Use of alternative time scales in Cox proportional hazard models: implications for time-varying environmental exposures

Issues surrounding choice of time scales in Cox proportional hazard regression models have received limited attention in the literature. Although the choice between time on study and ‘attained’ age time scales has been examined, the calendar time scale may be of interest when modeling health effects of environmental exposures with noteworthy secular trends such as ambient particulate matter air pollution in large epidemiological cohort studies. The authors use simulation studies to examine performance (bias, mean squared error, coverage probabilities, and power) of models using all three time scales when the primary exposure of interest depends on calendar time. Results show that performance of models fit to the calendar time scale varies inversely with the strength of the linear association between the time-varying primary exposure and calendar time. Although models fit to attained age and time on study that do not adjust for calendar time were relatively robust, the authors conclude that care should be exercised when using time scales that are highly correlated with exposures of interest.