Structural time series models in medicine

Structural time series models are formulated in terms of components, such as trends, seasonals and cycles, which have a direct interpretation. This article describes such models and gives examples of how they can be applied in medicine. Univariate models are considered first, and then extended to include explanatory variables and interventions. Multivariate models are then shown to provide a framework for modelling longitudinal data and for carrying out intervention analysis with control groups. The final sections deal with data irregularities and non-Gaussian observations.

[1]  Jim Q. Smith A Generalization of the Bayesian Steady Forecasting Model , 1979 .

[2]  Siem Jan Koopman,et al.  Stamp 5.0 : structural time series analyser, modeller and predictor , 1996 .

[3]  P. D. Jong The Diffuse Kalman Filter , 1991 .

[4]  U Helfenstein,et al.  Box-Jenkins modelling of some viral infectious diseases. , 1986, Statistics in medicine.

[5]  N. Shephard,et al.  Multivariate stochastic variance models , 1994 .

[6]  A. Harvey,et al.  Diagnostic Checking of Unobserved-Components Time Series Models , 1992 .

[7]  R. Kohn,et al.  Estimation, Filtering, and Smoothing in State Space Models with Incompletely Specified Initial Conditions , 1985 .

[8]  S. Zeger,et al.  Longitudinal data analysis using generalized linear models , 1986 .

[9]  P. Phillips,et al.  Models, methods, and applications of econometrics : essays in honor of A.R. Bergstrom , 1994 .

[10]  A. Harvey,et al.  The effect of seat belt legislation on British road casualties: a case study in structural time series modelling , 1986 .

[11]  J. Muth Optimal Properties of Exponentially Weighted Forecasts , 1960 .

[12]  G. Kitagawa Non-Gaussian state space modeling of time series , 1987, 26th IEEE Conference on Decision and Control.

[13]  J. Yorke,et al.  Recurrent outbreaks of measles, chickenpox and mumps. I. Seasonal variation in contact rates. , 1973, American journal of epidemiology.

[14]  J. Yorke,et al.  Recurrent outbreaks of measles, chickenpox and mumps. II. Systematic differences in contact rates and stochastic effects. , 1973, American journal of epidemiology.

[15]  M. West,et al.  Dynamic Generalized Linear Models and Bayesian Forecasting , 1985 .

[16]  N. Shephard Partial non-Gaussian state space , 1994 .

[17]  F. Javier Fernández,et al.  ESTIMATION AND TESTING OF A MULTIVARIATE EXPONENTIAL SMOOTHING MODEL , 1990 .

[18]  A. Harvey,et al.  Detrending, stylized facts and the business cycle , 1993 .

[19]  J. Durbin,et al.  Monte Carlo maximum likelihood estimation for non-Gaussian state space models , 1997 .

[20]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[21]  Agustín Maravall On Structural Time Series Models and the Characterization of Components , 1985 .

[22]  C. Granger,et al.  Co-integration and error correction: representation, estimation and testing , 1987 .

[23]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter. , 1991 .

[24]  Andrew Harvey,et al.  Time Series Models for Count or Qualitative Observations , 1989 .

[25]  Ulrich Helfenstein,et al.  Air pollution and diseases of the respiratory tracts in pre-school children: A transfer function model , 1991, Environmental monitoring and assessment.

[26]  J Schwartz,et al.  Short term fluctuations in air pollution and hospital admissions of the elderly for respiratory disease. , 1995, Thorax.

[27]  A. Raftery,et al.  Prediction Rules for Exponential Family State Space Models , 1993 .

[28]  James H. Stock,et al.  Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors , 1987 .

[29]  A. C. Harvey,et al.  The Effects of Seat Belt Legislation on British Road Casualties: A Case Study in Structural Time Series Modelling , 1986 .