Question

The Pap Smear has been used for decades as a preliminary screening mechanism for detecting potential cervical cancer. Estimates exist to suggest that the rate of cervical cancer in the female population is 0.1 percent (1 case per 1,000). Suppose that, each year, the test is used to screen 100,000 females. Out of those screened that have cervical cancer, the Pap Smear provided positive results (test is positive for presumptive cervical CA) in 56 females. Out of the those screened that do NOT have cervical cancer, the Pap Smear provided positive results (test is positive for presumptive cervical CA) in 1,998 females.

(A)        What is the number of true positives?

(B)        What is the number of false positives?

(C)        What is the number of true negatives?

(D)        What is the number of false negatives?

(E)        Estimate the sensitivity of the Pap Smear for detecting cervical CA

(F)         Estimate the specificity of the Pap Smear for ruling out the presence of cervical CA

(G)        Estimate the positive (PPV) and negative (NPV) predictive values for the Pap Smear test in this screening scenario

(H)        Estimate the positive (PLR) and negative (NLR) likelihood ratios for the Pap Smear test in this screening scenario

(I)           Overall, how would you evaluate the usefulness of this test in this screening scenario? What factor(s) might influence the overall result?

(J)         What recommendations could be made to try and improve the overall usefulness/efficacy of the Pap Smear for detecting potential cervical cancer?

Answer 1

Those screened that have cervical cancer, the Pap Smear provided positive results = 56 females.

Those do NOT have cervical cancer, the Pap Smear provided positive results = 1998 females.

Total positive results = 0.1% of 100,000 = 100 females

	Present	Absent	Total
positive	56	1998
negative
Total	100		100000

The complete table is,

	Present	Absent	Total
positive	56	1998	2054
negative	44	97902	97946
Total	100	99900	100000

(A)

number of true positives = 56

(B)

number of false positives = 1998

(C)

number of true negatives = 97902

(D)

number of false negatives = 44

The table is,

	Present	Absent	Total
positive	a	c	a+c
negative	b	d	b+d
Total	a+c	c+d	a+b+c+d

a = 56

b = 44,

c = 1998,

d = 97902

(E)

(F)

(G)

(H)

(I)

The usefulness of this test can be evaluated by the two measures sensitivity and specificity together. Sensitivity is the probability of a positive test result with the disease and the Specificity is the probability of a negative test result without the disease. this test has low sensitivity and high specificity.

(J)

Sensitivity need to be increase.