Cohort Study AnalysisCohort Study Analysis

Standard 2 X 2 tableStandard 2 X 2 table(Relation between exposure and (Relation between exposure and

outcome)outcome)DISEASE DISEASE STATUSSTATUS

PresenPresent t AbsentAbsent TotalTotal

EXPOSUREXPOSURE STATUSE STATUS

PresentPresent aa bb a + ba + b

AbsentAbsent cc dd c + dc + d

TotalTotal a + ca + c b + db + d NN

Two types of measures for Two types of measures for raterate

►Cumulative incidence = Proportion of Cumulative incidence = Proportion of study subjects getting the outcome study subjects getting the outcome during the study periodduring the study period

► Incidence rate = New cases/ Person-Incidence rate = New cases/ Person-time under observationtime under observation

Comparing risks in different Comparing risks in different groupsgroups

►Relative risk OR Risk ratio (RR)Relative risk OR Risk ratio (RR)►Attributable risk OR Risk difference Attributable risk OR Risk difference

(AR)(AR)►Attributable risk percent (AR%)Attributable risk percent (AR%)►Population attributable risk (PAR)Population attributable risk (PAR)►Population attributable risk percent Population attributable risk percent

(PAR%)(PAR%)►Odds Ratio (OR)Odds Ratio (OR)

Relative risk OR Risk ratioRelative risk OR Risk ratio►Ratio of the risk among exposed to the risk Ratio of the risk among exposed to the risk

among unexposed among unexposed [Risk (Exp) / Risk (Unexp)][Risk (Exp) / Risk (Unexp)]

►Risk of disease among exposed Risk of disease among exposed = = [a/ [a+ b)] [a/ [a+ b)] ►Risk of disease among unexposed Risk of disease among unexposed = = [c/ [c [c/ [c

+d)] +d)] ►RR = RR = [a/ [a +b)] / [c/ [c +d)][a/ [a +b)] / [c/ [c +d)]►For null hypothesis, Risk ratio will equal For null hypothesis, Risk ratio will equal

‘one’‘one’

Risk difference vs. Relative Risk difference vs. Relative riskrisk

Relative risk

1

22

Absolute risk

Attributable risk OR Risk Attributable risk OR Risk difference difference (Absolute differences in (Absolute differences in

risks or rates)risks or rates)► Attributable Risk = Attributable Risk = Risk (Exp) – Risk (Unexp)Risk (Exp) – Risk (Unexp)► Risk of disease among exposed = Risk of disease among exposed = [a/ [a +b)] [a/ [a +b)] ► Risk of disease among unexposed = Risk of disease among unexposed = [c/ [c [c/ [c

+d)] +d)] ► Risk difference = Risk difference = [a/ [a +b)] - [c/ [c +d)][a/ [a +b)] - [c/ [c +d)]► For null hypothesis, Risk difference will For null hypothesis, Risk difference will

equal ‘zero’equal ‘zero’

Risk difference vs. Relative Risk difference vs. Relative riskrisk

Attributable risk percent among Attributable risk percent among exposedexposed

►Among exposed, what percent of the total Among exposed, what percent of the total risk for disease is due to the exposurerisk for disease is due to the exposure

►AR% (Exposed) AR% (Exposed) = = [Risk (Exp) – Risk (Unexp)]/ Risk (Exp) X 100[Risk (Exp) – Risk (Unexp)]/ Risk (Exp) X 100

= (RR – 1)/ RR X 100= (RR – 1)/ RR X 100= (OR – 1)/ OR= (OR – 1)/ OR X 100X 100 (if risk is small)(if risk is small)

Relative risk

% risk due to exposure

1

22

Absolute risks (Exp)

% risk due to background

Attributable Risk PercentAttributable Risk Percent

Attributable Risk PercentAttributable Risk PercentRelative risk

p0(RR-1)

p0

p0RR

p0RR

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Attributable risk Percent = (RR-1)/ RR Attributable risk Percent = (RR-1)/ RR *100*100

Population attributable riskPopulation attributable risk► In the general population, how much of In the general population, how much of

the total risk for disease is due to the risk the total risk for disease is due to the risk factorfactor

►Risk (Exp) – Risk (Unexp)Risk (Exp) – Risk (Unexp)►Risk (Total) Risk (Total) = [Proportion population Exp X Risk (Exp)] += [Proportion population Exp X Risk (Exp)] + [Proportion population Unexp X Risk [Proportion population Unexp X Risk

(Unexp)](Unexp)]

Population attributable risk Population attributable risk percentpercent

►Among the general population, what Among the general population, what percent of the total risk for disease is percent of the total risk for disease is due to the risk factordue to the risk factor

►PAR% PAR% = = [Risk (Exp) – Risk (Unexp)]/ Risk (Total) X [Risk (Exp) – Risk (Unexp)]/ Risk (Total) X 100100

= [Pe (RR – 1)]/ [1+ Pe (RR – 1)] X 100= [Pe (RR – 1)]/ [1+ Pe (RR – 1)] X 100

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(RR-1)(1-Pe)Pe(RR-1)

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Population attributable risk Population attributable risk percentpercent

Population Attributable risk Percent Population Attributable risk Percent = [Pe (RR – 1)]/ [1+ Pe (RR – 1)] X 100 = [Pe (RR – 1)]/ [1+ Pe (RR – 1)] X 100

RR

1

Odds RatioOdds Ratio► Ratio of the odd among exposed to the odd Ratio of the odd among exposed to the odd

among unexposed among unexposed [Odd (Exp) / Odd (Unexp)][Odd (Exp) / Odd (Unexp)]

►Odd of disease among exposed = Odd of disease among exposed = [a/ b] [a/ b] ►Odd of disease among unexposed = Odd of disease among unexposed = [c/ d] [c/ d] ►OR = OR = [a/ b] / [c/ d] = ad/ bc[a/ b] / [c/ d] = ad/ bc► RR = [a/ a+b] / [c/ c+d] RR = [a/ a+b] / [c/ c+d] ► For null hypothesis, Risk ratio will equal ‘one’For null hypothesis, Risk ratio will equal ‘one’► Under most circumstances, the OR is a good Under most circumstances, the OR is a good

estimate of RR; thus may be used as an estimate of RR; thus may be used as an estimate of RRestimate of RR

Odds ratio in a Cohort studyOdds ratio in a Cohort study►An important measure in cohort study An important measure in cohort study

alsoalso►Link between case control study and Link between case control study and

cohort studycohort study►Link to mainstream analytical process Link to mainstream analytical process

– Logistic regression– Logistic regression►What if we are interested in reverse of What if we are interested in reverse of

the event (survival and not death; non-the event (survival and not death; non-disease and not diseased)disease and not diseased)

Which side is up in the risk Which side is up in the risk ratio or odds ratio?ratio or odds ratio?

DISEASE DISEASE STATUSSTATUS

PresenPresent t AbsentAbsent TotalTotal

T/t T/t STATUSSTATUS

PresentPresent aa bb a + ba + b

AbsentAbsent cc dd c + dc + d

TotalTotal a + ca + c b + db + d NN

Absolute and Relative risk Absolute and Relative risk reductionreduction

Risk ReductionRisk Reduction► Risk (T/t) = Risk (T/t) = a/(a+b)a/(a+b)► Risk (Exp) = cRisk (Exp) = c/(c+d)/(c+d)► RR = RR = Risk (T/t)/ Risk (Exp)Risk (T/t)/ Risk (Exp)► ARR = ARR = Risk (Exp) – Risk (T/t)Risk (Exp) – Risk (T/t)► RRR = RRR = [Risk (Exp) – Risk (T/t)] / Risk (Exp)[Risk (Exp) – Risk (T/t)] / Risk (Exp) = 1-Risk(T/t)/Risk(Exp)= 1-Risk(T/t)/Risk(Exp)

= 1-RR= 1-RR►NNT = 1/ARRNNT = 1/ARR = 1/Risk(Exp)*RRR= 1/Risk(Exp)*RRR►NNHNNH

Thank you