Download Seung et al, New Engl J Med 2008

Primer on Statistics
for Interventional
Cardiologists
Giuseppe Sangiorgi, MD
Pierfrancesco Agostoni, MD
Giuseppe 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
Why a glance at advanced stats?
• Like in a live case, we want to expose you
to the next level of statistical analysis
• It is not highly complex in itself, but only
builds upon a solid knowledge of standard
statistics, ie what we have seen today
• If you are interested in more, let us
know…
What you will learn
• Advanced statistics at a glance:
–
–
–
–
–
–
–
–
Mulivariable analysis
Multiple linear regression
Logistic regression
Cox proportional hazards model
Generalized linear models
Propensity analysis
Resampling methods
Meta-analysis
A hierarchy of analysis levels
• Statistical analyses can be distinguished in
– Univariate (eg describing a variable such as
lesion length)
– Bivariate (eg comparing two different variables
such as CKMB release and subsequent LVEF)
– Multivariable (eg appraising the impact of two or
more independent/moderator variables on a
single dependent variable)
– Multivariate (eg appraising the impact of two or
more independent/moderator variables on two
or more dependent variables)
An example of multivariable analysis
Vlaar et al, Lancet 2008
An example of multivariable analysis
Vlaar et al, Lancet 2008
An example of multivariable analysis
Vlaar et al, Lancet 2008
What you will learn
• Advanced statistics at a glance:
–
–
–
–
–
–
–
–
Mulivariable analysis
Multiple linear regression
Logistic regression
Cox proportional hazards model
Generalized linear models
Propensity analysis
Resampling methods
Meta-analysis
Multiple linear regression
• How can I predict the impact of balloon dilation
pressure on angiographic late loss, taking
concomitantly into account diabetes status and
ACC/AHA lesion type?
Multiple linear regression
• How can I predict the impact of balloon dilation
pressure on angiographic late loss, taking
concomitantly into account diabetes status and
ACC/AHA lesion type?
In other words, how can I predict the impact of a
given variable (aka independent) on another
continuous variable (aka dependent), taking
concomitantly into account other variables?
Multiple linear regression
• Multiple linear regression is just an
extension of bivariate linear regression
• Thus we can move from bivariate
regression to multivariable regression
analysis
• A great deal of emphasis should be placed
on model building and validation, eg
checking residuals and avoiding overfitting
Identifying predictors of late loss
Sangiorgi et al, AHJ 2008
Identifying predictors of late loss
Sangiorgi et al, AHJ 2008
What you will learn
• Advanced statistics at a glance:
–
–
–
–
–
–
–
–
Mulivariable analysis
Multiple linear regression
Logistic regression
Cox proportional hazards model
Generalized linear models
Propensity analysis
Resampling methods
Meta-analysis
Logistic regression
• How can I predict the impact of left ventricular
ejection fraction (LVEF) on the 12-month risk of
ARC-defined stent thrombosis?
Logistic regression
• How can I predict the impact of left ventricular
ejection fraction (LVEF) on the 12-month risk of
ARC-defined stent thrombosis?
In other words, how can I predict the impact of a
given variable (aka independent) on another
dichotomous variable (aka dependent)
Logistic regression
• Logistic regression is based on the logit which
transforms a dichotomous dependent variable
into a continuous one
• Thus a number of assumptions should be valid
to trust its results
• Logistic regression can also be applied to
multivariable and polichotomous analyses
• Emphasis should again be placed on model
building and validation, eg checking residuals
and avoiding overfitting
Logistic regression
Logistic regression
Sangiorgi et al, AHJ 2008
What you will learn
• Advanced statistics at a glance:
–
–
–
–
–
–
–
–
Mulivariable analysis
Multiple linear regression
Logistic regression
Cox proportional hazards model
Generalized linear models
Propensity analysis
Resampling methods
Meta-analysis
Cox proportional hazard model
• How can I predict the impact of left ventricular
ejection fraction (LVEF) on the risk of ARCdefined stent thrombosis over a variable period
of follow-up?
In other words, how can I predict the impact of a
given variable (aka independent) on another
dichotomous variable (aka dependent), but with
variable follow-up and aiming to exploit as much
as possible all event data
Cox proportional hazard model
• Cox proportional hazard analysis is a
parametric analysis that can be used for
dichotomous dependent variables occurring
over time and to test its association with one
or more independent variables
• A number of assumptions should hold true
• In particular, hazards should be constant
over time → log−log survival function
Cox proportional hazard model
Agostoni et al, Am J Cardiol 2005
Cox proportional hazard model
Agostoni et al, Am J Cardiol 2005
Cox proportional hazard model
Marroquin et al, New Engl J Med 2008
What you will learn
• Advanced statistics at a glance:
–
–
–
–
–
–
–
–
Mulivariable analysis
Multiple linear regression
Logistic regression
Cox proportional hazards model
Generalized linear models
Propensity analysis
Resampling methods
Meta-analysis
First things first
• The generalized linear model (GLM) is a flexible
generalization of ordinary least squares
regression
• It relates the random distribution of the
measured variable of the experiment (the
distribution function) to the systematic (nonrandom) portion of the experiment (the linear
predictor) through a function called the link
function (g)
First things first
Earth
Oxford
Generalized linear model (GLM)
• Through differing link functions, GLM
corresponds to other well known models
Distribution
Name
Normal
Exponential
Identity
Inverse
Gamma
Inverse
Gaussian
Inverse
squared
Poisson
Log
Binomial
Logit
Link Function
Mean
Function
What you will learn
• Advanced statistics at a glance:
–
–
–
–
–
–
–
–
Mulivariable analysis
Multiple linear regression
Logistic regression
Cox proportional hazards model
Generalized linear models
Propensity analysis
Resampling methods
Meta-analysis
Propensity analysis
• How can appraise the impact of a specific stent
type on long-term risk of stent thrombosis
outside the context of a randomized controlled
trials?
In other words, how assess the independent
impact of a given independent/moderator
variable when my dataset is not based on
randomization and likelihood of underlying
confounding is very high
Propensity analysis
• Propensity analysis is a peculiar type of
multivariable analysis in which the propensity
to choose one treatment versus the other(s)
is explictly assessed and measured
• Building upon such propensity (usually by
means of non-parsimonious scores), the
dataset is matched and/or analysed
• Propensity are usually exploited in: a)
matched pairs, b) quintiles/deciles, or c) in
logistic/Cox regression models
Propensity score analysis
Seung et al, New Engl J Med 2008
Propensity score analysis
Seung et al, New Engl J Med 2008
Propensity score analysis
Seung et al, New Engl J Med 2008
Propensity score analysis
Seung et al, New Engl J Med 2008
What you will learn
• Advanced statistics at a glance:
–
–
–
–
–
–
–
–
Mulivariable analysis
Multiple linear regression
Logistic regression
Cox proportional hazards model
Generalized linear models
Propensity analysis
Resampling methods
Meta-analysis
Resampling methods
• A friendly question for our best pupil: how can I
build 95% confidence intervals for medians?
In other words, how can I make statistical
inference when the variable I am focusing onto
does not follow standard statistical distributions,
is highly skewed or sparse?
Resampling methods
• Resampling methods are powerful validation
and quantitation tools, as they can be much
more distribution-independent than all other
statistical methods
• The 2 most commonly used resampling
methods are:
- Jacknife
- bootstrap
Bootstrap
What you will learn
• Advanced statistics at a glance:
–
–
–
–
–
–
–
–
Mulivariable analysis
Multiple linear regression
Logistic regression
Cox proportional hazards model
Generalized linear models
Propensity analysis
Resampling methods
Meta-analysis
Meta-analysis
• How can I decide whether first generation DES
increase stent thrombosis given the plethora of
several small, conflicting, and/or inconclusive
pertinent clinical studies?
In other words, how can I combine data from
several small, conflicting, and/or inconclusive
primary studies?
Meta-analysis
• Meta-analysis is a group of statistical
methods used to combine quantitative
estimates from several primary research
studies
• Meta-analysis increase statistical power,
boost external validity, and can test/explore
secondary hypotheses (eg meta-regression)
• When conducted in the context of a
systematic literature review and focusing only
on randomized clinical trials, they are
considered the top level of clinical evidence
Study-level meta-analysis
De Luca et al, Eur Heart J 2008
Study-level meta-analysis
De Luca et al, Eur Heart J 2008
Study-level meta-analysis
De Luca et al, Eur Heart J 2008
Study-level meta-analysis
De Luca et al, Eur Heart J 2008
Study-level meta-analysis
De Luca et al, Eur Heart J 2008
Patient-level meta-analysis
Mauri et al, New Engl J Med 2007
Patient-level meta-analysis
Pooled patient-level analysis for protocol-defined stent thrombosis
Mauri et al, New Engl J Med 2007
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