1

2

Statistics

• Objectives:

1. Try to differentiate between the P value and alpha value

2. When to perform a test

3. Limitations of different tests and how to over come them

3

Statistics • Why should I care about the statistics?

I can prove anything by statistics except the truth (George Canning)

• What are statistics?

Statistics are used much like a drunk uses a lamppost: for support, not illumination (Vin Scully)

• What is a theory?

A supposition or a system of ideas intended to explain something, especially one based on general principles independent of the thing to be explained

4

• How to prove a theory

1. Null Hypothesis ( H0 )

2. Alternate Hypothesis

• Calculate statistics like mean, median, standard deviation, normal distribution curve, standard normal distribution curve, Z value etc

• Next step, checking whether our results are random by chance vs real

5

• Traditional Method: Define critical values and see whether we reached them or not

• P value method:

1. What is P value?

p-value is the probability of obtaining a test statistics at least as extreme as the one that was actually observed, assuming that the null hypothesis is true

2. What is α value (type 1 error)

Level of significance 0.01%, 0.005%, 0.1%

What is the relation between P value and α value

If P value < α value then the null hypothesis is rejected

If P value > α value, we fail to reject null hypothesis.

6

Diagnosis • We make the diagnosis based on the either pattern

reorganization or probability.

• Pattern reorganization could be considered as a pre-test probability

• When do we need to perform a test?

1. When we are in doubt?

2. When our lawyers are asking?

3. Do we need a test during low probability scenarios?

4. Do we need a test when we are certain about the diagnosis?

7

• Always think pretest probability

• Lets assume, zero is normal and 100 is the diagnosis.

• Disease is a spectrum

0% 100%

Low probability High probability

Test threshold Treatment threshold

We shouldn’t perform any diagnostic test at ends

8

Critical appraisal tests

• Specificity: It’s the ability of the test to correctly identify those patients without the disease.

Specificity=true negatives/(true negative + false positives)

• Sensitivity: It’s the ability of the test to correctly identify those patients with the disease.

Sensitivity= true positives/(true positive + false negative)

9

• Positive Predictive Value

How likely is it that this patient has the disease given that the test result is positive?

PV+= true positive/(true positive + false positive)

• Negative Predictive Value

How likely is it that this patient has the disease that the test result is negative?

PV-= true negatives/(true negatives +false negatives)

10

Why are we having ,four tests instead of two?

• This is our favorite 2x2 table lets see whether it is going to give us an answer.

Have disease

Doesn’t have disease

Positive test

TP FP Positive predictive value

Negative test

FN TN Negative Predictive value

Sensitivity Specificity

11

Have disease Doesn’t have disease

Positive Test 20 5 80

Negative Test 5 20 80

25

Sensitivity: 80

25

Specificity:80

50 patients total

12

Have disease Doesn’t have disease

Positive test 8 16 33.3

Negative test 2 24 92

10

Sensitivity 80

40

Specificity 80

50

13

Have disease Doesn’t have disease

Test positive 24 4 85

Test negative 6 16 72

30Sensitivity 80

20Specificity 80

50 patients

14

Examples in an article

15

16

• Pre-test probability

• Post-test Probability

• Likelihood Ratio (LR):

How likely the test result found is to be found in diseased when compared with non disease

Probability of an individual with a condition having positive result

Probability of an individual without condition having a positive result

17

Rule in infection: High LR+

Rule out infection: High LR-

Post test odds: Pre-test odds x LR

18

19

20

D dimers and PE

• A 56 year old male with a history of stage 3 colorectal cancer s/p colectomy nearly 3 weeks back presented to emergency department for having chest pain, and trouble breathing. Since surgery he started noticing bilateral lower extremity swelling. PE significant for the bilateral edema, vitals are significant for the HR of 115/mt, RR 19/mt, and 02 sats of 92%.

• D dimers by quantitative ELISA are 150 ng/ml (black in color/negative).

• Next Step: Do you want to get a CTA or not

21

• A 56 year old male who was discharged from the hospital nearly 4 days back for the hip fracture s/p repair presented to ED for having right sided chest pain. His vitals are afebrile, HR 120/mt, RR 20/mt, 02 sats of 96%. PE exam is negative for any edema. D dimers were ordered, and the box is black in color.

• Next Step: CTA or not

22

• A 56 year old male without any PMH presented to the ED for having right sided chest pain. His vitals are afebrile, HR 120/mt, RR 20/mt, 02 sats of 96%. PE exam is negative for any edema. D dimers were ordered, and the box is black in color.

• Next Step?

23

• Quantitative rapid ELISA post test probability if the test (d-dimers) is negative

Low pretest probability- 0.5 to 2%

Moderate High pretest probability- 5 to 6%

High pretest probability- 19 to 28%

• Negative predictive value (NPV) of 94.2% (ranges from 91%-100% depending on study)

24

• Sensitivity: 95%

• Specificity: 40-68% in patients without PE. It falls more if we add CRF

• Now we know the answers for the three questions.

25

26

1. How to incorporate discussions about statistics during rounding

2. How will we educate our learners to evaluate pre-test probability before ordering a test

3. How will we make our learners to exercise clinical scenarios of both positive and negative results before ordering the test instead of after getting the result

4. How will we educate them about advancing further in diagnostic algorithm

5. Do we really need to bother about all these numbers and statistics ?

27