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Primer on Statistics for Interventional Cardiologists Giuseppe Sangiorgi, MD Pierfrancesco Agostoni, MD Giuseppe Biondi-Zoccai, MD

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### Primer on Statistics for Interventional CardiologistsGiuseppe Sangiorgi, MDPierfrancesco Agostoni, MDGiuseppe Biondi-Zoccai, MD

What you will learnWhat you will learnWhat you will learnWhat you will learn

What you will learn

Introduction

Basics

Descriptive statistics

Probability distributions

Inferential statistics

Finding differences in mean between two groups

Finding differences in mean between more than 2 groups

Linear regression and correlation for bivariate analysis

Analysis of categorical data (contingency tables)

Analysis of time-to-event data (survival analysis)

Advanced statistics at a glance

Conclusions and take home messages

What you will learn

Introduction

Basics

Descriptive statistics

Probability distributions

Inferential statistics

Finding differences in mean between two groups

Finding differences in mean between more than 2 groups

Linear regression and correlation for bivariate analysis

Analysis of categorical data (contingency tables)

Analysis of time-to-event data (survival analysis)

Advanced statistics at a glance

Conclusions and take home messages

What you will learn

- Analysis of categorical data (contingency tables)
- Estimating a proportion with the binomial test
- Comparing proportions in two-way contingency tables
- Relative risk and odds ratio
- Fisher exact test for small samples
- McNemar test for proportions using paired samples
- Comparing proportions in three-way contingency tables with the Cochran-Mantel-Haenszel test

Types of variables

Variables

CATEGORY

QUANTITY

nominal

ordinal

discrete

continuous

Death: yes/no

TLR: yes/no

measuring

counting

ordered

categories

ranks

BMI

Blood pressure

QCA data (MLD, late loss)

Stent diameter

Stent length

TIMI

flow

Radial/brachial/femoral

Types of variables

Variables

CATEGORY

nominal

ordinal

Death: yes/no

TLR: yes/no

ordered

categories

ranks

TIMI

flow

Radial/brachial/femoral

What you will learn

- Analysis of categorical data (contingency tables)
- Estimating a proportion with the binomial test
- Comparing proportions in two-way contingency tables
- Relative risk and odds ratio
- Fisher exact test for small samples
- McNemar test for proportions using paired samples
- Comparing proportions in three-way contingency tables with the Cochran-Mantel-Haenszel test

Is the percentage of diabetics in this sample

comparable with the known CAD population?

We fix the population rate at 15%

Is the percentage of diabetics in this sample

comparable with the CAD population?

We fix the population rate at 15%

Agostoni et al. AJC 2007

What you will learn

- Analysis of categorical data (contingency tables)
- Estimating a proportion with the binomial test
- Comparing proportions in two-way contingency tables
- Relative risk and odds ratio
- Fisher exact test for small samples
- McNemar test for proportions using paired samples
- Comparing proportions in three-way contingency tables with the Cochran-Mantel-Haenszel test

χ2 test or chi-square test

The first basis for the chi-square test

is the contingency table

ENDEAVOR II. Circulation 2006

χ2 test or chi-square test

χ2 test or chi-square test

The second basis is the “observed”-“expected” relation

TVF

χ2 test or chi-square test

χ2 test or chi-square test

A

B1

B2

C

Total

no

Count

3

3

0

2

8

% within DIABETES

37,5%

37,5%

,0%

25,0%

100,0%

DIABETES

yes

Count

1

0

3

1

5

% within DIABETES

20,0%

,0%

60,0%

20,0%

100,0%

Total

Count

4

3

3

3

13

% within DIABETES

30,8%

23,1%

23,1%

23,1%

100,0%

Compare discrete variables

More than 2x2 contingency tables

Post-hoc comparisons

Is there a difference between diabetics and non-dabetics in the rate of AHA/ACC type lesions?

the chi-square test was used to determine differences between groups with respect to the primary and secondary end points. Odds ratios and their 95 percent confidence intervals were calculated. Comparisons of patient characteristics and survival outcomes were tested with the chi-square test, the chi-square test for trend, Fisher\'s exact test, or Student\'s t-test, as appropriate.

This is a sub-group !

Bonferroni !

The level of significant

p-value should be

divided by the number

of tests performed…

Or the computed p-value,

multiplied for the number

of tests… P=0.12 and not P=0.04 !!

Wenzel et al, NEJM 2004

- Analysis of categorical data (contingency tables)
- Estimating a proportion with the binomial test
- Comparing proportions in two-way contingency tables
- Relative risk and odds ratio
- Fisher exact test for small samples
- McNemar test for proportions using paired samples
- Comparing proportions in three-way contingency tables with the Cochran-Mantel-Haenszel test

No TVF

TVF

a

b

Driver

Endeavor

c

d

Absolute Risk = [ d / ( c + d ) ]

Absolute Risk Reduction = [ d / ( c + d ) ] - [ b / ( a + b ) ]

Relative Risk = [ d / ( c + d ) ] / [ a / ( a + b ) ]

Relative Risk Reduction = 1 - RR

Odds Ratio = (d/c)/(b/a) = ( a * d ) / ( b * c )

Absolute Risk (AR) 7.9% (47/592) &15.1% (89/591)

Absolute Risk Reduction (ARR)7.9% (47/592) – 15.1% (89/591) = -7.2%

Relative Risk (RR)7.9% (47/592) / 15.1% (89/591) = 0.52(given an equivalence value of 1)

Relative Risk Reduction (RRR)1 – 0.52 = 0.48 or 48%

Odds Ratio (OR) 8.6% (47/545) / 17.7% (89/502) = 0.49(given an equivalence value of 1)

Odds Ratio Reduction (ORR)1 – 0.49 = 0.51 or 51%

Compare event rates

Relative Risk (RR)7.9% (47/592) / 15.1% (89/591) = 0.52 or 52%(given an equivalence value of 1)

Odds Ratio (OR) 8.6% (47/545) / 17.7% (89/502) = 0.49 or 49%(given an equivalence value of 1)

For small event rates (b and d) OR ~ RR

Compare event rates

No TVF

TVF

a

b

Driver

c

d

Endeavor

RR = [ d / ( c + d ) ] / [ a / ( a + b ) ]

OR = (d/c)/(b/a) = ( a * d ) / ( b * c )

*152 pts in the invasive vs 150 in the medical group

ARc:56%

ARt:46.7%

ARR: 9.3%

RR: 0.83

RRR: 17%

OR: 0.69

ROR: 31%

SHOCK, NEJM 1999

- Absolute Risk Reduction (ARR)7.9% (47/592) – 15.1% (89/591) = -7.2%
- Number Needed to Treat (NNT)1 / 0.072= 13.8 ~ 14
- I need to treat 14 patients with Endeavor instead of Driver to avoid 1 TVF
- The larger the ARR, the smaller the NNTLow NNT => Large benefit

ENDEAVOR II. Circulation 2006

To compute Confidence Intervals for ARR, RR, OR, NNT

SPSS is not so good…

Confidence Interval Analysis (CIA) downloadable software

[with the book “Statistics with Confidence”, Editor: DG Altman,

BMJ Books London (2000)]

https://www.som.soton.ac.uk/cia/

“Incidence study” (RCTs) for Relative Risk

“Unmatched case control study” for Odds Ratio

http://www.quantitativeskills.com/sisa/statistics/twoby2.htm

Free in internet,

always available!

http://www.quantitativeskills.com/sisa/statistics/twoby2.htm

http://www.quantitativeskills.com/sisa/statistics/twoby2.htm

- Analysis of categorical data (contingency tables)
- Estimating a proportion with the binomial test
- Comparing proportions in two-way contingency tables
- Relative risk and odds ratio
- Fisher exact test for small samples
- McNemar test for proportions using paired samples
- Comparing proportions in three-way contingency tables with the Cochran-Mantel-Haenszel test

- Every time we use conventional tests or formulas, we ASSUME that the sample we have is a random sample drawn from a specific distribution (usually normal, chi-square, or binomial…)
- It is well known that as N increases, an established and specific distribution may be ASYMPTOTICALLY assumed (usually N≥30 is ok)

- Whenever asymptotic assumptions cannot be met (small, non-random, skewed samples, with sparse data, major imbalances or few events), EXACT TESTS should be employed
- Exact tests are computationally burdensome (they involve PERMUTATIONS)*, but they do not rely on any underlying assumption
- If in a 2x2 table a cell has an expected event rate ≤5, Pearson chi-square test is biased (ie ↑alpha error), and Fisher exact test is warranted

*6! is a permutation, and equals 6x5x4x3x2x1=720

- Analysis of categorical data (contingency tables)
- Estimating a proportion with the binomial test
- Comparing proportions in two-way contingency tables
- Relative risk and odds ratio
- Fisher exact test for small samples
- McNemar test for proportions using paired samples
- Comparing proportions in three-way contingency tables with the Cochran-Mantel-Haenszel test

- The McNemar test is a non parametric test applicable to 2x2 contingency tables
- It is used to show differences in dichotomous data (presence/absence; +/-; Y/N) before and after a certain event / therapy / intervention (thus to evaulate the efficacy of these), if data are available as frequencies

Migraine and PFO closure

a+b = a+c

c+d =b+d

b = c

The test determines whether the row and columnmarginal frequencies are equal

- Analysis of categorical data (contingency tables)
- Estimating a proportion with the binomial test
- Comparing proportions in two-way contingency tables
- Relative risk and odds ratio
- Fisher exact test for small samples
- McNemar test for proportions using paired samples
- Comparing proportions in three-way contingency tables with the Cochran-Mantel-Haenszel test

A

B1

B2

C

Total

no

Count

3

3

0

2

8

% within DIABETES

37,5%

37,5%

,0%

25,0%

100,0%

DIABETES

yes

Count

1

0

3

1

5

% within DIABETES

20,0%

,0%

60,0%

20,0%

100,0%

Total

Count

4

3

3

3

13

% within DIABETES

30,8%

23,1%

23,1%

23,1%

100,0%

3-way contingency tables

This is a 2-way 2x4 contingency table…

And if we know the ratio of smokers?

3-way 2x4x2 contingency table!

That means 2 different 2-ways 2x4 contingency tables

The Cochran-Mantel-Haenszel chi-square tests the null hypothesis that two nominal variables are conditionally independent in each stratum, assuming that there is no three-way interaction. It works in a 3-way (3-dimensional) contingency table, where the last dimension refers to the strata

Thank you for your attentionFor any correspondence: [email protected] further slides on these topics feel free to visit the metcardio.org website:http://www.metcardio.org/slides.html

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