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Stage line diagram: An age-conditional reference diagram for tracking development

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Author: Buuren, S. van · Ooms, J.C.L.
Institution: TNO Kwaliteit van Leven
Source:Statistics in Medicine, 11, 28, 1569-1579
Identifier: 241543
doi: doi:10.1002/sim.3567
Keywords: Health · Leefomgeving en gezondheid · Graphic tool · Growth · Puberty · Quantification · Tanner stages · Adolescent · Age Factors · Analysis of Variance · Breast · Child · Confidence Intervals · Data Interpretation, Statistical · Female · Growth · Humans · Internet · Likelihood Functions · Longitudinal Studies · Male · Models, Biological · Probability · Puberty · Reference Standards · Stochastic Processes · Young Adult


This paper presents a method for calculating stage line diagrams, a novel type of reference diagram useful for tracking developmental processes over time. Potential fields of applications include: dentistry (tooth eruption), oncology (tumor grading, cancer staging), virology (HIV infection and disease staging), psychology (stages of cognitive development), human development (pubertal stages) and chronic diseases (stages of dementia). Transition probabilities between successive stages are modeled as smoothly varying functions of age. Age-conditional references are calculated from the modeled probabilities by the mid-P value. It is possible to eliminate the influence of age by calculating standard deviation scores (SDS). The method is applied to the empirical data to produce reference charts on secondary sexual maturation. The mean of the empirical SDS in the reference population is close to zero, whereas the variance depends on age. The stage line diagram provides quick insight into both status (in SDS) and tempo (in SDS/year) of development of an individual child. Other measures (e.g. height SDS, body mass index SDS) from the same child can be added to the chart. Diagrams for sexual maturation are available as a web application at The stage line diagram expresses status and tempo of discrete changes on a continuous scale. Wider application of these measures scores opens up new analytic possibilities. Copyright © 2009 John Wiley & Sons, Ltd.