Basic Statistics

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Basic Statistics
Evidence-Based Medicine Noon conference series
2006-7
EBM

• Terry Shaneyfelt, MD, MPH

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Objectives

• Accurately interpret study findings
• Understand how data is summarized
• Understand the differences between p-values and
  confidence intervals
• Understand the effect of chance, bias and
  confounding on study findings

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There are 3 kinds of lies- lies, damned lies,
and statistics - Mark Twain
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• Case Presentation
• Symptom clusterSweaty palms Pale Increased
  heart rateGlassy-eyed stareLoss of affect

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Diagnosis

• Photonumerophobia
• The fear that ones fear of numbers will come to
  light

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Clopidogrel and Aspirin vs. Aspirin Alone for the
Prevention of Atherothrombotic Events
CHARISMA Trial

• In patients at high risk for atherothrombosis, is
  long-term treatment with clopidogrel plus ASA
  more effective than ASA alone in reducing
  cardiovascular events?
• Methods
• RCT (concealed, blinded)
• Clopidogrel ASA vs. ASA placebo
• Outcome MI or stroke or cardiovascular death
• ITT analysis, 99.5 f/u

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Baseline Characteristics
Continuous variable
Dichotomous variable
Variables
Quality, characteristic, constituent of a person
or thing that can be measured
Bhatt, D. et al. N Engl J Med 20063541706-1717
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Why we have statistics?

• Descriptive Statistics
• identify patterns
• leads to hypothesis generation
• Inferential Statistics
• distinguish true differences from random
  variation (chance)
• allows hypothesis testing

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• Continuous Data
• Use measures of central tendency dispersion

• Dichotomous Data
• Summarized by proportions (s)

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Descriptive Statistics Describing Data with
Numbers

• Measures of Central Tendency (Center of Data)
• MEAN -- average
• MEDIAN -- middle value of ordered data
• MODE -- most frequently observed value(s)
• Measures of Dispersion (Spread of Data)
• RANGE - highest to lowest values
• STANDARD DEVIATION - how closely do values
  cluster around the mean value of the actual
  sample data
• STANDARD ERROR inferential stability of the
  mean to the theoretical universal population from
  which the sample came

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Extreme values affect the mean
Why not describe the mean age of the 2 cohorts?
39, 47, 41, 43, 95 Median 39, 41, 43, 47,
95 Mean 53
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At 28 months 6.8 of patients on clopidogrel
ASA suffered a primary outcome event compared to
7.3 on ASA alone
ARE THESE NUMBERS DIFFERENT?
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6.8
7.3
Clopid/ASA
ASA only
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Statistics and EBM

• All the terms used to summarize outcomes in
  studies are compared using inferential statistics
• Diagnosis sensitivity, specificity, LR
• Therapy RRR, ARR, NNT
• Prognosis survival rates, median survival,
  survival curves
• Harm OR, RR

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Inferential Statistics

• Used to determine the likelihood that a
  conclusion based on data from a sample is true
• Alternative explanations for the conclusion
• Chance / Random Variation
• Confounding
• Bias

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Statistical Tests

• Mathematical formulas that produce p-values to
  assess the likelihood that chance accounts for
  the results observed in the study
• Many different tests. Choice depends on several
  factors
• Type of data (continuous, dichotomous, etc)
• Distribution of data (normally distributed or
  not)
• Study design ( of groups, etc)

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The Normal Distribution

• Mean median mode
• 68 of values fall between 1 SD
• 95 of values fall between 2 SDs

Mean, Median, Mode
1?
2?
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TRUTH
Difference
No difference
Alpha/ Type I error
Difference
P-value
Study Conclusion
Beta/ Type II error
No difference
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Beta / Type II Error

• Study doesnt find a difference when in fact one
  exists
• Most important in negative study
• Main determinant sample size
• Convention 10-20
• Used to determine POWER of the study
• 1 Beta error
• Probability of finding a difference when one
  exists

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TRUTH
Difference
No difference
Alpha/ Type I error
Difference
POWER
Study Conclusion
Beta/ Type II error
No difference
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CHARISMA

• Statistical Analysis
• We estimated that 15,200 patients (7600 per
  group) and 1040 primary events would be necessary
  to detect a 20 percent relative risk reduction in
  the primary efficacy end point, with 90 percent
  power at the two-sided 0.05 significance level in
  this event-driven trial...
• A type I error of 0.049 was preserved for the
  final analysis.

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TRUTH
Clopid better
No difference
4.9
90
Clopid better
Charisma
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No difference
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2 methods to assess the role of chance

• Hypothesis testing
• Confidence Intervals (Estimation)

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Statistical Approach to Compare 2 Groups
Group A
Group B

• Calculate
• Main effect
• Variance in main effect

State a null hypothesis (the main effect is 0)
Calculate the 95 confidence interval around the
main effect
Calculate the test statistic to determine p value
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P-value

• Probability that the results seen could have
  occurred by chance alone
• No p-value, however small, excludes chance
  completely
• Type I error rate (false positive rate)
• lt 0.05 usual (arbitrary) cut-off for statistical
  significance

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P-value

• Cannot tell you if there is bias in the study
• Doesnt determine if effect is clinically
  significant
• Small effect in a study with large sample size
  can have the same p value as a large effect in a
  small study
• Depends on
• How large the effect was
• How many patients were studied
• How consistent the effect was

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CHARISMA
Since the 95 CI of the RR crosses 1.0, the
difference is not significant
95 C.I.
1.05
0.93
0.83
Risk could be this high (increased by 5)
Risk could be this low (reduced by 17)
1.0
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Confidence Intervals
p ns
No difference between groups
Plt0.05
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Confidence Intervals

• Range of plausible values
• 95 CI
• X 1.96 SE (or SD)
• 95 of such intervals will contain the true
  population value
• Range of values within which we can be 95 sure
  that the population value lies
• Clinical statistical significance
• Larger the trial the narrower the CI

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Alternative Explanations for the Observed
Conclusions of a Study

• Chance / Random variation
• Bias
• Confounding

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Bias

• Systematic error in a study that results in an
  incorrect association
• May mask an association or cause a spurious one
• May cause over or underestimation of the effect
  size
• Minimized through
• Rigorous design considerations
• Meticulous conduct of study
• Particular study designs are most vulnerable to
  certain types of bias
• Users Guides designed to detect biases in a study

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Alternative Explanations for the Observed
Conclusions of a Study

• Chance / Random variation
• Bias
• Confounding

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Confounding

• Distortion of the effect of exposure (clopidogrel
  / ASA) on the disease (Stroke) by that of a third
  factor (e.g. hyperlipidemia)
• Confounder has to be associated with BOTH the
  exposure and the disease but not just a link in
  the causal chain
• May cause over or underestimation of the true
  effect
• May even change direction of observed effect

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Confounding
Clopidogrel / Aspirin
Stroke
Hyperlipidemia
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Confounding

• Can be controlled for in the design phase
• Randomization
• Restriction
• Matching
• Stratification
• Can be controlled in the analysis phase
• Stratified analysis
• Multivariable analysis

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Multivariable Analysis

• Statistical techniques to control for multiple
  confounders simultaneously
• Linear regression analysis
• Continuous outcome
• Logistic regression analysis
• Dichotomous outcome
• Cox proportional hazards analysis
• Time-to-event outcome

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Take Home Points

• Statistical significance is a requirement for
  determining clinical significance, but is not
  enough to signify a clinically important
  difference
• The P-value tells us the risk that the finding
  was due to chance / random variation
• Statistical tests generate p-values
• P-value only assesses statistical significance

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Take Home Points-2

• Confidence intervals help us to understand how
  close the study estimate is to the "truth"
• CIs assess both statistical and clinical
  significance
• Findings in a study could be due to
• Truth
• Chance / random variation
• Bias
• Confounding

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Photonumerophobia
CURED