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A Study of Log‐Logistic Model in Survival Analysis
Author(s) -
Gupta Ramesh C.,
Akman Olcay,
Lvin Sergey
Publication year - 1999
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/(sici)1521-4036(199907)41:4<431::aid-bimj431>3.0.co;2-u
Subject(s) - mathematics , statistics , residual , confidence interval , failure rate , maximum likelihood , term (time) , survival analysis , logistic regression , interval (graph theory) , econometrics , combinatorics , algorithm , physics , quantum mechanics
In survival analysis when the mortality reaches a peak after some finite period and then slowly declines, it is appropriate to use a model which has a nonmonotonic failure rate. In this paper we study the log‐logistic model whose failure rate exhibits the above behavior and its mean residual life behaves in the reverse fashion. The maximum likelihood estimation of the parameters is examined and it is proved analytically that unique maximum likelihood estimates exist for the parameters. A lung cancer data set is analyzed. Confidence intervals for the parameters as well as for the critical points of the failure rate and mean residual life functions are obtained for the high performance status (PS) and low PS subgroups, where the term performance status is a measure of general medical status.