Biostatistics Advance Access published online on August 3, 2005
Biostatistics, doi:10.1093/biostatistics/kxi047
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1 Department of Biostatistics, Harvard University, Boston, MA 02115
* To whom correspondence should be addressed. The statistical literature on assessing the accuracy of risk factors or disease markers as diagnostic tests deals almost exclusively with settings where the test, Y, is measured concurrently with disease status D. In practice, however, disease status may vary over time and there is often a time lag between when the marker is measured and the occurrence of disease. One example concerns the Framingham Risk Score as a marker for the future risk of cardiovascular events, events that occur after the score is ascertained. To evaluate such a marker, one needs to take the time lag into account since the predictive accuracy may be higher when the marker is measured closer to the time of disease occurrence. We therefore consider inference for sensitivity and specificity functions that are defined as functions of time. Semi-parametric regression models are proposed. Data from a cohort study are used to estimate model parameters. One issue that arises in practice is that event times may be censored. In this research, we extend in several respects the work by Leisenring, Pepe and Longton (1997) that dealt only with parametric models for binary tests and uncensored data. We propose semi-parametric models that accommodate continuous tests and censoring. Asymptotic distribution theory for parameter estimates is developed and procedures for making statistical inference are evaluated with simulation studies. We illustrate our methods with data from the Cardiovascular Health Study, relating the Framingham risk score measured at enrollment to subsequent risk of cardiovascular events.
Received August 25, 2004
Revised July 26, 2005
Accepted July 27, 2005
Article
The Sensitivity and Specificity of Markers for Event Times
2 Division of Public Health Sciences, Fred Hutchinson Cancer Research Center, Seattle, WA 98109
3 Department of Biostatistics, University of Washington, Seattle, Washington 98195
4 Department of Pathology, College of Medicine , University of Vermont, Burlington, Vermont 05405
Tianxi Cai, E-mail: tcai{at}hsph.harvard.edu
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