Chapter 8

Multiple Tests

Extra Problems

Copyright 2010, Thomas B. Newman and Michael A. Kohn

Supplementary to: Newman TB, Kohn MA. Evidence-based diagnosis. Cambridge ; New York: CambridgeUniversity Press; 2009.

5. PIOPED – Combining a Clinical Prediction Rule with a VQ Scan

Pulmonary Embolism (PE) is a serious condition that is fatal in 25% of cases if left untreated. With anticoagulation treatment, the risk of mortality is reduced to 1%. Hunink’s textbook (1) considered this, along with the mortality risk of anticoagulating patients without PE (0.8%) and the mortality (0.5%) associated with the gold standard test for PE, pulmonary angiogram, to calculate the following thresholds:

For pulmonary angiogram as a test to guide anticoagulation treatmentfor PE,

No Treat-Test threshold = 0.02

Test-Treat threshold = 0.375

The PIOPED study(2) presented data on the results of using a clinical prediction rule and a ventilation-perfusion scan (VQ) to update the probability of PE. Here are the data on the rule and the scan separately.

CLINICAL PREDICTION RULE / PE + / PE − / LR
High / 61 / 24.2% / 29 / 4.6% / 5.30
Intermediate / 170 / 67.5% / 399 / 62.8% / 1.07
Low / 21 / 8.3% / 207 / 32.6% / 0.26
Total / 252 / 100.0% / 635 / 100.0%
V/Q Scan / PE+ / PE- / LR
High / 103 / 40.9% / 15 / 2.4% / 17.30
Intermediate / 104 / 41.3% / 241 / 38.0% / 1.09
Low / 40 / 15.9% / 256 / 40.3% / 0.39
Normal / 5 / 2.0% / 123 / 19.4% / 0.10
Total / 252 / 100.0% / 635 / 100.0%

a)What was the prevalence of PE in the PIOPED study?

In the following table, we calculated LRs for the 3 × 4 = 12 possible combinations of the clinical prediction rule and VQ results by multiplying the LR for the clinical prediction rule’s result by the LR for the VQ result. We also sorted the result combinations in descending order by LR.

V/Q / CLINICAL PREDICTION RULE / LR
High / High / 91.71
High / Intermediate / 18.58
Intermediate / High / 5.76
High / Low / 4.42
Low / High / 2.07
Intermediate / Intermediate / 1.17
Normal / High / 0.54
Low / Intermediate / 0.42
Intermediate / Low / 0.28
Normal / Intermediate / 0.11
Low / Low / 0.10
Normal / Low / 0.03

b)Check our calculation for the LR when the V/Q result is “Low” and the clinical prediction rule result is “High.” Show your work.

c)What assumption have we made about the V/Q scan and the clinical prediction rule as tests for PE when calculating LR in that way?

d)Assume that the prior probability of PE (before clinical prediction or VQ) is the same as in the PIOPED Study. Use the No Treat-Test threshold of 0.02 to determine which combinations of VQ and clinical prediction rule results are reassuring enough that you can stop testing without doing a pulmonary angiogram and withhold anticoagulation (maintaining the assumption mentioned above).

e)Now use the Test-Treat threshold of 0.375 above to determine which combinations of VQ and clinical prediction rule results are so convincing that you can forego the pulmonary angiogram and treat presumptively for PE with anticoagulation.

6. In Chapter 5, Problem 8 we mentioned a study by Tanz et al.,(3) which found that the observed sensitivity and specificity of office-based tests for group A strep depended on the prior probability of strep throat. In that study, the prior probability was estimated using the Mc Isaac Score, which gives 1 point for each of the following items (range of scores 0 to 5):

  • history of temperature of >38°C
  • absence of cough
  • tender anterior cervical lymph nodes
  • tonsillarswelling or exudates
  • age of <15 years
  1. Recall that the study showed that the sensitivity and specificity of the office-based strep tests varied with the prior probability of strep. Using terminology from this chapter, how can we describe the relationship between the McIsaac Score and the office-based strep tests?
  2. Table 5 from that paper is reprinted below. The text says: "Table 5 shows that McIsaac scores >2 were significantly associated with positive results for each diagnostic test. No other information about the odds ratios in Table 5 is included. (Note: RADT= Rapid Antigen Detection Test; BAP = Blood Agar Plate (Culture))
  1. What is being compared in this table?
  1. Can you find any errors in the table? (One is obvious and the other is subtle)
  2. (Extra credit? Ignoring the errors, do these odds ratios provide evidence of significant spectrum bias?

TABLE 5 Odds Ratios for Positive Diagnostic Test Results With McIsaac Scores of >2

Test / Odds Ratio (95% CI) / P
RADT / 3.44 (2.66–4.44) / <.001
Office BAP / 2.75 (2.15–5.34) / <.001
Laboratory BAP / 2.81 (3.20–3.60) / <.001

The baseline score level was 0 to 2.

7. We return to the study of the new sensitive Troponin I test for acute myocardial infarction already featured in Chapters 4 and 5.(4) Figure 1 from that study is reprinted again below for your convenience.

Suppose that results of both the Troponin I and Troponin T tests are reported back in an hour or less and that treatment is more effective if given within 6 hours of onset of chest pain and less effective thereafter. Further, suppose that the Troponin I test costs $500, but the Troponin T test costs only $50. Based on the ROC curves below, what would be a reasonable strategy for ordering these two tests?

1.Hunink MGM. Decision making in health and medicine : integrating evidence and values. Cambridge ; New York: Cambridge University Press; 2001.

2.PIOPED. Value of the ventilation/perfusion scan in acute pulmonary embolism. Results of the prospective investigation of pulmonary embolism diagnosis (PIOPED). The PIOPED Investigators. Jama. 1990;263(20):2753-9.

3.Tanz RR, Gerber MA, Kabat W, Rippe J, Seshadri R, Shulman ST. Performance of a rapid antigen-detection test and throat culture in community pediatric offices: implications for management of pharyngitis. Pediatrics. 2009 Feb;123(2):437-44.

4.Keller T, Zeller T, Peetz D, Tzikas S, Roth A, Czyz E, et al. Sensitive troponin I assay in early diagnosis of acute myocardial infarction. N Engl J Med. 2009 Aug 27;361(9):868-77.