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**Statistical Fridays J C Horrow, MD, MSSTAT**

Clinical Professor, Anesthesiology Drexel University College of Medicine

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**Goals Introduce / reinforce statistical thinking**

Understand statistical models Appreciate model assumptions Perform simple statistical tests

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**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.

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**Session #1: Summary Sensitivity / specificity Predictive value**

Effect of disease prevalence The ROC curve

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**Sensitivity / Specificity**

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

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**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

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**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)

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**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)

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**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)

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**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)

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**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.

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**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

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**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?

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**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%

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**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.

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**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.

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**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

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**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?

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**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)

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ROC Curve

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**Session #1: Review Sensitivity / specificity Predictive value**

Effect of disease prevalence The ROC curve

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ROC Curve

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