Quiz 1.4:

Question:

A dose-response function can be used to describe the increase in risk associated with the increase in exposure to various hazards. For example, the risk of contracting lung cancer depends, among other things, on the number of cigarettes a person smokes per day. The risk can be described by a linear dose-response function. For example it is known that smoking 10 cigarettes per day increases a person's probability of contracting lung cancer by a factor of 25, while smoking 20 cigarettes a day increases the probability by a factor of 50.

a) Find a formula for \(i(c)\), the increase in the probability of contracting lung cancer for a person who smokes \(c\) cigarettes per day as compared to a non-smoker.

b) Evaluate and interpret \(i(0) \)

c) Interpret the slope of \(i(c)\)

Solution:

a)
\( c = \) # of cigarettes smoked per day
\( i = \) increase in the probability of contracting lung cancer compared to a non-smoker

\( c \): Input
\( i \): Output

Two given pairs \( (c , i) \): \( (10,25),(20,50) \)

Rate of Change \( = \frac{\Delta i}{\Delta c} =\frac{50-25}{20-10}=2.5 \)

\( i(c)-25=2.5 (c-10) \)
\( i(c) = 2.5c \)

b)
\( i(0) = 0 \), which means that a non-smoker has no increased risk of contracting lung cancer compared to a non-smoker.

c)
Every increase in 1 cigarette smoked per day relates to a 2.5% increase in the likelihood of contracting lung cancer compared to a non-smoker.
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