Chapter 4 Exercises 

4.1 - 4.6   See pp. 95 - 96 in the text.

4.7 Cross-tabulated diagnostic results from two independent raters are:

 

Rater B

 

Rater A

+

-

Total

+

150

31

181

-

28

239

267

Total

178

270

448

Calculate the kappa statistic for these results. Interpret this finding. [You may check your calculations with the “Screening Calculator” under the “Counts” folder in http://www.openepi.com.]

4.8 Calculate this test's sensitivity and specificity.

 

Gold Standard

 

Test

+

-

Total

+

15

7

22

-

3

145

148

Total

18

152

170

4.9 Why is exercise 4.7 a reproducibility analysis? Why is exercise 4.8 a validity analysis?

4.10 Predicting tornadoes, kappa. During four months in 1884, J. P. Finley predicted whether or not one or more tornadoes would occur in each of eighteen areas of the United States (Murphy, 1996). One of Finley's summary tables is shown below (source: Goodman & Kruskal, 1959, pp. 127-128). From this table we can say that Finley's predictions were correct (11 + 906) / 934 = 0.9818 = 98.2% of the time. However, this statistic ignores random agreement: I would be correct 920 / 934 = 98.5% of this time if I merely always predicted "no tornado"!)  Calculate the kappa statistic for Finley's data. Discuss the degree to which Finley’s predictions exceeded “random guessing.”

 

Actual occurrence

 

Prediction

+

-

Total

+

11

14

25

-

3

906

909

Total

14

920

934

4.11 Predicting tornadoes, predictive value positive. Calculate the predictive value positive of Finley’s predictions using the data in exercise 4.10. How did Finley do? [Consider the finding in this question and the findings in question 4.10.]

4.12 Screening for bladder cancer. A screening test for bladder cancer uses the staining properties of exfoliated cells in the urine to detect potential bladder cancer cases.  Two pathologists review 500 samples and come up with the following diagnoses:

 

 

Pathologist B

 

Pathologist A

+

-

Total

+

9

2

11

-

0

489

489

Total

9

491

500

 

a.    Explain why this is a reproducibility analysis, and not a validity analysis.

b.    Assess the reproducibility of these results.

c.     Further development of the test proves it to have a sensitivity of 90% and specificity of 98%. This test is used in 100,000 individuals from a population in which the prevalence of subclinical bladder cancer is 0.1% (i.e., 0.001).  Set up a 2-by-2 table showing the number of true positives, true negatives, false positives, and false negatives expected when using this screening test in this population. 

d.    What is the predictive value of a positive test in this population?

e.    What is the predictive value or a negative test in this population?

f.     The same test is used in a patient population demonstrating chronic hematuria and other symptoms of possible bladder cancer. The prevalence of bladder cancer in this clinical population is 1 in 10. Set up a 2-by-2 table showing the distribution of true positives, true negatives, false positives, and false negatives expected when using the test in 1000 people from this clinical population.

g.    What is the predictive value of a positive test when used in the clinical population described in item f?

h.    Why is the predictive value positive of the test in the clinical population so much greater than in the general population?


4.13 Updating the Case Study in the text. The case study that begins on p. 98 in the text provides a way to acquaint yourself with strengths and limitations of population-based screening procedures. It is, however, out of date in terms of sensitivity and specificity specifications. We might consider redoing this case study assuming the EIA screening kit described on p. 99 has a sensitivity of 98% and its specificity is 98.83%  – see http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0008217#top for current estimates of specificty. Also, now assume Western Blot (WB) test considered on page 101 has a sensitivity of 97% (.97) and specificity of 99.99% (.9999). 

4.14 Interexaminer Reliability Of A Leg Length Analysis (Holt et al., 2009). A study to evaluate the interexaminer reliability of a leg length analysis protocolbetween an experienced chiropractor and an inexperienced chiropractic student who has undergone an intensive training program found these data for examination in the supine extended leg position:

 

Rater B

 

Rater A

+

-

Total

+

12

2

14

-

4

28

32

Total

16

30

46

 

a. Calculate the percent agreement between the raters.

b. Calculate the kappa statistic and interpret this result.