Question

One current value for the slope of the dose-response curve for inorganic arsenic and lung cancer is 3.7 (mg per kg bw per d)^-1. What dose corresponds to an excess lifetime risk of 1 in 1000?

a) 0.037 µg per kg bw per d      

b) 0.027 µg per kg bw per d      

c) 2.7 µg per kg bw per d      

d) depends on the weight of the individual, so can’t be calculated

e) 0.27 µg per kg bw per d

Answer 1

Given, One current value for the slope of the dose-response curve for inorganic arsenic and lung cancer is 3.7 (mg per kg bw per d)-1.

Risk level = 1 in 1000
=1/1000

So, Dose corresponds to an excess lifetime risk= risk level / current value for the slope of the dose response curve
= (1/1000)/3.7 (mg per kg bw per day)^-1
=(1/1000×3.7) mg per kg bw per d
= 2.7 × 10^-4 mg per kg bw per d
=2.7 ×(10^-1)×(10^-3 mg) per kg bw per d
=0.27 ×( 10^-3 mg) per kg bw per d
=0.27 micrograms per kg bw per d. (as 1 mg(milligrams) =1000 micrograms, or, 1000 micrograms= 1 mg, or, 1 micrograms = 10^-3 mg)

Therefore, 0.27 micrograms per kg bw per d dose corresponds to an excess lifetime risk of 1 in 1000.
Option (e) is correct.