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Statistical Fridays

Statistical Fridays. J C Horrow, MD, MS STAT Clinical Professor, Anesthesiology Drexel University College of Medicine. Goals. Introduce / reinforce statistical thinking Understand statistical models Appreciate model assumptions Perform simple statistical tests. What topics will we cover?.

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Statistical Fridays

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  1. Statistical Fridays J C Horrow, MD, MSSTAT Clinical Professor, Anesthesiology Drexel University College of Medicine

  2. Goals • Introduce / reinforce statistical thinking • Understand statistical models • Appreciate model assumptions • Perform simple statistical tests

  3. What topics will we cover? • Statistical concepts. Sensitivity/Specificity • Descriptive statistics. Hypothesis Formulation • Hypothesis testing. • Normal Distribution. aand b errors. • Student’s t distribution. Paired /unpaired tests. • Categorical data. Chi square tests.

  4. Session #1: Summary • Sensitivity / specificity • Predictive value • Effect of disease prevalence • The ROC curve

  5. Sensitivity / Specificity Given the following: • N independent events • A test with a dichotomous result (Y/N) • Known “truth” for each event

  6. Sensitivity / Specificity We can set up a 2x2 square describing how successful the test has been:

  7. Sensitivity Sensitivity = TP / (TP+FN)

  8. Specificity Specificity = TN / (FP+TN)

  9. Positive Predictive Value PPV = TP / (TP+FP)

  10. Negative Predictive Value NPV = TN / (FN+TN)

  11. Worked Example 50 patients are tested for hyperlipidemia. Of the 10 with the disorder, 8 test positive. Of the 40 without the disorder, 4 test positive. Calculate sensitivity, specificity, and positive and negative predictive values.

  12. Sensitivity / Specificity First, set up the 2x2 square :

  13. Worked Example Now calculate the values: Sensitivity = 8/10 = 80% Specificity = 36/40 = 90% PPV = 8/12 = 67% NPV = 36/38 = 95% What do you think of this test? Is it a “good” test? When?

  14. Effect of Disease Prevalence Assume that a serum potassium < 4.0 mEq/L predicts dysrhythmia 80% of the time. However, 20% of patients without dysrhythmia also have values < 4 mEq/L. Note: sensitivity = specificity = 80%

  15. Effect of Disease Prevalence We will find the PPV and NPV of this test (serum K < 4.0 mEq/L) if the prevalence of dysrhythmia is 10%. Then we will do the same for prevalence of 70%, and see how the results differ.

  16. Effect of Disease Prevalence Assume 100 patients. 10 have dysrhythmia. PPV = 8/26 = 31%  a useless test to predict dysrhythmia. NPV = 72/74 = 97% a good test to rule out dysrhythmia.

  17. Effect of Disease Prevalence For the same 100 patients, 70 have dysrhythmia : PPV = 56/62 = 62%  a better test to predict dysrhythmia NPV = 24/38 = 63% not as good a test to rule out dysrhythmia

  18. Effect of Disease Prevalence Why pick serum K < 4.0 mEq/L? Would another discriminant yield better sensitivity and specificity (and therefore better PPV and NPV)? Which discriminant is the best?

  19. Receiver Operating Characteristic Curve Vary the discriminant throughout the range of possible test result values… Calculate the sensitivity and specificity at each value… Plot sensitivity v. (1-specificity)

  20. ROC Curve

  21. Session #1: Review • Sensitivity / specificity • Predictive value • Effect of disease prevalence • The ROC curve

  22. ROC Curve

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