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Immortal person-time

In the setting of a prospective cohort study that starts after the time of an index event (such as a natural disaster, one-time toxicant exposure, or disease diagnosis), how do you deal with events that were reported and person-time that occurred between the time of the index event and study enrollment (for example, if a study started 2 years after the index event)? Modern Epidemiology states the following:

The correct approach to handling immortal person-time in a study is to exclude it from any denominator, even if the analysis does not focus on mortality...To avoid this bias [immortal person-time], if a study has a criterion for a minimum amount of time before a subject is eligible to be in a study, the time during which the eligibility criterion is met should be excluded from the calculation of incidence rates.

Can you help me understand why this is the case for outcomes other than death? In the case of a study whose enrollment started 2 years after the index event, does this mean that you can’t conduct time-to-event analyses including these first two years? Based on this Modern Epidemiology excerpt and other reading, it is my understanding that time zero should be set to the time of study enrollment (and not the time of the index event), but it is not intuitive why this is the case. 

The guideline is that you can only include person-time of observation from the time a subject comes under observation. In your example, the subject came under observation 2 years after the exposure event. You can only start counting person-time from that time onwards. During the first 2 years since the exposure event occurred, those affected by the exposure were not under your observation, and therefore you do not know whether some developed the outcome of interest (any outcome) during that 2 year interval; so you cannot count person-years for those 2 years when you are not observing for occurrence of the outcome. Hope this helps

Thank you for your response. If you have retrospectively reported information (from questionnaire data at the time they enrolled) on whether or not they experienced the outcome of interest in the time between the exposure event and enrollment, is this still the case? 

I think the detailed answer to your question depends on a lot of things; in particular, you'd want to know about whether the exposure affects time until enrolment and other issues.  Our paper (Hernán et al JCE 2016) maybe helpful in clearing this up.  We look at this in the context of Miguel's "target trial" principle, and note that immortal time bias and related problems occur when eligibility (enrolment), treatment, and start of follow-up time are misaligned, and in particular when this mis-alignment is differential between groups.

In your example, if you expect that events occurring in those first two years are not associated with the exposure (e.g., cancers that take time to develop), then ignoring those events is probably appropriate. It would be important to ignore the first two years in the same way for all subjects. But if those events are differential between groups it is perhaps a problem.

The key issue is, if you record person-time of observation during a time interval, and you fail to attempt to ascertain the occurrence of the outcome during that interval, you will get immortal time bias, because in essence by counting only person-time of observation, what you are saying is that your population lived through that interval; without developing the outcome, and this may not be accurate, as some of your subjects may have developed the outcome during that interval, but you ignore them and made no attempt to ascertain them, hence you artificially and erroneously credit them with outcome-free life throughout the interval, hence creating the immortal time bias.

We have reviewed Hernán et al JCE 2016, and still don't understand intuitively why including the events that occurred in the interim may cause bias. We have information on whether the outcome occurred in this interval. At the time of enrollment (which occurred some time X after the index event of interest), we asked "Have you ever experienced health outcome Y; if so, when?". Thus, for those who survived the interval between the index event and enrollment (i.e., the participants in the study), we have ascertained whether the outcome occurred during the interval. The question is whether we can include these events? With regard to induction time, let's assume the outcome is not cancer and the induction time may be short. Does this mean that these types of outcomes cannot be examined in relation to the index event exposure?  Also, let's assume exposure does not affect time to enrollment.

You made the point that you retrospectively obtained information in a questionnaire on whether subjects experienced the outcome during the 2 years prior to enrollment. There is more than immortal time involved now.

First, if you are sure that all the subjects you enrolled 2 years after the event are composed of  everyonewho was initially exposed to the event at its time of occurrence, and then you retrospectively obtained in a questionnaire whether they developed the outcome or not, then is no immortal time bias involved and you can start counting person-years andthe outcome from the time of occurrence of the event throughout those initial 2 years. Please note that both person-time andthe outcome must be recorded throughout these 2 years.

However, if the subjects you enrolled in your study do not represent everyone who was present at the time of occurrence of the initial event, then your study population is only a sample of the subjects who were initially exposed. Several separate issues now arise:

1)    Is your sample is a truly representative sample of all subjects who were initially exposed? If it is, and you retrospectively obtained information from everyonein the sample whether they developed the outcome or not, here again immortal time bias would not be an issue, and you can count person-time andthe outcome from the time the event started.

2)    However, if your sample is not a truly random sample of all who were initially exposed, then selection bias by itself may be an issue, and the bias may go either way, depending on whether you preferentially enrolled persons with or without the outcome.

My conclusion is that given the scenario you present, selection bias and not immortal time bias (counting person-time when subjects are not under observation for occurrence of the outcome) is the issue. Hope this helps.


Eric Johnson