A 45-year-old man comes to the office for a routine visit. The patient has a first-degree relative with Alzheimer dementia and is concerned about his chances of developing the disease. He has read in the newspaper that decreased consumption of yellow and orange fruits and vegetables has been associated with Alzheimer disease and would like to know how likely he is to develop the disease. A medical literature review uncovers a recent cohort study that evaluated the association between blood carotene concentration and Alzheimer disease. The development of the disease was evaluated in a 20-year follow-up study of 200 middle-aged subjects who have a first-degree relative with Alzheimer disease. The results are as follows:
| Low carotene level | Normal carotene level | Total | |
| Developed Alzheimer disease | 18 | 42 | 60 |
| Did not develop Alzheimer disease | 27 | 113 | 140 |
| Total | 45 | 155 | 200 |
Assuming the patient has low carotene levels, what is his 20-year risk of developing Alzheimer disease?
Risk is the probability of developing a disease or other health outcome over the study period. In this example, it represents the probability of developing Alzheimer disease over a 20-year period among middle-aged subjects who have a first-degree relative with the disease. To calculate this probability in subjects with low carotene levels, divide the number of subjects who develop Alzheimer disease in the low carotene group (18) by the overall number of subjects in the low carotene group (18 + 27 = 45).
Risk of developing Alzheimer disease among subjects with low carotene = 18 / (18 + 27)
= 18 / 45 = 0.40
This means that, among subjects with low carotene levels, there is a 40% probability of developing Alzheimer disease in 20 years.
Note that this is different from the relative risk (RR) of Alzheimer disease in subjects with low carotene levels compared to those with normal carotene groups:
RR = risk of developing Alzheimer disease among subjects with low carotene levels / risk of developing Alzheimer disease among subjects with normal carotene levels = 0.4 / [42 / (42 + 113)] = 0.4 / 0.27 = 1.48
As the data is not presented in the standard 2 × 2 (contingency) table format, care must be taken to perform the calculations without relying on memorized formulas.
(Choices A and D) The prevalence of low carotene (exposure) among subjects who do not develop Alzheimer disease is 27 / (27 + 113) = 27 / 140 = 0.19 (19%). The prevalence of low carotene (exposure) among subjects who develop Alzheimer disease is 18 / (18 + 42) = 18 / 60 = 0.3 (30%).
(Choice B) The prevalence of low carotene in the entire cohort is (18 + 27) / (18 + 42 + 27 + 113) = 45 / 200 = 0.23 (23%).
(Choice C) As noted in the RR calculation above, the 20-year risk of developing Alzheimer disease among subjects with normal carotene levels is 42 / (42 + 113) = 42 / 155 = 0.27 (27%).
Educational objective:
Risk is the probability of developing a disease over a certain period of time. To calculate this probability, divide the number of affected subjects by the total number of subjects in the corresponding exposure group.