What you will learn

Primer on Statistics for Interventional

Cardiologists

Giuseppe Sangiorgi, MDPierfrancesco Agostoni, MDGiuseppe Biondi-Zoccai, MD

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• Descriptive statistics

– frequency distributions– contingency tables – measures of location: mean, median, mode– measures of dispersion: variance, standard

deviation, range, interquartile range– coefficient of variation– graphical presentation: histogram, box-plot,

scatter plot– correlation





Cardiology

Counting and displaying dataAfter we have collected our data, we need to display them (tables, graphics and figures) Raw enumeration (eg lesion length by visual estimation in patients treated in Endeavor II trial: 14-27 mm)

……

Cardiology

example

Tabular display

Cardiology

example

DELAYED RRISC, JACC 2007

Tabular display

Cardiology

example

DELAYED RRISC, JACC 2007

Tabular display

Variables

nominalnominal ordinalordinal discretediscrete continuouscontinuous

orderedorderedcategoriescategories

ranksranks countingcounting measuringmeasuring

Types of variables

QUANTITYQUANTITYCATEGORYCATEGORY

Cardiology

Variable type

Nominal Ordinal Continuous

Patient ID Diabetes AHA/ACC Type

Lesion Length

1 Y A 18

2 N B1 24

3 N A 17

4 N C 25

5 Y B2 23

6 N A 15

7 N A 16

8 Y B2 18

9 N B1 21

10 Y B2 19

11 N B1 14

12 Y C 22

13 N C 27

Counting and displaying data

Create a database!

Cardiology

Frequency distribution

A frequency distribution is a list of the values that a variable takes in a sample. It is usually a list, ordered by quantity, showing the number of times each value appears

Diabetes n=13

Yes 5

No 8

AHA/ACC Type

n=13

A 4

B1 3

B2 3

C 3

Cardiology


A frequency distribution is a list of the values that a variable takes in a sample. It is usually a list, ordered by quantity, showing the number of times each value appears

Diabetes n=13

Yes 5 38.5%

No 8 61.5%

AHA/ACC Type

n=13

A 4 30.7%

B1 3 23.1%

B2 3 23.1%

C 3 23.1%

This introduces the concept of percentage or rate

Cardiology


ENDEAVOR III, JACC 2006

Cardiology


This simple tabulation has drawbacks. When a variable can take continuous values instead of discrete values or when the number of possible values is too large, the table construction is cumbersome, if not impossible

Lesion length

n=13

14 1 7.7%

15 1 7.7%

16 1 7.7%

17 1 7.7%

18 2 15.3%

19 1 7.7%

21 1 7.7%

22 1 7.7%

23 1 7.7%

24 1 7.7%

25 1 7.7%

27 1 7.7%

Cardiology


A slightly different tabulation scheme based on the range of values can be a solution in such cases

Lesion length n=13

14-20 mm 7 53.8%

21-27 mm 6 46.2%

However better solutions are coming later…





Cardiology

Contingency tables are used to record and analyse the relationship between two (or more) variables, most usually categorical variables


Diabetes n=13

Yes 5 38.5%

No 8 61.5%

AHA/ACC Type

n=13

A 4 30.7%

B1 3 23.1%

B2 3 23.1%

C 3 23.1%

Cardiology



3 3 0 2 8

1 0 3 1 5

4 3 3 3 13

no

yes

DIABETES

Total

A B1 B2 C

AHA/ACC type

Total

Cardiology



3 3 0 2 8

37,5% 37,5% ,0% 25,0% 100,0%

1 0 3 1 5

20,0% ,0% 60,0% 20,0% 100,0%

4 3 3 3 13

30,8% 23,1% 23,1% 23,1% 100,0%

Count

% within DIABETES

Count

% within DIABETES

Count

% within DIABETES

no

yesDIABETES

Total

A B1 B2 C

AHA/ACC type

Total

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

The answer will follow…





Cardiology

We need to describe the kind of values that we have (eg lesion length by visual estimation in patients treated in Endeavor II trial: 14-27 mm)

Raw enumeration

……

Measures of central tendency: rationale

Cardiology

xx

N

Characteristics:-summarises information well-discards a lot of information

(dispersion??)

Assumptions:-data are not skewed

– distorts the mean– outliers make the mean very different

-Measured on measurement scale– cannot find mean of a categorical measure

‘average’ stent diameter may be meaningless

Mean (arithmetic)

Cardiology

xx

N

Mean (arithmetic)

Lesion length

n=13

14 1 7.7%

15 1 7.7%

16 1 7.7%

17 1 7.7%

18 2 15.3%

19 1 7.7%

21 1 7.7%

22 1 7.7%

23 1 7.7%

24 1 7.7%

25 1 7.7%

27 1 7.7%

14+15+16+17+18+18+19+21+22+23+24+25+27

13

Mean = 19.92

Cardiology

TAPAS, Lancet 2008

Mean (arithmetic)

Cardiology

What is it?

– The one in the middle

– Place values in order

– Median is central

Definition:

– Equally distant from all other values

Used for:

– Ordinal data

– Skewed data / outliers

Median

Cardiology

MedianVariable

typeContinuous

Patient ID Lesion Length

1 18

2 24

3 17

4 25

5 23

6 15

7 16

8 18

9 21

10 19

11 14

12 22

13 27

Cardiology

MedianVariable

typeContinuous


1 18

2 24

3 17

4 25

5 23

6 15

7 16

8 18

9 21

10 19

11 14

12 22

13 27

Variable type

Continuous


11 14

6 15

7 16

3 17

1 18

8 18

10 19

9 21

12 22

5 23

2 24

4 25

13 27

Cardiology

What is it?

Definition:

– The most common value

Used (rarely) for:

– Discrete non interval data

– E.g. stent length, stent diameter…………

– MicroDriver is only available in 2.25, 2.50, 2.75 reporting the mean is meaningless

Mode

Cardiology

ModeVariable

typeContinuous


1 18

2 24

3 17

4 25

5 23

6 15

7 16

8 18

9 21

10 19

11 14

12 22

13 27

Lesion length

n=13

14 1 7.7%

15 1 7.7%

16 1 7.7%

17 1 7.7%

18 2 15.3%

19 1 7.7%

21 1 7.7%

22 1 7.7%

23 1 7.7%

24 1 7.7%

25 1 7.7%

27 1 7.7%

Cardiology

Mean is usually best– If it works– Useful properties (with standard deviation [SD])– But…

Driver Endeavor

17 21 19 2119 2117 2118 6

Mean 18 18Median 18 21

Lesion length

Comparing Measures of central tendency

Cardiology

It also depends on the underlying distribution…

Symmetric? mean = median = mode


Value

Fre

quen

cy

Cardiology

It also depends on the underlying distribution…

Asymmetric? mean ≠ median ≠ mode

0

5

10

15

20

25

30

0 1 2 3 4 5 6 7 8 9

Number of Endeavor implanted per patient

Fre

qu

ency

Mode Mode

Median Median

Mean Mean


Cardiology

Agostoni et al, AJC 2007

Median





Cardiology

Central tendency doesn’t tell us everything– We need to know about the spread, or

dispersion of the scores

Is there a difference? And if yes, how big is it?

We can only tell if we know data dispersion

Group Late loss(mm)Endeavor 0.61Driver 1.03

Measures of dispersion: rationale

ENDEAVOR II, Circulation 2006

Cardiology

0 0.30 0.60 0.90 1.20 1.50

Late loss

Fre

qu

en

cy

DriverEndeavor

Measures of dispersion: examples

Cardiology

0 0.30 0.60 0.90 1.20 1.50

Late loss

Fre

qu

en

cy

DriverEndeavor


Cardiology

0 0.30 0.60 0.90 1.20 1.50

Late loss

Fre

qu

en

cy

DriverEndeavor


Cardiology

Value

Fre

quency

Gaussian, normal or “parametric” distributionGaussian, normal or “parametric” distribution

Shape of distribution

Cardiology

Value

Fre

qu

ency

Non-normal, right-skewedNon-normal, right-skewed

Departing from normality

Cardiology

Non-normal, left-skewedNon-normal, left-skewed

Value

Fre

qu

en

cyDeparting from normality

Cardiology

20

10

0

Fre

qu

ency

Value

Departing from normality

Outliers

Cardiology

• Standard deviation (SD)– Used with mean– Parametric tests

• Range– First to last value– Not commonly used

• Interquartile range– Used with median– 25% (1/4) to 75% (3/4) percentile– Non-parametric tests

Measures of dispersion: types

Cardiology

Standard deviation (SD):

– approximates population σ

as N increases

Advantages:

– with mean enables powerful synthesis

mean±1*SD 68% of data

mean±2*SD 95% of data (1.96)

mean±3*SD 99% of data (2.86)

Disadvantages:

– is based on normal assumptions

1

)( 2

-

-N

xxSDSD

Standard deviation

Variance

Cardiology

1

)( 2

-

-N

xxSDSD

Standard deviationVariable

typeContinuous


1 18

2 24

3 17

4 25

5 23

6 15

7 16

8 18

9 21

10 19

11 14

12 22

13 27

Mean 19.92

(18-19.92)2+(24-19.92)2+(17-19.92)2+…+(27-19.92)2

12

Variance = 16.58

SD = √16.58 = 4.07

Cardiology

-1 SD mean +1 SD

Fre

qu

ency

68%

Mean ± Standard deviation

Cardiology

-1 SD +1 SD-2 SD +2 SD

95%

mean

Fre

qu

ency


Cardiology

-1 SD +1 SD-2 SD +2 SD

99%

-3 SD +3 SDmean

Fre

qu

ency


Cardiology

TAPAS, Lancet 2008

Standard deviation

Cardiology

TAPAS, NEJM 2008

Standard deviation

Cardiology

TAPAS, NEJM 2008

Why not mean ± SD?

Cardiology

Rules of thumb

1. Refer to previous data or analyses (eg landmark articles, large databases)

2. Inspect tables and graphs (eg outliers, histograms)

3. Check rough equality of mean, median, mode

4. Perform ad hoc statistical tests• Levene’s test for equality of means

• Kolmogodorov-Smirnov tests

• …

Testing normality assumptions

Cardiology

Range

Lesion length

n=13

14 1 7.7%

15 1 7.7%

16 1 7.7%

17 1 7.7%

18 2 15.3%

19 1 7.7%

21 1 7.7%

22 1 7.7%

23 1 7.7%

24 1 7.7%

25 1 7.7%

27 1 7.7%

First to last value

Range = 14 – 27or

Range = 13

Cardiology

Range

RRISC, JACC 2006

Cardiology

Interquartile rangeVariable

typeContinuous


11 14

6 15

7 16

3 17

1 18

8 18

10 19

9 21

12 22

5 23

2 24

4 25

13 27

16.5

23.5

25% to 75% percentile

or

1° to 3° quartile

MedianInterquartile Range

=16.5 – 23.5

Cardiology


Interquartile range

Cardiology

Cardiology

Statistics

Lesion Length13

0

19,9231

19,0000

18,00

4,07148

13,00

14,00

27,00

16,5000

19,0000

23,5000

Valid

Missing

N

Mean

Median

Mode

Std. Deviation

Range

Minimum

Maximum

25

50

75

Percentiles

Lesion Length

1 7,7 7,7 7,7

1 7,7 7,7 15,4

1 7,7 7,7 23,1

1 7,7 7,7 30,8

2 15,4 15,4 46,2

1 7,7 7,7 53,8

1 7,7 7,7 61,5

1 7,7 7,7 69,2

1 7,7 7,7 76,9

1 7,7 7,7 84,6

1 7,7 7,7 92,3

1 7,7 7,7 100,0

13 100,0 100,0

14,00

15,00

16,00

17,00

18,00

19,00

21,00

22,00

23,00

24,00

25,00

27,00

Total

ValidFrequency Percent Valid Percent

CumulativePercent

Cardiology

Reporting data

If parametric:Mean and

Standard Deviation

Mean ± SDMean (SD)

Age (y): 63 ± 13Age (y): 63 (13)

If non-parametric:Median and InterQuartile Range

Median [IQR]

NIH vol (mm3): 1.3 [0–13.1]

Mode and Range less commonly used





Coefficient of Variation•The coefficient of variation (CV) is a normalized measure of dispersion of a probability distribution. It is defined as the ratio of the standard deviation to the mean

•This is only defined for non-zero mean, and is most useful for variables that are always positive. The coefficient of variation should only be computed for continuous data•A given standard deviation indicates a high or low degree of variability only in relation to the mean value •It is easier to get an idea of variability in a distribution by dividing the standard deviation with the mean

Coefficient of Variation•Advantages

•The CV is a dimensionless number

•The CV is particularly useful when comparing dispersion in datasets with: markedly different means or, different units of measurement

•Distributions with CV<1 are considered low-variance, while those with CV>1 are considered high-variance

•Disadvantages

•When the mean is near zero, the CV is sensitive to small changes in the mean, limiting its usefulness

•Unlike the standard deviation, it cannot be used to construct confidence intervals for the mean





Cardiology

Histograms

DIABETES

10

10

8

6

4

2

0

no yes

ENDEAVOR II, Circulation 2006

Very good for categorical variables

Cardiology

HistogramsNot so good for continuous variables, but…

Cardiology

exampleboth restenotic and both restenotic and

non-restenotic SESnon-restenotic SES


Histograms

Cardiology

example

non-restenotic SESnon-restenotic SES


shape of distributionshape of distribution

Shape of distributions

Cardiology

Box (& whiskers) plots

Cardiology


Median (Q2)Interquartile

range

Max (Q4) or Q3+1.5(IQR)

Q1

Q3

Min (Q0) or Q1-1.5(IQR)

Cardiology


Margheri, Biondi Zoccai, et al, AJC 2008

Cardiology

Scatter plots

A scatter plot is a type of display using Cartesian coordinates to display values for two variables for a set of data. The data is displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable

determining the position on the vertical axis

Usually it is done with 2 continuous variables to visually assess the degree of correlation between them

But it can be also used with one categorical variable and one continuous variable (mainly if sample size is small)

Cardiology

Scatter plots

Abbate, Biondi Zoccai, et al, Circulation 2002

Cardiology

Scatter plots

Mintz, et al, AJC 2005

Cardiology

Agostoni, et al, IJC 2007

Scatter plots

Thank you for your attention

For any correspondence: [email protected]

For further slides on these topics feel free to visit the metcardio.org website:

http://www.metcardio.org/slides.html

mailto:[email protected]



Documents

What you will learn