Contiguity of probability measures for the gamma frailty Cox model

• Grant number: 10/05967-9
• Support Opportunities: Scholarships abroad - Research
• Start date: July 10, 2010
• End date: July 24, 2010
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Antonio Carlos Pedroso de Lima
• Grantee: Antonio Carlos Pedroso de Lima
• Host Investigator: Pranab Kumar Sen
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: University of North Carolina at Chapel Hill (UNC), United States
• Associated research grant: 04/15304-6 - Regression models and applications, AP.TEM

Abstract

The Cox Gamma frailty model is the most popular choice to model correlated survival data. Despite its popularity, the development of a test of independence (which could simplify further analyses on parameters of primary interest) has not been formally established. The main complication is related to the fact that in order to obtain independence, the Gamma distribution, which is reparameterized in such a way that it will depend on one parameter only, should lead to a degenerate variable, implicitly taking us to a boundary problem (the value of the parameter in this case is outside the parametric space). Moreover, to test for independence, we obtain likelihoods under the null and alternative hypotheses that are not "embedded". This fact naturally lead us to consider contiguity of the likelihoods, viewed as probability measures, so we are able to verify LeCam's Fist Lemma (see Hájek, Sidak and Sen, 1999, page 251) we would have the theoretical basis needed to a formal development of a new test. In this project we are working on verifying the suitability of the above mentioned lemma and, for the case where the only parameter of interest is that related to the independence, we were able to obtain this result. We are currently considering a more general case in which all the parameters of the Cox model with frailty are tested simultaneously. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

SEN, PRANAB K.; PEDROSO-DE-LIMA, ANTONIO C.. Contiguity and irreconcilable nonstandard asymptotics of statistical tests. BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS, v. 25, n. 3, p. 444-470, NOV 2011. (10/05967-9)