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Victor Babes UNIVERSITY OF MEDICINE AND
PHARMACY TIMISOARA

• DEPARTMENT OF
• MEDICAL INFORMATICS AND BIOPHYSICS
• Medical Informatics Division
• www.medinfo.umft.ro/dim
• 2007 / 2008

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CORRELATION ANALYSISEPIDEMIOLOGY

• COURSE 6

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• 1. RELATIONS BETWEEN TWO QUANTITATIVE VARIABLES
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• 1.1. DEPENDENCY DEGREE .
• STATE SPACE (DIAGRAM)
• 1 INDIVIDUAL 1 POINT

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a) INDEPENDENT VARIABLES HG hemoglobin
concentration h height
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b) DEPENDENT VARIABLES Causal relation -
mathematical model O2 in the blood -
atmospheric pO2
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c) CORRELATED VARIABLES G weight, h height
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• 1.2. LINEAR CORRELATION
• a) CORRELATION COEFFICIENT (Pearson)
• rxy sxy / sx sy
• sxy covariance
• sx variance of x
• sy variance of y

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• b) PROPERTIES
• VALUES -1, 1
• r gt 0 gt DIRECT CORRELATION
• r lt 0 gt INVERSE CORRELATION
• WEAK / STRONG CORRELATION
• WEAK CLOSE TO 0
• STRONG CLOSE TO -1 OR 1
• TESTING r WITH t TEST - significance

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Direct and inverse correlations
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1.3. REGRESSION LINE(best line among the
points)

• a) EXAMPLE
• HEIGHT CHILDREN - PARENTS
• hc gt hp
• SLOPE lt 1 gt REGRESSION
• TENDENCY TOWARDS MIDDLE REGION
• b) LINE PARAMETERS y a b x
• a INTERCEPT
• b SLOPE

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1.5. NONLINEAR CORRELATIONS

• a) EXPONENTIAL
• y a . e b.x
• Increasing (b gt 0) ABSORBTION
• Decreasing (b lt 0) CLEARANCE

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• b) LOGARITHMIC
• y a b . log x
• WEBER - FECHNER LAW (Sensation)
• c) POWER
• y a . x b
• STEVANS LAW (Neural frequency)

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• d) HYPERBOLIC
• (x - a) . (y - b) k
• HILL LAW (Muscular contraction), ABBEY
• e) LOGISTIC
• y a . x / (k x)
• MICHAELIS - MENTEN (Enzymatic kinetics)
• ARIENS (Dose - response curves)

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2. CORRELATIONS FOR ORDINAL VARIABLES

• 2.1. RANK CORRELATION COEFFICIENT
• SPEARMAN R
• Comparing two classifications
• 2.2. KENDALL CORRELATION COEFFICIENT
• Appl. for ordinal and nominal variables

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2. EPIDEMIOLOGICAL BIOSTATISTICS
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1. RISK ANALYSIS

• 1.1. RISK FACTORS
• a) DEFINITION
• Hypothetical cause for disease occurrence or
  facilitation
• b) CLASSIFICATION
• Environmental
• Social
• Behaviorial
• Biological

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1.2. DATA TABLES (Contingency tables)
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• 1.3. METHODS

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• 1.3. METHODS
• A- EXPERIMENTAL
• RISK FACTOR CONTROL
• DISADVANTAGE ETHICAL REASONS
• B- OBSERVATION-BASED

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• a) CROSS - SECTIONAL
• TRANSVERSAL Moment situation in a large sample
• b) COHORT - PROSPECTIVE
• LONGITUDINAL
• Two groups Exposed / Unexposed
• c) COHORT - RETROSPECTIVE
• d) CASE - CONTROL
• Two groups Disease / No-disease
• e) Comparison
• EXP gt COH.pr. gt COH.ret. gt CASE-C. gt CR.S.

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• 1.4. FONDAMENTAL PARAMETERS IN EPIDEMIOLOGY
• ODD INDEX (success / fail)
• ODD (E) N11 / N12
• ODD (E-) N21 / N22
• ODDS RATIO (OR)
• OR ODD(E) / ODD(E-)
• OR N11 . N22 / N12 . N21

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• ABSOLUTE RISK (success rate)
• R (E) N11 / L1
• R (E-) N21 / L2
• RELATIVE RISK (RR)
• RR R(E) / R(E-)
• RR N11 . L2 / N21 . L1
• Usually OR gt RR
• IF OR gt 1 (RR gt 1) gt RISK !

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3. SURVIVALANALYSIS
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• 1. CHARACTERISTICS
• missing data, long duration of study
• heterogenous conditions
• several influencing factors
• 2. DATA PROCESSING
• life tables
• actuarial method
• Kaplan Mayer curves

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Data collection
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Actuarial method
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Kaplan Mayer plots
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• 3.3. INDICATORS
• Life Years (Survival years)
• QoL Index Quality of Life
• Adjusting Life Years to QALY (Quality Adjusted
  Life Years)

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- e n d -