Bias due to left truncation and left censoring in longitudinal studies of developmental and disease processes

In longitudinal studies of developmental and disease processes, participants are followed prospectively with intermediate milestones identified as they occur. Frequently, studies enroll participants over a range of ages including ages at which some participants' milestones have already passed. Ages at milestones that occur prior to study entry are left censored if individuals are enrolled in the study or left truncated if they are not. The authors examined the bias incurred by ignoring these issues when estimating the distribution of age at milestones or the time between 2 milestones. Methods that account for left truncation and censoring are considered. Data on the menopausal transition are used to illustrate the problem. Simulations show that bias can be substantial and that standard errors can be severely underestimated in naïve analyses that ignore left truncation. Bias can be reduced when analyses account for left truncation, although the results are unstable when the fraction truncated is high. Simulations suggest that a better solution, when possible, is to modify the study design so that information on current status (i.e., whether or not a milestone has passed) is collected on all potential participants, analyzing those who are past the milestone at the time of recruitment as left censored rather than excluding such individuals from the analysis.