Time-to-Event Analysis of Longitudinal Follow-up of a Survey: Choice of the Time-scale

Following individuals sampled in a large-scale health survey for the development of diseases and/or death offers the opportunity to assess the prognostic significance of various risk factors. The proportional hazards regression model, which allows for the control of covariates, is frequently used for the analysis of such data. The authors discuss the appropriate time-scale for such regression models, and they recommend that age rather than time since the baseline survey (time-on-study) be used. Additionally, with age as the time-scale, control for calendar-period and/or birth cohort effects can be achieved by stratifying the model on birth cohort. Because, as discussed by the authors, many published analyses have used regression models with time-on-study as the time-scale, it is important to assess the magnitude of the error incurred from this type of incorrect modeling. The authors provide simple conditions for when incorrect use of time-on-study as the time-scale will nevertheless yield approximately unbiased proportional hazards regression coefficients. Examples are given using data from the first National Health and Nutrition Examination Survey (NHANES I) Epidemiologic Followup Study. Additional issues concerning the analysis of longitudinal follow-up of survey data are briefly discussed.