Chapter 4 Exercises 

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

4.7  Cross-tabulated diagnoses from independent raters are shown here. Calculate the kappa statistic for results and interpret your findings. 

4.8  Calculate this test's sensitivity and specificity.

4.9 Why is exercise 4.7 a reproducibility analysis? Why is exercise 4.8 is 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, which will be frequent given that tornados usually do not occur. (A completely ignorant person could predict "no tornado" and attain agreement 920 / 934 = 98.5% of the time~)  Calculate the kappa statistic for Finley's data and discuss the degree to which his predictions exceeded random concurrence.

4.11 Predicting tornadoes, predictive value positive and predictive value negative. Reread Exercise 4.10. Now calculate the PVP of Finley's predictions. 

4.12 Screening for bladder cancer (based on an exercise written by Phillip Cole). A screening test for bladder cancer uses the staining properties of exfoliated cells in the urine to detect possible cancer cases. The test has a sensitivity of 80% and specificity of 96%. Suppose we use this test in 100,000 individuals from a population in which the prevalence of subclinical bladder cancer is 0.005. 

(A) Set up a 2-by-2 table showing the number of TPs, TNs, FNs, and FPs we expect when  using this screening test in this population. 
(B) How many people in the population will have positive tests? Of these, what proportion will be true positives (i.e., what is the predictive value positive of a test result)?
(C) How many people will have negative test results? Of these, what proportion will be true negatives (i.e., what is the predictive value negative of a test result)?
(D) What would the PVP of the test be if the SENsitivity of the test was  increased from 80% to 90% (keeping SPEC at 96%)? 
[Hint: You can solve this problem by building a new table of expected counts and then determining the PVP, or you could use the Bayesian formula 4.8 on p. 88.]
(E) What would the PVP be if SPECificity were increased from 96% to 98% (keeping SEN at 80%)?
(F) Based on your answers to (G) and (H), what has greater influence on the PVP of the test, increasing the SEN or increasing the SPEC? Does either result in a test that has good predictive value? If not, what practice can effectively increase the predictive value of a positive test?  

4.13 Updating The Case Study of Screening for Antibodies to the Human Immunodeficiency Virus. The case study that begins on p. 98 in the text is an excellent way to acquaint yourself with strengths and limitations of screening for a disease in the population. It is, however, a little out of date. For the sake of practice, redo this case study assuming the EIA screening kit described on p. 99 has a sensitivity of 98% (.98) and its specificity is 99% (.99). Also, now assume Western Blot (WB) test considered on page 101 has a sensitivity of 97% (.97) and specificity of 99.99% (.9999). 

Key  Last update: 05/21/2009