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Proportional Hazards Regression in Epidemiologic Follow-up Studies: An Intuitive Consideration of Primary Time Scale

Cologne, Johna; Hsu, Wan-Linga; Abbott, Robert D.a; Ohishi, Wakab; Grant, Eric J.c; Fujiwara, Saekob; Cullings, Harry M.a

doi: 10.1097/EDE.0b013e318253e418

In epidemiologic cohort studies of chronic diseases, such as heart disease or cancer, confounding by age can bias the estimated effects of risk factors under study. With Cox proportional-hazards regression modeling in such studies, it would generally be recommended that chronological age be handled nonparametrically as the primary time scale. However, studies involving baseline measurements of biomarkers or other factors frequently use follow-up time since measurement as the primary time scale, with no explicit justification. The effects of age are adjusted for by modeling age at entry as a parametric covariate. Parametric adjustment raises the question of model adequacy, in that it assumes a known functional relationship between age and disease, whereas using age as the primary time scale does not. We illustrate this graphically and show intuitively why the parametric approach to age adjustment using follow-up time as the primary time scale provides a poor approximation to age-specific incidence. Adequate parametric adjustment for age could require extensive modeling, which is wasteful, given the simplicity of using age as the primary time scale. Furthermore, the underlying hazard with follow-up time based on arbitrary timing of study initiation may have no inherent meaning in terms of risk. Given the potential for biased risk estimates, age should be considered as the preferred time scale for proportional-hazards regression with epidemiologic follow-up data when confounding by age is a concern.

From the Departments of a Statistics; b Clinical Studies; and c Epidemiology, Radiation Effects Research Foundation, Hiroshima, Japan.

Submitted 15 August 2011; accepted 6 February 2012; posted 18 April 2012.

Sources of funding: The Radiation Effects Research Foundation (RERF), Hiroshima and Nagasaki, Japan, is a private, nonprofit foundation funded by the Japanese Ministry of Health, Labour, and Welfare (MHLW) and the US Department of Energy (DOE), the latter in part through the National Academy of Sciences. This publication was supported by RERF Research Protocols RP 18-61, RP 2-75, and RP 3-05. The authors reported no other financial interests related to this research.

Correspondence: John B. Cologne, Department of Statistics, Radiation Effects Research Foundation, 5-2 Hijiyama Park, Minami-ku, Hiroshima 732-0815 Japan. E-mail:

© 2012 Lippincott Williams & Wilkins, Inc.