Handout14 - Lecture 14 1. Example: comparing two tests for...

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Lecture 14 1. Example: comparing two tests for tuberculosis exposure 2. ConFdence intervals 3. Bootstrap with Proc Surveyselect 4. Bootstrap a Spearman correlation 1 Correlation between two diagnostic tests for tuberculosis exposure Standard test for exposure to tuberculosis is the tuberculin skin test (TST): • Inject test protein under the skin, a red bump forms • 48 hours later, measure the diameter of the bump. • Bump diameter > 10mm indicates person has been exposed to tuberculosis. A new test, Quantiferon , measures tuberulosis antigens (IN±- ) in a blood sample. Antigens above a certain level are considered a positive test. Study compared results of Quantiferon and TST in 195 immigrants. C. Baker, et.al. Am. J. Tropical Medicine and Hygiene, 2009, 80:628–633. 2
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Correlation: Pearson or Spearman? 3 Spearman Correlation Coefficients Prob > |r| under H0: Rho=0 Number of Observations Quantiferon TST Quantiferon 1.00000 0.66569 <.0001 198 195 For correlation, common practice is to give a point estimate r with a p -value. The p -value comes from H 0 : Ω = 0. Is it possible that population correlation Ω = 0? If not, then is this p -value relevant or helpful? 95% con±dence interval would be much more useful. 4
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Proc Corr data=ph6470.QFT spearman gives Spearman correlation fisher ( biasadj=no ) ; gives CI var Quantiferon TST ; Spearman Correlation Statistics (Fisher’s z Transformation) With Sample Variable Variable N Correlation Fisher’s z Quantiferon TST 195 0.66569 0.80296 Spearman Correlation Statistics (Fisher’s z Transformation) With p Value for Variable Variable 95% Confidence Limits H0:Rho=0 Quantiferon TST 0.579372 0.737243 <.0001 This confdence interval assumes both QuantiFeron and TST were normally distributed. 5 What would graph oF QuantiFeron and TST look like iF they were normally distributed? Variable N Mean Std Dev Median Quantiferon 198 4.51823 6.77807 0.50000 TST 195 10.30769 9.65208 12.00000 Spearman Correlation Coefficients Prob > |r| under H0: Rho=0 Number of Observations Quantiferon TST Quantiferon 1.00000 0.66569 <.0001 198 195 Simulate correlated normal ordered pairs with means, SDs, and correlation as observed. Done using a macro that calls Proc IML , a matrix algebra procedure. 6
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Simulated normal data with same mean, SD, and correlation as observed:
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Handout14 - Lecture 14 1. Example: comparing two tests for...

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