When to Censor?

Abstract

Loss to follow-up is an endemic feature of time-to-event analyses that precludes observation of the event of interest. To our knowledge, in typical cohort studies with encounters occurring at regular or irregular intervals, there is no consensus on how to handle person-time between participants' last study encounter and the point at which they meet a definition of loss to follow-up. We demonstrate, using simulation and an example, that when the event of interest is captured outside of a study encounter (e.g., in a registry), person-time should be censored when the study-defined criterion for loss to follow-up is met (e.g., 1 year after last encounter), rather than at the last study encounter. Conversely, when the event of interest must be measured within the context of a study encounter (e.g., a biomarker value), person-time should be censored at the last study encounter. An inappropriate censoring scheme has the potential to result in substantial bias that may not be easily corrected.

Figure 1.

Several illustrative study records for hypothetical individuals (numbered) in an interval cohort study under 2 different censoring schemes (last-encounter censoring, denoted A, and lost-to-follow-up (LTFU)-definition censoring, denoted B). Study visits are represented by stars. The outcome is captured (e.g., in a registry) outside of a study visit, and its occurrence is denoted by a circle. Outcomes included in the analysis are denoted by solid circles, while outcomes excluded from analysis (because they occur after the LTFU definition is met) are denoted by hollow circles. LTFU is defined as going 12 months without a study visit or occurrence of the outcome. For persons who are administratively censored (e.g., participant 4) or LTFU (e.g., participants 1 and 2), person-time could be included from study entry to the last study visit (last-encounter censoring) or from study entry to the point at which the definition of LTFU is met or to administrative censoring (LTFU-definition censoring). Included person-time under each censoring scheme is denoted by gray shaded rectangles. Note that application of last-encounter censoring results in complete exclusion of persons who never return for a follow-up visit (e.g., participant 2).

Figure 2.

Several illustrative study records for hypothetical individuals (numbered) in a clinical cohort study under 2 different censoring schemes (last-encounter censoring, denoted A, and lost-to-follow-up (LTFU)-definition censoring, denoted B). Study visits are represented by stars. A 5-pointed star indicates a visit at which the outcome has not yet occurred; a starburst indicates a visit at which the outcome is detected. The outcome is measured; its timing is unobserved, and its occurrence is denoted by a hollow circle. For persons whose outcome is observed (e.g., participant 4), person-time is included from study entry to the visit at which the outcome occurs. (Although the occurrence of the outcome could be thought of as interval-censored, interval censoring is rarely employed; see Web Appendix 2.) LTFU is defined as going 12 months without a study visit. For persons who are administratively censored (e.g., participant 5) or LTFU (e.g., participants 1–3), person-time could be included from study entry to the last study visit (last-encounter censoring) or from study entry to the point at which the definition of LTFU is met or to administrative censoring (LTFU-definition censoring). Included person-time under each censoring scheme is denoted by gray shaded rectangles. Note that application of last-encounter censoring results in complete exclusion of persons who never return for a follow-up visit (e.g., participant 2). Further note that, because the outcome is not observable outside of the context of a study visit, the outcome for individual 3 is unobserved and is not included in the analysis, despite its occurrence during person-time included under LTFU-definition censoring.

Figure 3.

Estimated cumulative incidence (simulation results) of a captured event Y (event detectable outside a study visit) under A = 1 if persons who are lost to follow-up (LTFU) are censored when they met the definition of LTFU (LTFU-definition censoring) or at their last study encounter, compared with truth (absence of LTFU).