribution arises from latent competing risk scenarios, where the lifetime associated scenario, with a particular risk, is not observable, rather we observe only the maximum lifetime value among all risks, and the presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its reliability, hazard and quantile functions and order statistics. The parameter estimation is based on the usual maximum-likelihood approach. A simulation study assesses the performance of the estimation procedure. We compare the new distribution with its particular cases, as well as with the long-term Weibull distribution on three real data sets, observing its potential and competitiveness in comparison with some usual long-term lifetime distributions.

Renal Function at Hospital Admission and Mortality Due to Acute Kidney Injury after Myocardial Infarction

Background: The role of an impaired estimated glomerular filtration rate (eGFR) at hospital admission in the outcome of acute kidney injury (AKI) after acute myocardial infarction (AMI) has been underreported. The aim of this study was to assess the influence of an admission eGFR<60 mL/min/1.73 m(2) on the incidence and early and late mortality of AMI-associated AKI. Methods: A prospective study of 828 AMI patients was performed. AKI was defined as a serum creatinine increase of >= 50% from the time of admission (RIFLE criteria) in the first 7 days of hospitalization. Patients were divided into subgroups according to their eGFR upon hospital admission (MDRD formula, mL/min/1.73 m(2)) and the development of AKI: eGFR >= 60 without AKI, eGFR<60 without AKI, eGFR >= 60 with AKI and eGFR<60 with AKI. Results: Overall, 14.6% of the patients in this study developed AKI. The admission eGFR had no impact on the incidence of AKI. However, the admission eGFR was associated with the outcome of AMI-associated AKI. The adjusted hazard ratios (AHR, Cox multivariate analysis) for 30-day mortality were 2.00 (95% CI 1.11-3.61) for eGFR, 60 without AKI, 4.76 (95% CI 2.45-9.26) for eGFR >= 60 with AKI and 6.27 (95% CI 3.20-12.29) for eGFR, 60 with AKI. Only an admission eGFR of <60 with AKI was significantly associated with a 30-day to 1-year mortality hazard (AHR 3.05, 95% CI 1.50-6.19). Conclusions: AKI development was associated with an increased early mortality hazard in AMI patients with either preserved or impaired admission eGFR. Only the association of impaired admission eGFR and AKI was associated with an increased hazard for late mortality among these patients.