Extension of Life-Table Methodology to Allow for Left-Censoring in Survival Studies of Pacing Devices Followed by Commercial Monitoring Services

The actuarial life-table is commonly used to describe lifetime data of living subjects and manufactured products. The life-table method allows subjects to come under observation at different times and, thus, to have differing lengths of follow-up, by assuming all subjects begin their lifetimes relative to the outcome of interest at some common point in time. As time progresses, subjects are withdrawn from the life-table when their period of observation has elapsed. This pattern of follow-up is often termed "right-censoring." An important feature of the classical life table approach is that the time at which the subject is placed at risk is known, and the status relative to the outcome of interest is known for the entire time at risk. Sometimes, however, subjects cannot be observed for some period after the beginning of their lifetimes. The example to be considered involves follow-up data collected by a commercial pacemaker monitoring service, to which patients subscribe, generally at some point following the actual implant of the pacemaker. Since the outcome of interest is device failure after implant, some means of dealing with the lack of information between implant and initiation of follow-up is needed. The extension of the actuarial life-table to accommodate this "left-censoring" will be described in this paper.