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Owen Yang
Do I have cancer?
Will this drug work?
Risk is a fundamental concept in medical science. Not all scientists are comfortable with breathing and living in ‘a world of risk.’ This is because in many aspects we are still trained in a binary world, and world of simple logic.
The probability that you have cancer is 30%.
The drug works in 17% of individuals.
The way we describe risks is based on probabilities or rates of an event. The word ‘rates’ can include a broader meaning at times. ‘Prevalence rates’ are the proportion of individuals are affected by a condition, such as diabetes. ‘Incident rates’ are proportion of individuals who do not have condition will become affected by a condition.
The denominator of rates are those who are eligible for the event
In order to make these rates make sense, it is important to know that the denominator of these rates are theoretically individuals who can have the condition. Therefore, it is reasonable to assume that when we say prevalence rate of diabetes, the denominators are those who can reasonably have diabetes, or ‘eligible’ for having diabetes, for example they have to be alive. In reality this eligibility can be vague and open to interpretation. It is always good to specify the denominator to a reasonable level, for example ‘the prevalence rate of diabetes in 50 year old men in the UK in 2005.’
The numerator of rates are events among the denominator
Following this thinking process, the denominator of the incidence rate of diabetes would have to be those who do not have diabetes, and the numerator should be new diabetes that occur among them.
It sounds ridiculous to point out this, but it is very common for someone forgot to check that the events has to occur among the denominators. If you have a fixed population of 100, 10 have diabetes before the starting time, and 20 developed diabetes during the observation period, the denominator is 90 and the incidence rate is 20 in 90 (around 22%). If you have a non-fixed population where 20 additional individuals moved after the start of observation to make it 120 in total at the end of observation, and 7 of them have new diabetes, then this is where it cause confusion. The best way here is only to make the original 90 ‘eligible’ and only count new diabetes within these 90 individuals (so still 22%).
Person-time as a new default unit of rate
Person-time 30 years ago was such a niche concept but unfortunately this is something that every medical researcher (or any medical person really) needs to understand. The consensus now is that when we describe incidence rate of a disease, we put it on a time scale so that it can somehow compared on a like-for-like basis. So instead of saying the incidence rate is 8% for diabetes in men in their 70s, the 8% will always need a time unit, say 8% every year. This means when we observe 100 ‘eligible’ individuals for a year we expect 8 to have new diabetes. Here we say 8 events occur among 100 person-years.
Now you ask: if it is 8% per person-year in men in their 70s, will we expect 8 diabetes if we follow one person for 100 years?
The answer is of course no because of several reasons. First, a person cannot live for 100 years. Second, one person cannot have 8 diabetes, and once this person has diabetes, the person-time after that time will not be eligible and therefore you will not be able to follow up from then. Third, in this case it is likely that the incidence vary by age, and therefore one person cannot have 100 person-years in his 70s.
But if the 8% per person-year is true, you will expect 8 diabetes to occur if the you can follow a group of men in 70s for 100 eligible person-years in total.
Test yourself
In the beginning of 2007 there were 100 individual in an area and 20 already had diabetes. If the incidence rate is 10% per year, how many individuals are expected to have diabetes by the end of 2010?
