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The Cox proportional hazards model is routinely used to determine the time until an event of interest. Two time scales are used in practice: follow up time and chronological age. The former is the most frequently used time scale both in clinical studies and longitudinal observational studies. However, there is no general consensus about which time scale is the best. In recent years, papers have appeared arguing for using chronological age as the time scale either with or without adjusting the entry-age. Also, it has been asserted that if the cumulative baseline hazard is exponential or if the age-at-entry is independent of covariate, the two models are equivalent. Our studies do not satisfy these two conditions in general. We found that the true factor that makes the models perform significantly different is the variability in the age-at-entry. If there is no variability in the entry-age, time scales do not matter and both models estimate exactly the same coefficients. As the variability increases the models disagree with each other. We also computed the optimum time scale proposed by Oakes and utilized them for the Cox model. Both of our empirical and simulation studies show that follow up time scale model using age at entry as a covariate is better than the chronological age and Oakes time scale models. This finding is illustrated with two examples with data from Diverse Population Collaboration. Based on our findings, we recommend using follow up time as a time scale for epidemiological analysis.
Time Scale, Baseline Age, Time-to-event, Left Truncation, Profile Likelihood, Baseline Hazard
Date of Defense
August 14, 2009.
A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Includes bibliographical references.
Daniel L. McGee, Sr., Professor Co-Directing Dissertation; Eric Chicken, Professor Co-Directing Dissertation; Elwood Carlson, Outside Committee Member; Debajyoti Sinha, Committee Member.
Florida State University
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