““Victor Babes” Victor Babes” UNIVERSITY OF MEDICINE UNIVERSITY OF MEDICINE

AND PHARMACY AND PHARMACY TIMISOARATIMISOARADEPARTMENT OFDEPARTMENT OF

MEDICAL INFORMATICS AND BIOPHYSICSMEDICAL INFORMATICS AND BIOPHYSICS

Medical Informatics DivisionMedical Informatics Divisionwww.medinfo.umft.ro/dimwww.medinfo.umft.ro/dim

2007 / 20082007 / 2008

CORRELATION ANALYSISCORRELATION ANALYSISEPIDEMIOLOGYEPIDEMIOLOGY

COURSE 6COURSE 6

• 1. RELATIONS BETWEEN 1. RELATIONS BETWEEN TWO QUANTITATIVE TWO QUANTITATIVE

VARIABLES .VARIABLES .• 1.1. DEPENDENCY DEGREE 1.1. DEPENDENCY DEGREE

. .– STATE SPACE (DIAGRAM)STATE SPACE (DIAGRAM)– 1 INDIVIDUAL = 1 POINT1 INDIVIDUAL = 1 POINT

a) INDEPENDENT VARIABLESa) INDEPENDENT VARIABLESHG = hemoglobin concentrationHG = hemoglobin concentrationh = heighth = height

b) DEPENDENT VARIABLESb) DEPENDENT VARIABLES Causal relation - mathematical modelCausal relation - mathematical model [O [O22] in the blood - atmospheric pO] in the blood - atmospheric pO22

c) CORRELATED VARIABLESc) CORRELATED VARIABLESG = weight, h = heightG = weight, h = height

• 1.2. LINEAR CORRELATION1.2. LINEAR CORRELATION

• a) CORRELATION COEFFICIENT a) CORRELATION COEFFICIENT (Pearson)(Pearson)

• rrxyxy = s = sxyxy / s / sxx s syy • ssxyxy = covariance = covariance• ssxx = variance of x = variance of x• ssyy = variance of y = variance of y

• b) PROPERTIES:b) PROPERTIES:– VALUES = [ -1, +1]VALUES = [ -1, +1]– r > 0 ==> DIRECT CORRELATIONr > 0 ==> DIRECT CORRELATION– r < 0 ==> INVERSE CORRELATIONr < 0 ==> INVERSE CORRELATION– WEAK / STRONG CORRELATIONWEAK / STRONG CORRELATION

• WEAK = CLOSE TO 0WEAK = CLOSE TO 0• STRONG = CLOSE TO -1 OR +1STRONG = CLOSE TO -1 OR +1

– TESTING TESTING rr : WITH : WITH tt TEST - significance TEST - significance

Direct and inverse correlationsDirect and inverse correlations

1.3. REGRESSION LINE1.3. REGRESSION LINE(“best line” among the points)(“best line” among the points)

• a) EXAMPLE:a) EXAMPLE:– HEIGHT: CHILDREN - PARENTSHEIGHT: CHILDREN - PARENTS

– hhcc > h > hpp

– SLOPE < 1 ==> REGRESSIONSLOPE < 1 ==> REGRESSION– TENDENCY TOWARDS MIDDLE REGIONTENDENCY TOWARDS MIDDLE REGION

• b) LINE PARAMETERS: y = a + b xb) LINE PARAMETERS: y = a + b x– a = INTERCEPTa = INTERCEPT– b = SLOPEb = SLOPE

1.5. NONLINEAR CORRELATIONS1.5. NONLINEAR CORRELATIONS

• a) EXPONENTIALa) EXPONENTIAL

y = a . ey = a . e b.x b.x

• Increasing (b > 0): ABSORBTIONIncreasing (b > 0): ABSORBTION

• Decreasing (b < 0): CLEARANCEDecreasing (b < 0): CLEARANCE

• b) LOGARITHMIC:b) LOGARITHMIC:

y = a + b . log xy = a + b . log x• WEBER - FECHNER LAW (Sensation)WEBER - FECHNER LAW (Sensation)

• c) POWER:c) POWER:

y = a . xy = a . x b b

• STEVANS LAW (Neural frequency)STEVANS LAW (Neural frequency)

• d) HYPERBOLIC:d) HYPERBOLIC:

(x - a) . (y - b) = k(x - a) . (y - b) = k• HILL LAW (Muscular contraction), ABBEYHILL LAW (Muscular contraction), ABBEY

• e) LOGISTIC:e) LOGISTIC:

y = a . x / (k + x)y = a . x / (k + x)• MICHAELIS - MENTEN (Enzymatic kinetics)MICHAELIS - MENTEN (Enzymatic kinetics)

• ARIENS (Dose - response curves)ARIENS (Dose - response curves)

2. CORRELATIONS FOR ORDINAL 2. CORRELATIONS FOR ORDINAL VARIABLESVARIABLES

• 2.1. RANK CORRELATION 2.1. RANK CORRELATION COEFFICIENTCOEFFICIENT– SPEARMAN “R”SPEARMAN “R”– Comparing two classificationsComparing two classifications

• 2.2. KENDALL CORRELATION 2.2. KENDALL CORRELATION COEFFICIENTCOEFFICIENT– Appl. for ordinal and nominal variablesAppl. for ordinal and nominal variables

2. EPIDEMIOLOGICAL 2. EPIDEMIOLOGICAL BIOSTATISTICSBIOSTATISTICS

1. RISK ANALYSIS1. RISK ANALYSIS

• 1.1. RISK FACTORS1.1. RISK FACTORS– a) DEFINITION : a) DEFINITION : – Hypothetical cause for disease Hypothetical cause for disease

occurrence or facilitationoccurrence or facilitation– b) CLASSIFICATION :b) CLASSIFICATION :

• EnvironmentalEnvironmental• SocialSocial• BehaviorialBehaviorial• BiologicalBiological

1.2. DATA TABLES 1.2. DATA TABLES (Contingency tables)(Contingency tables)

D+(disease)

D-(no dis.)

Totallines

E+(exposed)

N11 N12 L1

E-(unexpos.)

N21 N22 L2

Totalcolumns

C1 C2 N

• 1.3. METHODS1.3. METHODS

• 1.3. METHODS1.3. METHODS

– A- EXPERIMENTAL A- EXPERIMENTAL • RISK FACTOR CONTROLRISK FACTOR CONTROL• DISADVANTAGE: ETHICAL DISADVANTAGE: ETHICAL

REASONSREASONS

– B- OBSERVATION-BASEDB- OBSERVATION-BASED

• a) CROSS - SECTIONAL a) CROSS - SECTIONAL – TRANSVERSAL: Moment situation in a large sampleTRANSVERSAL: Moment situation in a large sample

• b) COHORT - PROSPECTIVEb) COHORT - PROSPECTIVE– LONGITUDINALLONGITUDINAL– Two groups: Exposed / UnexposedTwo groups: Exposed / Unexposed

• c) COHORT - RETROSPECTIVEc) COHORT - RETROSPECTIVE• d) CASE - CONTROLd) CASE - CONTROL

– Two groups: Disease / No-diseaseTwo groups: Disease / No-disease• e) Comparison:e) Comparison:

– EXP > COH.pr. > COH.ret. > CASE-C. > CR.S.EXP > COH.pr. > COH.ret. > CASE-C. > CR.S.

• 1.4. FONDAMENTAL 1.4. FONDAMENTAL PARAMETERS IN EPIDEMIOLOGYPARAMETERS IN EPIDEMIOLOGY

• ‘‘ODD’ INDEX (success / fail):ODD’ INDEX (success / fail): ODD (E+) = N11 / N12ODD (E+) = N11 / N12 ODD (E-) = N21 / N22ODD (E-) = N21 / N22

• ODDS RATIO (OR):ODDS RATIO (OR): OR = ODD(E+) / ODD(E-)OR = ODD(E+) / ODD(E-)

OR = N11 . N22 / N12 . N21 OR = N11 . N22 / N12 . N21

• ‘‘ABSOLUTE’ RISK (success rate):ABSOLUTE’ RISK (success rate): R (E+) = N11 / L1R (E+) = N11 / L1 R (E-) = N21 / L2R (E-) = N21 / L2

• RELATIVE RISK (RR):RELATIVE RISK (RR): RR = R(E+) / R(E-)RR = R(E+) / R(E-)

RR = N11 . L2 / N21 . L1 RR = N11 . L2 / N21 . L1 • Usually OR > RRUsually OR > RR• IF OR > 1 (RR > 1) ==> RISK !IF OR > 1 (RR > 1) ==> RISK !

3. SURVIVAL3. SURVIVALANALYSISANALYSIS

1. CHARACTERISTICS1. CHARACTERISTICS• missing data, long duration of studymissing data, long duration of study• heterogenous conditionsheterogenous conditions• several influencing factorsseveral influencing factors 2. DATA PROCESSING2. DATA PROCESSING• life tableslife tables• actuarial methodactuarial method• Kaplan Mayer curvesKaplan Mayer curves

Data collectionData collection

Actuarial methodActuarial method

Bitmap Image

Kaplan Mayer plotsKaplan Mayer plots

3.3. INDICATORS3.3. INDICATORS

• Life Years (Survival years)Life Years (Survival years)• QoL Index = Quality of LifeQoL Index = Quality of Life• Adjusting “Life Years” to QALY Adjusting “Life Years” to QALY

(Quality Adjusted Life Years)(Quality Adjusted Life Years)

- e n d -- e n d -