Statistics For Residents

What you never thought you would understand… Brad E. Dicianno, MD University of Pittsburgh Medical Center Dept. of Physical Medicine & Rehabilitation VA Pittsburgh Health Care System Human Engineering Research Laboratories

Overview: When reading (or writing) a paper, you should be able to: Classify and describe the data  What does ‘nominal’ mean again?

Decide what tests are appropriate  How am I supposed to know if I am supposed to run a T-test?

Understand the significance of the tests  It gave me a p value. Am I done now?

Know how data should be reported  And be able to catch their mistakes!

Overview: You should then be able to… Evaluate the utility of the Diagnostic Tests  Does a + result mean anything?

Evaluate efficacy of Therapies  Did the interventions actually do anything?

Evaluate relevance of Exposures  Did those at risk suffer any harm?

Know more than you need to know for boards

Classifying and Describing Data

Step 1: Classify your Variables

Categorical Categories, groups Gender, Race, Job, Favorite color Yes/No

Ordinal Ordered; data goes in specific direction Dividing doesn’t make sense PGY1, PGY2, PGY3… Always, Sometimes, Never…

Continuous Numerical Scale You can divide the numbers Weight, Height, Exam Score

Try it out… FIM score Arm temperature Med route (po, NG, IV) Modified Ashworth Score Plantar response Type of insurance Albumin level

Try it out… FIM score Arm temperature Med route (po, NG, IV) Modified Ashworth Score Plantar response Type of insurance Albumin level Ordinal Continuous Categorical Ordinal Categorical Categorical Continuous

Step 2: Normal or Not Normal?

Normal = Parametric

Not Normal = Non Parametric

Skewness Excess skewness is NOT normal

Mean Median Negatively Skewed Mode Mean Median Mode Symmetric (Not Skewed) Mode Median Positively Skewed Mean

Kurtosis Excess kurtosis is NOT normal

Options for determining normal distributions Graph the frequencies on y axis and value of variable on x axis OR Run a program like SPSS   Skewness -1 to 1 is normal Kurtosis -1 to 1 is normal

Other descriptives Mean (average) Median (middle value) Mode (most often occurring) Standard Deviation Ranges (low to high) 122333444455555

Step 3: Decide what you want to do with the data

Looking for associations Is pain related to medication use?

Is gender related to exam scores?

Is alcohol use related to albumin levels?

Predicting/Correlations Does weight go up if height goes up?

Does BP go down if exercise level goes up?

Does HR increase with prolonged bedrest?

Prediction/Regression Y=mx + b Does body fat percentage (x) predict body image satisfaction (y)?

Do pain scores (x) predict participation in PT (y)?

Step 4: Choose the test. Use the handout.

Step 5: Report the results.

Hypothesis (Null hypothesis) Alpha level P value Be careful with reporting “no differences…” Remember, just because you didn’t find a difference, doesn’t mean it doesn’t exist.

Evaluating Diagnostic Tests Likelihood Ratio (LR)  Likelihood of the test result in patients with a condition compared to the likelihood of test result in those without the condition Post test Odds (PTO)  How likely to have the condition if testing +

Likelihood Ratio Test + Test Condition + A C Condition B D LR = A/(A+C) / B/(B+D) PTO = LR * Pretest odds

Example: Pregnancy test A pregnancy test gives a + result in 75 out of 100 women who are pregnant, and a – result to the other 25.

In women who are not pregnant, it tells 50 they are +, and 50 they are -.

How likely is a woman to be pregnant if she gets a + result? Assume she is 50% confident she is pregnant.

Fill in the blanks… Test + Condition + A Condition B Test C D LR = A/(A+C) / B/(B+D) PTO = LR * Pretest odds

Likelihood Ratio Test + Test Condition + A 75 C 25 Condition B 50 D 50 LR = A/(A+C) / B/(B+D) PTO = LR * Pretest odds

Likelihood Ratio Test + Test Condition + A 75 C 25 Condition B 50 D 50 LR = A/(A+C) / B/(B+D) = 75/100 / 50/100 = 1.5

PTO = 1.5 * 0.5 = 0.75 = 75%

Evaluating Diagnostic Tests Likelihood Ratio   Likelihood of the test result in patients with a condition compared to the likelihood of test result in those without the condition LR = 1.5

   PTO = 75% Positive result is 1.5 times more likely in pregnant women than non-pregnant With a + test, odds of being pregnant increase to 75%

Evaluating Diagnostic Tests Sensitivity Positive Predictive Value Specificity Negative Predictive Value

Example: Evaluating the usefulness of a net designed to catch green fish

Evaluating Diagnostic Tests Sensitivity  True positives/everyone with condition you want to pick up True True False True + False + False + True -

Evaluating Diagnostic Tests Sensitivity = ½ = 0.5

 True positives/everyone with condition you want to pick up True True You caught 1 of the 2 fish you should have caught.

False True + False + False + True -

Evaluating Diagnostic Tests Positive Predictive Value  True positives/all positives True True False True + False + False + True -

Evaluating Diagnostic Tests Positive Predictive Value = 1/3  True positives/all positives True 1 of the 3 fish you did catch was of the right kind True False True + False + False + True -

Evaluating Diagnostic Tests Specificity  True negatives/everyone w/o condition True True False True + False + False + True -

Evaluating Diagnostic Tests Specificity = 3/5  True negatives/everyone w/o condition True True Your net correctly ignored 3 of the 5 fish it wasn’t supposed to catch.

False True + False + False + True -

Evaluating Diagnostic Tests Negative Predictive Value  True negatives/all negatives True True False True + False + False + True -

Evaluating Diagnostic Tests Negative Predictive Value = 3/4  True negatives/all negatives True True The net correctly ignored 3 of the 4 fish it didn’t catch.

False True + False + False + True -

Evaluating Therapies Relative Risk (risk ratio) (RR)  Ratio of risk in treated group to risk in control group Relative Risk Reduction (RRR)  % reduction in risk in treated group compared to controls Absolute Risk Reduction (ARR)  Diff. in risk between controls and treated Number needed to treat (NNT)  # you have to treat to prevent one adverse outcome

Treatment Effects Treated Control Outcome + A Outcome B Risk in each group Y=A/(A+B) C D X=C/(C+D)

Treatment Effects Treated Control Outcome + A Outcome B Risk in each group Y=A/(A+B) C D X=C/(C+D) RR = Y/X RRR= 1 – RR * 100% ARR = X – Y NNT = 1/ARR

Fictional Example: A New HIV vaccine 100 people at high risk of HIV are given HIV vaccine, and 100 people are given nothing. They are followed over time.

25 of the people with the vaccine develop HIV.

All of the people without the vaccine develop HIV.

Should you recommend the vaccine?

Fill in the Boxes… HIV+ HIV New HIV Vaccine Control A C B D RR = Y/X RRR= 1 – RR * 100% ARR = X – Y NNT = 1/ARR Risk in each group Y=A/(A+B) = X=C/(C+D) = RR = RRR = ARR = NNT =

Treatment Effects HIV+ HIV New HIV Vaccine Control A 25 C 100 RR = Y/X RRR= 1 – RR * 100% ARR = X – Y NNT = 1/ARR B 75 D 0 Risk in each group Y=A/(A+B) = X=C/(C+D) = RR = RRR = ARR = NNT =

Treatment Effects HIV+ HIV New HIV Vaccine Control A 25 C 100 RR = Y/X RRR= 1 – RR * 100% ARR = X – Y NNT = 1/ARR B 75 D 0 Risk in each group Y=A/(A+B) = 0.25

X=C/(C+D) = 1.00

RR = 0.25

RRR = 75% ARR = 0.75

NNT = 1.33

Evaluating Therapies Relative Risk (risk ratio) (RR)  Ratio of risk in treated group to risk in control group  0.25

 Those without vaccine have 4 times the risk of getting HIV

Evaluating Therapies Relative Risk Reduction (RRR)  % reduction in risk in treated group compared to controls  75%  Those with vaccine have a 75% reduced risk of getting HIV

Evaluating Therapies Absolute Risk Reduction (ARR)  Diff. in risk between controls and treated  0.75

 Those with Vaccine have a risk 0.75 greater than controls.

Evaluating Therapies Number needed to treat (NNT)  # you have to treat to prevent one adverse outcome  1.33

 You need to give the vaccine to at least 2 people to prevent HIV in one person.

Evaluating Exposures Relative Risk (risk ratio) (RR)  Ratio of risk in exposed control group group to risk in Odds Ratio  How many times more likely someone is to have been exposed (compared to controls)

Evaluating Exposures Exposed Outcome + A Outcome B Risk in each group Y=A/(A+B) Control C D X=C/(C+D) RR = Y/X OR = AD/BC

Fictional Example: 25 out of 100 people on the Atkins diet had heart attacks.

10 out of 100 people on regular diets had heart attacks.

Would you discourage the Atkins diet?

Fill in the boxes… Exposed Outcome + A Outcome B Risk in each group Y=A/(A+B) Control C D X=C/(C+D) RR = Y/X OR = AD/BC

Evaluating Exposures Exposed Control RR = Y/X OR = AD/BC Outcome + A 25 C 10 Outcome B 75 D 90 Risk in each group Y=A/(A+B) = 0.25

X=C/(C+D) = 0.10

RR = 2.5

OR = 3

Evaluating Exposures Relative Risk (risk ratio) (RR)  Ratio of risk in exposed control group group to risk in Odds Ratio  How many times more likely someone with a disease is to have been exposed (compared to controls)

Evaluating Exposures Relative Risk (risk ratio) (RR)  Ratio of risk in exposed control group group to risk in  2.5

 Heart attacks occur 2.5 times more often in those on Atkins diet.

Evaluating Exposures Odds Ratio  How many times more likely someone with a disease is to have been exposed (compared to controls)  3.0

 Those having a heart attack were 3 times more likely to have been on the Atkins diet than on a regular diet.

Errors Accept H 0 Reject H 0 Null Hypo TRUE 1 - alpha alpha Type I Error Null Hypo FALSE Beta Type II Error 1- Beta POWER