Chapter 5, Problem 97P

A previous study found that people consuming large quantities of vegetables containing lutein (mainly spinach) were less likely to develop macular degeneration, a common eye disease among older people (age 65+) that causes a substantial loss in visual acuity and in some cases can lead to total blindness. To follow up on this observation, a clinical trial is planned in which participants 65+ years of age without macular degeneration will be assigned to either a high-dose lutein supplement tablet or a placebo tablet taken once per day. To estimate the possible therapeutic effect, a pilot study was conducted in which 9 people 65+ years of age were randomized to placebo and 9 people 65+ years of age were randomized to lutein tablets (active treatment). Their serum lutein level was measured at baseline and again after 4 months of follow-up. From previous studies, people with serum lutein ≥ 10 mg/dL are expected to get some protection from macular degeneration. However, the level of serum lutein may vary depending on genetic factors, dietary factors, and study supplements.

Suppose for the sake of simplicity that the incidence of macular degeneration is 1% per year among people 65+ years of age in the therapeutic range (≥10 mg/dL) and 2% per year among people 65+ years of age with lower levels of lutein (< 10 mg/dL).

What is the expected incidence rate of macular degeneration among lutein-treated participants? (Hint: Use the total-probability rule.)