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 journalArticle

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

Fingerprint

Multiple Sclerosis
Count
Time series
Relapsing-Remitting Multiple Sclerosis
Modeling
Maximum Likelihood Estimation
Siméon Denis Poisson
Markov Chains
Chronic Disease
Population Growth
Magnetic Resonance Imaging
EM Algorithm
Model
Alternate
Markov chain
Trends
Class

ASJC Scopus subject areas

  • Epidemiology

Cite this

Time series for modelling counts from a relapsing-remitting disease : Application to modelling disease activity in multiple sclerosis. / Albert, P. S.; McFarland, H. F.; Smith, M. E.; Frank, J. A.

In: Statistics in Medicine, Vol. 13, No. 5-7, 1994, p. 453-466.

Research output: Contribution to journalArticle

Albert, P. S. ; McFarland, H. F. ; Smith, M. E. ; Frank, J. A. / Time series for modelling counts from a relapsing-remitting disease : Application to modelling disease activity in multiple sclerosis. In: Statistics in Medicine. 1994 ; Vol. 13, No. 5-7. pp. 453-466.
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