Exercise 2 solution

claims = [
    ("Gene variant doubles risk of condition X", 0.01, 2.0),
    ("Gene variant doubles risk of condition Y", 0.20, 2.0),
    ("Variant raises risk of condition Z by half", 0.0002, 1.5),
]
for text, base, rr in claims:
    new = base * rr
    extra = new - base
    print(text)
    print("  from", base, "to", round(new, 5), "| extra", round(extra, 5),
          "| about 1 extra case per", round(1 / extra), "people")
    if new > 1:
        print("  impossible: risk above 100%")

Output:

Gene variant doubles risk of condition X
  from 0.01 to 0.02 | extra 0.01 | about 1 extra case per 100 people
Gene variant doubles risk of condition Y
  from 0.2 to 0.4 | extra 0.2 | about 1 extra case per 5 people
Variant raises risk of condition Z by half
  from 0.0002 to 0.0003 | extra 0.0001 | about 1 extra case per 10000 people

Reading it: the same headline, doubled risk, means one extra case in 100 people for a rare condition and one in 5 for a common one. Always ask for the baseline risk (the absolute risk) before reacting to a relative risk. The third example shows how a 'raised by half' headline can mean about one extra case per 10,000 people.