Time series for modelling counts from a relapsing-remitting disease: application to modelling disease activity in multiple sclerosis.
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.
Albert
P S
PS
Biometry and Field Studies Branch, National Institute of Neurological Disorders and Stroke, Bethesda, MD 20892.
McFarland
H F
HF
Smith
M E
ME
Frank
J A
JA
D000465:Algorithms; D001921:Brain / Q000473:pathology; D003661:Decision Support Techniques; D004185:Disability Evaluation; D005500:Follow-Up Studies; D006801:Humans; D016013:Likelihood Functions; D008279:Magnetic Resonance Imaging; D008390:Markov Chains; D015233:Models, Statistical; D009103:Multiple Sclerosis / Q000175:diagnosis / Q000453:epidemiology* / Q000628:therapy; D016012:Poisson Distribution; D012008:Recurrence