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Basic Tools in Medical Decision Making

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Medical Decision Making

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Abstract

We introduce the basic analytical tools used in medical decision making such as the a priori probability of illness and the sensitivity and specificity of a test. Each chapter provides illustrations, examples and exercises to sharpen the reader’s understanding of the issues discussed.

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Notes

  1. 1.

    Dooling, R.—White Man’s Grave—Picador, New York—1995, p. 70.

  2. 2.

    \( 30\cdot 0.8+10\cdot 0.2=26 \)

  3. 3.

    \( {\left(30-26\right)}^2\cdot 0.8+{\left(10-26\right)}^2\cdot 0.2=64 \)

  4. 4.

    AWMF = ‘Arbeitsgemeinschaft der Wissenschaftlichen Medizinischen Fachgesellschaften’, Association of the Scientific Medical Societies in Germany

References

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Author information

Authors and Affiliations

  1. Department of Business and Economics, University of Basel, Basel, Switzerland

    Stefan Felder

  2. School of Business Studies, Stralsund University of Applied Sciences, Stralsund, Germany

    Thomas Mayrhofer

Authors
  1. Stefan Felder
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  2. Thomas Mayrhofer
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Exercises

Exercises

  1. 1.

    There is a diagnostic test for prostate cancer which measures the concentration of PSA (prostate-specific antigens) in the blood. If the concentration exceeds a certain threshold, the physician applies advanced diagnostics and performs a biopsy. A positive outcome of the biopsy leads to a radical prostatectomy. If the PSA concentration is unremarkable, the physician will take another blood test one year later.

    To determine the quality of the PSA test, Hoffman et al. (2002) conducted the test as well as a biopsy on 2620 men of age 40 or older in the U.S. state of New Mexico. The biopsies revealed prostate cancer in 930 men. With a cutoff value of 4 ng/ml, the PSA test detected 800 true cases of sick men and 558 true cases of healthy men.

    1. (a)

      Calculate sensitivity and specificity for a critical serum concentration of 4 ng/ml.

    2. (b)

      Fill out the 2 × 2 table for four age groups if the following 10-year prevalence rates apply for Germany:

      Age group

      Prevalence rate (in percent)

      <60

      0.1

      60–69

      2.3

      70–79

      4.9

      >80

      5.5

      All

      0.8

      1. Source: Robert Koch Institut (2010), p. 102
    3. (c)

      Use the positive likelihood ratio to calculate the odds of a true positive case for each age group. Explain the relationship between the a priori and the a posteriori odds of identifying a true positive patient.

    4. (d)

      Regarding the calculated a posteriori odds for the four age groups, how useful is the test result given a cutoff value of 4 ng/ml? Which parameters would improve the test?

    5. (e)

      Calculate a prevalence rate at which 90 out of 100 men who were tested positive will in fact be sick (at a cutoff value of 4 ng/ml). Compared to the pertinent prevalence rate in Germany, what conclusions can be drawn from this case about the usefulness of the PSA test as a screening method?

    6. (f)

      Early AWMFFootnote 4 (2002) guidelines advised a critical value of 4 ng/ml for all age groups. Argue why this is not tenable, given the different prevalence rates in the age groups.

    7. (g)

      According to these guidelines, family background (genetics) and fat intake are further risk factors for prostate cancer. Is it justified to offer the PSA test to targeted subgroups of the population?

  2. 2.

    The following table lists the sensitivity and specificity for PSA cutoff values between 1 and 20 ng/ml (see Hoffman et al. 2002) for men of age 40 and older.

    PSA

    Sensitivity

    Specificity

    1

    98

    9

    2

    95

    20

    3

    91

    26

    4

    86

    33

    5

    75

    44

    6

    63

    57

    7

    56

    66

    8

    49

    74

    9

    42

    80

    10

    38

    84

    15

    23

    93

    20

    17

    97

    1. (a)

      Draw the ROC curve.

    2. (b)

      Calculate the positive likelihood ratio for each PSA cutoff value. How do sensitivity and specificity change along the ROC curve?

    3. (c)

      Which consequences would arise from reducing the cutoff value from 4 to 2 ng/ml?

    4. (d)

      In 2003, the German parliament called for coverage of PSA tests under the Social Health Insurance for all men older than 45. State the pros and cons of such a policy.

  3. 3.

    Prove that a test’s likelihood ratio improves if either sensitivity or specificity increases.

  4. 4.

    Describe the distribution of the diagnostic measurement values for the sick and the healthy in Fig. 2.1 for a perfect test (sensitivity and specificity equal to unity). Where is the optimal cutoff value for testing?

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Felder, S., Mayrhofer, T. (2017). Basic Tools in Medical Decision Making. In: Medical Decision Making. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53432-8_2

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  • DOI: https://doi.org/10.1007/978-3-662-53432-8_2

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  • Print ISBN: 978-3-662-53431-1

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