3 What topics will we cover? Statistical concepts. Sensitivity/SpecificityDescriptive statistics. Hypothesis FormulationHypothesis testing.Normal Distribution. a and 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 prevalenceThe ROC curve
5 Sensitivity / Specificity Given the following:N independent eventsA 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:Truly YESTruly NOTOTALTested YESTrue PosFalse PosTP+FPTestedNOFalse NegTrue NegFN+TNTP+FNFP+TNN
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 :Truly YESTruly NOTOTALTested YES8412TestedNO23638104050
13 Worked Example Now calculate the values: Truly YES Truly NO TOTAL Test YES8412Test NO23638104050Sensitivity = 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.Truly YESTruly NOTOTALTest YES81826Test NO272741090100PPV = 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 :Truly YESTruly NOTOTALTest YES56662Test NO1424387030100PPV = 56/62 = 62% a better test to predict dysrhythmiaNPV = 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)