 # Statistical Fridays J C Horrow, MD, MSSTAT

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Statistical Fridays J C Horrow, MD, MSSTAT
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?
Statistical concepts. Sensitivity/Specificity Descriptive statistics. Hypothesis Formulation Hypothesis testing. Normal Distribution. a and b errors. Student’s t distribution. Paired /unpaired tests. Categorical data. Chi square tests.

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

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

Sensitivity / Specificity
We can set up a 2x2 square describing how successful the test has been: Truly YES Truly NO TOTAL Tested YES True Pos False Pos TP+FP TestedNO False Neg True Neg FN+TN TP+FN FP+TN N

Sensitivity = TP / (TP+FN)
Truly YES Truly NO TOTAL Tested YES True Pos False Pos TP+FP TestedNO False Neg True Neg FN+TN TP+FN FP+TN N Sensitivity = TP / (TP+FN)

Specificity = TN / (FP+TN)
Truly YES Truly NO TOTAL Tested YES True Pos False Pos TP+FP TestedNO False Neg True Neg FN+TN TP+FN FP+TN N Specificity = TN / (FP+TN)

Positive Predictive Value
Truly YES Truly NO TOTAL Tested YES True Pos False Pos TP+FP TestedNO False Neg True Neg FN+TN TP+FN FP+TN N PPV = TP / (TP+FP)

Negative Predictive Value
Truly YES Truly NO TOTAL Tested YES True Pos False Pos TP+FP TestedNO False Neg True Neg FN+TN TP+FN FP+TN N NPV = TN / (FN+TN)

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.

Sensitivity / Specificity
First, set up the 2x2 square : Truly YES Truly NO TOTAL Tested YES 8 4 12 TestedNO 2 36 38 10 40 50

Worked Example Now calculate the values: Truly YES Truly NO TOTAL
Test YES 8 4 12 Test NO 2 36 38 10 40 50 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?

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%

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.

Effect of Disease Prevalence
Assume 100 patients. 10 have dysrhythmia. Truly YES Truly NO TOTAL Test YES 8 18 26 Test NO 2 72 74 10 90 100 PPV = 8/26 = 31%  a useless test to predict dysrhythmia. NPV = 72/74 = 97% a good test to rule out dysrhythmia.

Effect of Disease Prevalence
For the same 100 patients, 70 have dysrhythmia : Truly YES Truly NO TOTAL Test YES 56 6 62 Test NO 14 24 38 70 30 100 PPV = 56/62 = 62%  a better test to predict dysrhythmia NPV = 24/38 = 63% not as good a test to rule out dysrhythmia

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?

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)

ROC Curve

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

ROC Curve

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