On the Non-identifiability Problem Arising on the Poly-Weibull Model

• Published in: Communications in statistics. Simulation and computation Vol. 33; no. 3; pp. 541 - 552
• Main Authors: Louzada-Neto, Francisco, Andrade, Christiano Santos, Zanforlin Almeida, Fernanda R.
• Format: Journal Article
• Language: English
• Published: Colchester Taylor & Francis Group 02.01.2004; Taylor & Francis
• Subjects: Bi-Weibull model; Exact sciences and technology; Hazard models; Hypothesis tests; Limit theorems; Mathematics; Multivariate analysis; Non-identifiability; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Sufficiency and information; TTT plot; Variance inflation; Correlation; Parameter estimation; Identifiability; Non parametric test; Correlation matrix; Competing risk; Shape parameter; Statistical estimation; Statistical simulation; Information matrix; Parametric method; Statistical method; Hypothesis test; Information measure; Model matching; Correlation analysis; Bootstrap; Numerical simulation; Application
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1081/SAC-200033292

The poly-Weibull model is a general family which arise on competing risk scenarios when there is no direct information about which risk was responsible for the failure. Its advantage over the single-Weibull model is to allow not only constant, increasing or decreasing hazard curves with zero or non zero asymptotes, but also nonmonotones ones, including bathtub-shaped. In this paper we consider the non-identifiability problem, which arises when the shape parameters of a poly-Weibull model are close. Theoretical calculation of the information and correlation matrixes are used to assess when a poly-Weibull model is likely to be feasible. From the practical point of view, a graphical method, based on the total-time-on-test plot and its simulated envelop, is considered for detecting when a poly-Weibull model is likely to be identifiable. We also provide a general framework for constructing hypothesis tests for non-identifiability by using parametric bootstrap-based methods. We set up a simulation study and show that the bootstrap tests have desirable properties with respect to size and power. In some situations only a single Weibull model is enough for fitting the data. We determine the cost of estimating the parameters of a single-Weibull model if a bi-Weibull model is considered instead.