. 2016 Nov 18;27(2):49–55. doi: 10.1016/j.je.2016.09.003

Table 2. Response types and their distribution in Table 1.

Response type	Response under		Description	Proportion of response types in

	Exposure	Non-exposure		Exposed^a	Unexposed^b	Total population^c
1	1	1	Doomed	p₁ = 1/2	q₁ = 0	r₁ = 1/4
2	1	0	Causal	p₂ = 0	q₂ = 0	r₂ = 0
3	0	1	Preventive	p₃ = 0	q₃ = 2/2	r₃ = 2/4
4	0	0	Immune	p₄ = 1/2	q₄ = 0	r₄ = 1/4

Effect of smoking cessation on lung cancer (1 = diseased, 0 = non-diseased). The associational risk difference is calculated as: (p₁ + p₂) − (q₁ + q₃) = 1/2 − 2/2 = −1/2. Note that the distribution in this table applies to scenario #2 in Table 3.

Causal risk difference in the exposed group is defined as: (p₁ + p₂) − (p₁ + p₃) = p₂ − p₃ = 0 − 0 = 0 .

Causal risk difference in the unexposed group is defined as: (q₁ + q₂) − (q₁ + q₃) = q₂ − q₃ = 0 − 2/2 = −2/2 .

As shown in Table 1, numbers of the exposed and unexposed groups are balanced, so a proportion of response type i in the total population, r_i, can be calculated as: p_i/2 + q_i/2. The causal risk difference in the total population is defined as: (r₁ + r₂) − (r₁ + r₃) = r₂ − r₃ = 0 − 2/4 = −2/4 .