Time series for modelling counts from a relapsing-remitting disease: Application to modelling disease activity in multiple sclerosis

P. S. Albert, H. F. McFarland, M. E. Smith, J. A. Frank

Research output: Contribution to journalArticlepeer-review

Abstract

Many chronic diseases are relapsing-remitting diseases, in which subjects alternate between periods with increasing and decreasing disease activity; relapsing-remitting multiple sclerosis is an example. This paper proposes two classes of models for sequences of counts observed from a relapsing-remitting disease. In the first, the relapsing-remitting nature of the data is modelled by a Poisson time series with a periodic trend in the mean. In this approach, the mean is expressed as a function of a sinusoidal trend and past observations of the time series. An algorithm that uses GLIM is developed, and it results in maximum-likelihood estimation for the amplitude, frequency and autoregressive effects. In the second class of models, the relapsing-remitting behaviour is described by a Poisson time series in which changes in the mean follow a latent Markov chain. An EM algorithm is developed for maximum-likelihood estimation for this model. The two models are illustrated and compared with data from a study evaluating the use of serial magnetic resonance imaging as a measure of disease activity in relapsing-remitting multiple sclerosis.

Original languageEnglish (US)
Pages (from-to)453-466
Number of pages14
JournalStatistics in Medicine
Volume13
Issue number5-7
StatePublished - 1994
Externally publishedYes

ASJC Scopus subject areas

  • Epidemiology

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