title: How many longitudinal covariate measurements are needed for risk prediction?
abstract: OBJECTIVE
  In epidemiologic follow-up studies, many key covariates, such as smoking, use of medication, blood pressure, and cholesterol, are time varying. Because of practical and financial limitations, time-varying covariates cannot be measured continuously, but only at certain prespecified time points. We study how the number of these longitudinal measurements can be chosen cost-efficiently by evaluating the usefulness of the measurements for risk prediction.
  
  
  METHODS
  The usefulness is addressed by measuring the improvement in model discrimination between models using different amounts of longitudinal information. We use simulated follow-up data and the data from the Finnish East-West study, a follow-up study, with eight longitudinal covariate measurements carried out between 1959 and 1999.
  
  
  RESULTS
  In a simulation study, we show how the variability and the hazard ratio of a time-varying covariate are connected to the importance of remeasurements. In the East-West study, it is seen that for older people, the risk predictions obtained using only every other measurement are almost equivalent to the predictions obtained using all eight measurements.
  
  
  CONCLUSIONS
  Decisions about the study design have significant effects on the costs. The cost-efficiency can be improved by applying the measures of model discrimination to data from previous studies and simulations.
authors.affiliation: Department of Mathematics and Statistics, University of Jyvaskyla, P.O. Box 35 (MaD), FI-40014 Jyvaskyla, Finland. Electronic address: jaakko.o.reinikainen@jyu.fi.
authors.forename: Jaakko
authors.initials: J
authors.lastname: Reinikainen
authors.affiliation: Department of Mathematics and Statistics, University of Jyvaskyla, P.O. Box 35 (MaD), FI-40014 Jyvaskyla, Finland.
authors.forename: Juha
authors.initials: J
authors.lastname: Karvanen
authors.affiliation: Department of Chronic Disease Prevention, National Institute for Health and Welfare, P.O. Box 30, FI-00271 Helsinki, Finland.
authors.forename: Hanna
authors.initials: H
authors.lastname: Tolonen
mesh_terms: D005544:Forecasting; D006801:Humans; D008137:Longitudinal Studies; D015233:Models, Statistical; D018570:Risk Assessment / Q000379:methods* / Q000706:statistics & numerical data*
keywords: Longitudinal measurements; Model discrimination; Risk prediction; Study design