### 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 language | English (US) |
---|---|

Pages (from-to) | 453-466 |

Number of pages | 14 |

Journal | Statistics in Medicine |

Volume | 13 |

Issue number | 5-7 |

State | Published - 1994 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Epidemiology

### Cite this

*Statistics in Medicine*,

*13*(5-7), 453-466.

**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.

Research output: Contribution to journal › Article

*Statistics in Medicine*, vol. 13, no. 5-7, pp. 453-466.

}

TY - JOUR

T1 - Time series for modelling counts from a relapsing-remitting disease

T2 - Application to modelling disease activity in multiple sclerosis

AU - Albert, P. S.

AU - McFarland, H. F.

AU - Smith, M. E.

AU - Frank, J. A.

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0028221510&partnerID=8YFLogxK

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M3 - Article

C2 - 8023028

AN - SCOPUS:0028221510

VL - 13

SP - 453

EP - 466

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 5-7

ER -