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Cohort Study Analysis. Standard 2 X 2 table (Relation between exposure and outcome). Two types of measures for rate. Cumulative incidence = Proportion of study subjects getting the outcome during the study period Incidence rate = New cases/ Person-time under observation. - PowerPoint PPT Presentation
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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 Ratio of the risk among exposed to the risk among unexposed risk among unexposed [Risk (Exp) / Risk (Unexp)][Risk (Exp) / Risk (Unexp)]
►Risk of disease among exposed Risk of disease among exposed = = [a/ [a+ [a/ [a+ b)] 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
Rela
tive ris
k
1
22
Ab
solu
te ris
k
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 [Risk (Exp) – Risk (Unexp)]/ Risk (Exp) X 100100
= (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)
Rela
tive ris
k
% ris
k d
ue to
exp
osu
re
1
22
Ab
solu
te ris
ks (E
xp
)
% risk due to background
Attributable Risk PercentAttributable Risk Percent
Attributable Risk PercentAttributable Risk PercentR
ela
tive ris
k
p0(R
R-1
)
p0
p0RR
p0R
R
1
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 the total risk for disease is due to the risk factorrisk factor
►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
0
20
40
60
80
100
120
140
160
180
Ab
solu
te r
isk o
f lu
ng
can
cer
death
per
100,0
00 a
du
lt m
ale
per
year
Smoker Nonsmoker
(RR-1)(1-Pe)Pe(RR-1)
(1-Pe)Pe
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
