Question

A study wanted to assess the accuracy of self-reported smoking status. Participants are asked whether they currently smoke or not. In addition, laboratory tests are performed on hair samples to determine presence or absence of nicotine. The laboratory assessment is considered the gold standard, or truth about nicotine. The data are as follows.
(a) What is the sensitivity of the self-reported smoking status?
(b) What is the specificity of the self-reported smoking status?

Nicotine absent Nicotine present
Self-reported nonsmoker 82 14
Self-reported smoker 12 52

Answer 1

Answer: a) 0.7878, b) 0.8723

Step-by-step explanation:

Since we have given that

                                              Nicotine present      Nicotine absent

Self-reported non smoker                  82                                      14

Self-reported smoker                          12                                      52

(a) What is the sensitivity of the self-reported smoking status?

$P(smoker|Nicotine\ present)=\dfrac{52}{52+14}=\dfrac{52}{66}=0.7878$

(b) What is the specificity of the self-reported smoking status?

$P(Non-smoker|Nicotine\ absent}=\dfrac{82}{82+12}=\dfrac{82}{94}=0.8723$

Hence, a) 0.7878, b) 0.8723