Risk meassure in an open cohort
Forrest Gump said that life is like a box of chocolates. It seems to me that it looks more like a movie theater. Here we are, watching the film, while there’re people coming and people leaving. Some stay a long time watching the movie, other leave fast. Some stay from the beginning, even before us, some come later on the film. Anyway, as the life course itself.
Same thing happens sometimes with cohort studies or clinical trials. Sometimes the number of participants is the same throughout the duration of the study, except for the losses during follow-up, which almost always occur. But other times participants, as if it were our life, come to and go from the study.
Risk meassure in an open cohort
Let’s consider a study that last from January to December. If it is an open cohort, participants can enter the study from the beginning or do it later. For example, imagine a subject A that enters from the beginning, another B coming in March and another C entering in October. Once entering the study, something similar can happen; they may stay in until the end of the study or leave before it for three reasons: they present the studied event, they die (poor them) or they’re lost to follow-up for whatever reason.
As it’s easy to understand, each patient contributes to follow-up with a different number of days. If we simply calculate the cumulative incidence at the endpoint by dividing the number of events by the number of participants we will have a rough idea about the risk of presenting the event, but not about how fast this may occur. To improve this we have to calculate another measure called incidence rate, that reflects the number of events per time-population unit.
This incidence rate would be equivalent to the cumulative incidence in studies with closed cohorts, where all participants have a similar time of follow-up. But, unlike cumulative incidence, which is a proportion, incidence rate is a rate, incorporating the passage of time in the denominator.
The way to calculate the incidence rate is to divide the number of new events during the study period by the total time each person was observed, totaled for all persons. For example, one case per 100 person-years would be the result of finding a case following a hundred people during one year or ten people during ten years. To better understand its meaning, it would be the same as saying that we have seen one event for 100 people each year of follow-up.
As you can see, the denominator of this rate represents the total time that the population has been exposed to the risk of the event under study. One problem with this method is that it assumes that risk is constant throughout the follow-up, which sometime cannot be true. For example, risk in many chronic diseases increases with time.
Incidence rate ratio
Finally, just say that this measure can be used to compare the risk of two populations, no matter the follow-up or the number of participants is different in the two groups. In a similar way that we calculated the relative risk in cumulative incidence studies, we can calculated the ratio of incidence rates to come up with the incidence rate ratio, which has a similar interpretation to that of relative risk.
And with that we’re done. We have not talked anything about how we consider those who get lost during follow-up. Do they present the event or not?, do they fall ill or not?. What is usually done is to consider they have been well over half of the period during which they get lost, removing them off the study after that. This is related to the matter of the so-called censored data in studies with a time-to-event outcome variable. But that’s another story…