Question

A mammogram was used to screen for breast cancer in 200 women with breast cancer diagnosed by a biopsy and in 500 age- and race-matched women without breast cancer. The results of the mammogram were positive in 150 of the women with breast cancer and in 100 of the women without breast cancer. b. Compute the i) sensitivity, ii) specificity, iii) positive predictive value, and iv) negative predictive value. c. Make a statement about each of the computations d. If the breast cancer prevalence increases, what effect, if any, would this have on i) sensitivity, ii) specificity, iii) positive predictive value, and iv) negative predictive value?

Answer 1

a.

The 2*2 contingency table is as follows.

	Mammogram result	Row total
Positive	Negative
Cancer	Yes	150	50	200
No	100	400	500
Column total	250	450	700

b.

(i)

(ii)

(iii)

(iv)

c.

(i)

The mammogram detects 75% of cancer patients correctly.

(ii)

The mammogram detects 80% of people correctly who are not cancer patients.

(iii)

When mammogram detects cancer it is correct in 60% cases. Here positive predictive value is not so much high.

(iv)

When mammogram detects absence of cancer it is correct in 88.89% cases.

d.

Breast cancer prevalence increases. So, number of false negative and false positive are expected to decrease.

(i)

In such situation, number of false negative decreases which is in the denominator. So, sensitivity increases.

(ii)

In such situation, number of false positive decreases which is in the denominator. So, specificity increases.

(iii)

In such situation, number of false positive decreases which is in the denominator. So, positive predictive value increases.

(iv)

In such situation, number of false negative decreases which is in the denominator. So, negative predictive value increases.