basic statistics: an oxymoron? (with a little epi thrown in…) urvashi vaid md, ms aug 2012
TRANSCRIPT
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BASIC STATISTICS:AN OXYMORON?
(With a little EPI thrown in…)
URVASHI VAID MD, MSAUG 2012
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OUTLINE
• Definition• Why do we need to know “statistics”?– Validity- external and internal– Reliability– Sensitivity– Specificity– Positive and negative predictive values
• ROC curves
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STATISTICS
• “the science that deals with the collection, classification, analysis, and interpretation of numerical facts or data, and that, by use of mathematical theories of probability, imposes order and regularity on aggregates of more or less disparate elements”
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BUT WHY?
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BUT WHY?
• To effectively conduct research• To read and evaluate journals• To develop critical and analytical thinking• To be an informed consumer• To know your limits
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Population
SampleTreatment group A
vs Treatment group B
InferenceSampling
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POPULATION
Target PopulationEg smokers
Study Population (eligible)
Eg Ages 55-74 yrs,≥ 30 pack years
Study Sample (enrolled)Eg geographic area,
site, consent
Target Population
Study Population
Study Sample
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Mean, Median and Mode
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Measures of dispersion
• Range• Standard deviation- Bell’s curve• Others
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NORMAL DISTRIBUTION
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VALIDITY AND RELIABILITY-quality of measurements
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VALIDITY AND RELIABILITY
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GENERALIZABILITY
• Also “External Validity”• how representative of the target population is
the study population and study sample?• Based on inclusion/exclusion criteria and
standard of care• Where• When• Who (subjects)• What (treatments, outcomes)• How (assessments, data collection)
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INTERNAL VALIDITY or no “bias”• Estimated effect in study sample is accurate reflection
of true effect in underlying study population
• Can be in jeopardy due “Systematic Error”– Selection or allocation bias– Information or recall bias or treatment related bias– Confounding– Cross over or lost to follow up
• Deal with this by creating a good study design and statistics
• Also- randomize, blind, quality control, adjust for co-variates
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RANDOMIZATION• Balances groups on known and unknown risk
factors in the long run • Provides statistical basis for estimation and
testing • Effort, time, cost• Ethics
– patient wants “best” treatment– physician wants to tailor treatment to individual patient
• Clinical Equipoise?
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HYPOTHESIS TESTING
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HYPOTHESIS TESTING
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HYPOTHESIS TESTING
• H0: Null Hypothesis--There is no association between an exposure and outcome
• H1: Alternative Hypothesis--There is an association between an exposure and outcome
• In general, epidemiologists attempt to reject the null
• One-sided (higher or lower) vs two-sided (different)
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H0 True (No Association)
H1 True (There is an Association)
Do Not Reject H0
Correct Decision Type II Error (β)
Reject H0
Type I Error (α) Correct Decision
TRUTHDECISION
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• Type I error (false positive, α)probability of rejecting null hypothesis, when it is true
• Type II error (false negative, β)probability of not rejecting null hypothesis, when it is false
• Power (1-β)probability of rejecting null hypothesis, when it is false
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POWER AND SAMPLE SIZE
• Ensure study worth doing and feasible• Have to consider
– study design– outcome (distribution, variability, etc.)– hypothesis to be tested (superiority, equivalence, etc.)– statistical analysis to be performed– clinically relevant/meaningful effect size to be detected
• Larger the effect size, smaller the sample size needed
• More subjects more power!
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Measures of diagnostic test performance
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SENSITIVITY
• A test’s ability to identify diseased individuals• Probability of a positive test among those with
disease
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SPECIFICITY
• A test’s ability to rule out disease• Probability of a negative test among those
without disease
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SENSITIVITY AND SPECIFICITY ARE FIXED ASPECTS OF A TESTDO NOT CHANGE BASED ON DISEASE PREVALENCE
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Disease + Disease - Total
Test + TP FP TP+FPTest - FN TN FN+TNTotal TP+FN FP+TN TP+FP+FN+TN
Sensitivity = True Positive /Those with disease = TP/(TP+FN)
Specificity = True Negative/Those without disease = TN/(TN+FP)
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EXAMPLE
• 200 patients• D-dimer positive in 50• CT angio positive in 60• CT angio and d-dimer negative in 120• Construct a 2 X 2 table and calculate
sensitivity and specificity.
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PE No PE
D-dimer positive 50
D-dimer negative 120
60 200
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PE No PE
D-dimer positive 30 20 50
D-dimer negative 30 120 150
60 140 200
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PE No PE
D-dimer positive 30 20 50
D-dimer negative 30 120 150
60 140 200
Sensitivity= TP/TP+FN= 30/30+30=50%
Specificity= TN/TN+FP= 120/120+20= 85%
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POSITIVE PREDICTIVE VALUE
• The probability of having disease given a positive test: P(D+|T+)
• ‘How likely is it that this patient has the disease given that the test result is positive?’
• Calculated as: (TRUE POSITIVE)/(TRUE POSITIVE + FALSE POSITIVE)
• Sensitivity is the probability of test positive given disease: P(T+|D+)
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Disease + Disease - Total
Test + 26 7 33Test - 97 1701 1798Total 123 1708 1831
What is the PPV?
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NEGATIVE PREDICTIVE VALUE
• The probability of not having disease given a negative test: P(D-|T-)
• ‘How likely is it that this patient does not have the disease given that the test result is negative?’
• Calculated as: (TRUE NEGATIVE)/(TRUE NEGATIVE + FALSE NEGATIVE)
• Specificity is the probability of testing negative given no disease: P(T-|D-)
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Disease + Disease - Total
Test + 26 7 33Test - 97 1701 1798Total 123 1708 1831
What is the NPV?
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• Sensitivity and specificity are characteristics of tests themselves
• Predictive values (positive and negative) are functions of both test characteristics and prevalence
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EFFECT OF PREVALENCE
• 4000 people, of which 2000 are ill and 2000 well• A screening test with 99% sensitivity and 99% specificity will
yield 1980 TP and 1980 TN and only 20 each for FP and FN• Hence PPV is 99%.• What if the number of ill people is only 200?• Then well people are 3800 and FP increase to 38 and PPV falls
to 84%
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Disease + Disease -
Test + 1980 20 2000
Test - 20 1980 2000
2000 2000 4000
Disease + Disease -
Test + 198 38 236
Test - 2 3762 3764
200 3800 4000
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ROC
• Receiver operator characteristic curves are a plot of false positives against true positives for all cut-off values
• The area under the curve of a perfect test is 1.0 and that of a useless test, no better than tossing a coin, is 0.5
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