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Markov chain Monte Carlo inference applied to a complex model for the longitudinal analysis of breast patterns
Author(s) -
Myles Jonathan P.,
Duffy Stephen W.,
Prevost Teresa C.,
Day Nicholas E.,
Hakama Matti,
Salminen Tiina
Publication year - 2002
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/1467-9876.00263
Subject(s) - markov chain monte carlo , inference , markov chain , computer science , monte carlo method , statistics , data mining , algorithm , series (stratigraphy) , statistical inference , econometrics , artificial intelligence , mathematics , machine learning , paleontology , biology
Summary. As part of a recently completed study of the effectiveness of breast cancer screening in Finland, 3975 women were invited to attend screens at 2‐yearly intervals and the screens were classified as `favourable' or `unfavourable' in a simplification of the Wolfe classification of mammographic patterns. There is interest in both the rate of change from favourable to unfavourable states and vice versa, and the error rates involved in classifying patterns, in particular in whether these vary with age. We discuss simplifying assumptions which need to be made, because of the very short time series that is involved (four or five observations), to enable transitions between states to be disentangled from classification errors. A model for the data is proposed, the likelihood for the data given this model is obtained and a Markov chain Monte Carlo method is used to obtain posterior distributions. We show how our estimation procedure was checked in advance of the availability of the data, by means of a simulation.