Brad E. Dicianno, MD Statistics For Residents University of Pittsburgh Medical Center Dept. of Physical Medicine & Rehabilitation VA Pittsburgh Health

Brad E. Dicianno, MD

Statistics For Residents

University of Pittsburgh Medical CenterDept. of Physical Medicine & RehabilitationVA Pittsburgh Health Care SystemHuman Engineering Research Laboratories

What you never thought you would understand…

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, groupsGender, Race, Job, Favorite colorYes/No

Ordinal

Ordered; data goes in specific directionDividing doesn’t make sensePGY1, PGY2, PGY3…Always, Sometimes, Never…

Continuous

Numerical ScaleYou can divide the numbersWeight, Height, Exam Score

Try it out…

FIM scoreArm temperatureMed route (po, NG, IV)Modified Ashworth ScorePlantar responseType of insuranceAlbumin level

Try it out…

FIM score OrdinalArm temperature ContinuousMed route (po, NG, IV) CategoricalModified Ashworth Score OrdinalPlantar response CategoricalType of insurance CategoricalAlbumin level Continuous

Step 2:

Normal or Not Normal?

Normal = Parametric

Not Normal = Non Parametric

SkewnessExcess skewness is NOT normal

NegativelySkewed

Mode

Median

Mean

Symmetric(Not Skewed)

MeanMedianMode

PositivelySkewed

Mode

Median

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

ORRun 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 DeviationRanges (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 levelP valueBe 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

Condition +

Condition -

Test + A B

Test - C 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…Condition +

Condition -

Test + A B

Test - C D


Likelihood RatioCondition +

Condition -

Test + A75

B50

Test - C25

D50


Likelihood RatioCondition +

Condition -

Test + A75

B50

Test - C25

D50

LR = A/(A+C) / B/(B+D) = 75/100 / 50/100 = 1.5PTO = 1.5 * 0.5 = 0.75 = 75%


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%


SensitivityPositive Predictive ValueSpecificityNegative Predictive Value

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


Sensitivity True positives/everyone with

condition you want to pick upTrue -

True +False -

False +False +

True -

True -


Sensitivity = ½ = 0.5 True positives/everyone with

condition you want to pick upTrue -

True +False -

False +False +

True -

True -

You caught 1 of the 2 fish you should have caught.


Positive Predictive Value True positives/all positives

True -

True +False -

False +False +

True -

True -


Positive Predictive Value = 1/3 True positives/all positives

True -

True +False -

False +False +

True -

True -

1 of the 3 fish you did catch was of the right kind


Specificity True negatives/everyone w/o

conditionTrue -

True +False -

False +False +

True -

True -


Specificity = 3/5 True negatives/everyone w/o

conditionTrue -

True +False -

False +False +

True -

True -

Your net correctly ignored 3 of the 5 fish it wasn’t supposed to catch.


Negative Predictive Value True negatives/all negatives

True -

True +False -

False +False +

True -

True -


Negative Predictive Value = 3/4 True negatives/all negatives

True -

True +False -

False +False +

True -

True -

The net correctly ignored 3 of the 4 fish it didn’t catch.

Evaluating Therapies

Relative Risk (risk ratio) (RR) Ratio of risk in treated group to risk in

control groupRelative Risk Reduction (RRR) % reduction in risk in treated group

compared to controlsAbsolute 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

Outcome+

Outcome-

Treated A B

Control C D

Risk in each group

Y=A/(A+B)

X=C/(C+D)

Treatment Effects

Outcome+

Outcome-

Treated A B

Control C D

RR = Y/X

Risk in each group

Y=A/(A+B)

X=C/(C+D)

RRR= 1 – RR * 100%ARR = X – YNNT = 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

A B

Control C D

RR = Y/X

Risk in each group

Y=A/(A+B) =

X=C/(C+D) =


RR = RRR = ARR = NNT =

Treatment Effects

HIV+ HIV-

New HIV Vaccine

A25

B75

Control C100

D0

RR = Y/X

Risk in each group

Y=A/(A+B) =

X=C/(C+D) =


RR = RRR = ARR = NNT =

Treatment Effects

HIV+ HIV-

New HIV Vaccine

A25

B75

Control C100

D0

RR = Y/X

Risk in each group

Y=A/(A+B) = 0.25

X=C/(C+D) = 1.00


RR = 0.25RRR = 75%ARR = 0.75NNT = 1.33


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


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


Absolute Risk Reduction (ARR) Diff. in risk between controls and

treated

0.75

Those with Vaccine have a risk 0.75 greater than controls.


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 group to risk

in control group

Odds Ratio How many times more likely someone

is to have been exposed (compared to controls)


Outcome+

Outcome-

Exposed A B

Control C D

RR = Y/X

Risk in each group

Y=A/(A+B)

X=C/(C+D)

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…Outcome+

Outcome-

Exposed A B

Control C D

RR = Y/X

Risk in each group

Y=A/(A+B)

X=C/(C+D)

OR = AD/BC

Evaluating ExposuresOutcome+

Outcome-

Exposed A25

B75

Control C10

D90

RR = Y/X

Risk in each group

Y=A/(A+B) = 0.25

X=C/(C+D) = 0.10

OR = AD/BC RR = 2.5OR = 3



in control group

Odds Ratio How many times more likely someone

with a disease is to have been exposed (compared to controls)



in control group

2.5

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


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.

ErrorsNull Hypo TRUE

NullHypo FALSE

Accept H0

1 - alpha

BetaType II Error

Reject H0

alphaType I Error

1- Beta

POWER

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Brad E. Dicianno, MD Statistics For Residents University of Pittsburgh Medical Center Dept. of Physical Medicine & Rehabilitation VA Pittsburgh Health