BASIC STATISTICS: AN OXYMORON? (With a little EPI thrown in…) URVASHI VAID MD, MS AUG 2012

OUTLINE Definition Why do we need to know “statistics”? – Validity- external and internal – Reliability – Sensitivity – Specificity – Positive and negative predictive values ROC curves

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”

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

Population Sample Treatment group A vs Treatment group B Inference Sampling

POPULATION Target Population Eg smokers Study Population (eligible) Eg Ages yrs, ≥ 30 pack years Study Sample (enrolled) Eg geographic area, site, consent Target Population Study Population Study Sample

Mean, Median and Mode

Measures of dispersion Range Standard deviation- Bell’s curve Others

NORMAL DISTRIBUTION

VALIDITY AND RELIABILITY-quality of measurements

VALIDITY AND RELIABILITY

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)

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

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?

HYPOTHESIS TESTING

H 0 : Null Hypothesis--There is no association between an exposure and outcome H 1 : 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)

H 0 True (No Association) H 1 True (There is an Association) Do Not Reject H 0 Correct Decision Type II Error ( β ) Reject H 0 Type I Error ( α ) Correct Decision TRUTH DECISIONDECISION

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

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!

Measures of diagnostic test performance

SENSITIVITY A test’s ability to identify diseased individuals Probability of a positive test among those with disease

SPECIFICITY A test’s ability to rule out disease Probability of a negative test among those without disease

SENSITIVITY AND SPECIFICITY ARE FIXED ASPECTS OF A TEST DO NOT CHANGE BASED ON DISEASE PREVALENCE

Disease +Disease -Total Test +TPFPTP+FP Test -FNTNFN+TN TotalTP+FNFP+TN TP+FP+FN+TN Sensitivity = True Positive /Those with disease = TP/(TP+FN) Specificity = True Negative/Those without disease = TN/(TN+FP)

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.

PENo PE D-dimer positive50 D-dimer negative

PENo PE D-dimer positive D-dimer negative

PENo PE D-dimer positive D-dimer negative Sensitivity= TP/TP+FN= 30/30+30=50% Specificity= TN/TN+FP= 120/120+20= 85%

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+)

Disease +Disease -Total Test Test Total What is the PPV?

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-)

Disease +Disease -Total Test Test Total What is the NPV?

Sensitivity and specificity are characteristics of tests themselves Predictive values (positive and negative) are functions of both test characteristics and prevalence

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%

Disease +Disease - Test Test Disease +Disease - Test Test

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