Transcript Stats

Statistics you can use:
Practical use of statistics in
reading medical research
literature
PAS 610
June 21, 2005
Robert D. Hadley
PhD, PA-C
The basics:
“There are three kinds of lies: lies, damned
lies, and statistics.”
Benjamin Disraeli, British politician (1804 - 1881)
The value of statistics:
Four economists are going to a meeting on the same
train as four statisticians. The economists can't help
noticing that the statisticians only buy a single ticket,
where they bought four. When they inquire, the
statisticians say, "Don't worry, you'll see."
They get on the train, and when the conductor starts in
their car the four statisticians all lock themselves in the
WC. When the conductor knocks on the WC door and
yells "TICKET", they slide the ticket out under the door,
and the conductor stamps it and slides it back. After
he's gone, the statisticians emerge.
At the station on the way back from the meeting, the
economists buy only one ticket, but they can't help
noticing that the statisticians don't buy any. When they
inquire, the statisticians say, "Don't worry, you'll see.“
As the conductor approaches their car, the
economists all pile in the nearest WC and lock the
door. One of the statisticians goes and knocks on the
door; the economists slide the ticket out. The
statisticians take the ticket and lock themselves in the
WC at the other end of the car, repeating their
maneuver of the previous trip. The economists get
thrown off the train.
Moral: Don't use statistical methods you don't
understand.
“Practical” vs. STA 570
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Ways to represent data
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Ways to compare data
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Sample vs. population
e.g. Chi-square, Student’s t-test, ANOVA/
ANCOVA, Odds ratios and CI, Cox
proportional hazard model, Spearman
ranked correlation coefficients, multivariate
regression analysis
Appropriateness of test for the way
data were collected
Terms: basics
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Mean
Median
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Quartiles, tertiles, etc.
Mode
Rank
Nominal
Ordinal
Population
Sample
Variance
Standard deviation
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Normal distribution
Z-scores, T-scores
Correlation
Parametric vs.
Nonparametric
Hypothesis testing
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1- vs. 2-tailed
Significance levels
Confidence intervals
Statistical power
Terms: medical literaturespecific
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Intention to treat
Kaplan-Meier curves
ROC curves
Meta-analysis representations
Odds ratios/Relative Risk
Risk reduction
Number needed to treat
 Over what time period?
 For what outcome?
Number needed to harm
Concepts
Descriptive vs. inferential statistics
 Type I and II errors
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Descriptive
Statistics
Includes
 Collecting
 Organizing
 Summarizing
 Presenting
data
Inferential
Statistics
Includes
 Making inferences
 Hypothesis testing
 Determining
relationships
 Making predictions
Inferential errors
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Type I (alpha)
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Type II (beta)
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Incorrectly reject the
null hypothesis
Infer that something is
significant when it is
not
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Incorrectly accept the
null hypothesis
Infer that something is
not significant when it
really is
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So, which is better to do?
Which way does “intention to treat” skew the
inference?
Study design
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Ask the right question in the right way
Statistical power
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Choose the appropriate sample size
Standard deviation and Zscores
Note: “normal” range for
lab tests is ± 2 s.d.
Z and T scores in medicine
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Bone density data are reported as T-scores
and Z-scores. T-scores represent the
number of SDs from the normal young adult
mean bone density values, whereas Zscores represent the number of SDs from
the normal mean value for age- and sexmatched control subjects.
Results showing Z-scores of −2.0 or lower
may suggest a secondary cause of
osteoporosis.
Osteoporosis drug treatment
Data Representation
Relative risk, odds ratios, likelihood
ratios, hazard ratios
 Odds ratios in meta-analyses
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Relative risk
What do unequal CI
bars mean?
Meta-analyses
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“Gold standard” is randomized, placebocontrolled, multi-center, double blind clinical
trial
“Platinum standard” is a meta-analysis of
multiple “gold standard” trials by different
investigators addressing the same question
(rarely available)
Can make use of small studies that by
themselves do not achieve statistical
significance
Meta-analyses
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How it’s done:
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Search on a specific topic
Use predefined inclusion/exclusion criteria
for studies that relate to topic
• e.g. must be RCT, must measure same specific
outcome (like cardiovascular events), etc.
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Combine all studies that meet criteria
Use statistics appropriate to the way data
were gathered in the included studies
Arrive at a conclusion that was impossible
with the individual studies that were included
Other anti-platelet
drug
(Reg. 1)
Aspirin
(Reg. 2)
Antiplatelet therapy for CVD
BMJ 2002; 324:71-86
Data Representation
Kaplan-Meier survivorship, and
cumulative incidence of events
 Both are a cumulative measure of
something happening
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Kaplan-Meier
Bortezomib or High-Dose Dexamethasone for Relapsed Multiple Myeloma
N Engl J Med 2005;352:2487-98
Use of quintiles to choose
cutoff points
ASCOT-LLA: Trial Stopped Nearly
2 Years Early
Cumulative incidence (%)
4
Atorvastatin 10 mg
No. of events: 100
Placebo (diet and exercise only) No. of events: 154
3
36% RRR
nonfatal MI
+ fatal CHD
All patients counseled on
diet and exercise
2
(P =.0005)
1
What is
approximate NNT
for 1 year?
0
0.0
0.5
1.0
1.5
2.0
Years
Sever PS et al. Lancet. 2003;361:1149-1158.
2.5
3.0
3.5
Data Representation
2x2, PPV, Chi-Square
 ROC curves
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ROC
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Receiver operator characteristic
curves
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Radar operators’ ability to distinguish
signal from noise
Higher area under curve (AUC),
higher reliability for a given test
 Plot true positives vs. false positives
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ROC
ROC value: 0.65 (0.61-0.70)
Data Representation
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Correlation
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many statistical methods
Correlation of clinical data
Correlation of clinical data
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Is r=0.16 a
strong
correlation?
Can we
conclude that
CRP and LDL
are related?
Box plots (not common)
25th percentile, median
and 75th percentile
indicated in each box
Other interesting data
representation
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Neater than a
true scatter plot
Simple to
interpret
Nissen et al, N Engl J Med
2005;352:29-38
An example:
Peterson RC, Thomas RG, Grandman
M, Bennet D, Doody R, Ferris S, et al.
Vitamin E and Donepezil for the
Treatment of Mild Cognitive
Impairment. N Engl J Med
2005;352:2379-88.
 Available at:
http://content.nejm.org/cgi/content/full/
352/23/2379
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Questions:
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What kind of study is this?
How large is the study?
What are the inclusion/exclusion criteria?
What is the outcome measured?
What is the intervention?
What are the statistical tests, and are they
appropriate?
What data representations are used?
Is the result statistically significant?
Is the result clinically significant?
How does this knowledge affect my practice?