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Design and Analysis of Clinical Study Odds ratio and relative risk
Dr. Tuan V. Nguyen
Garvan Institute of Medical Research
Sydney, Australia
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Smoking Fracture No-fracture
Yes 5 195
No 15 985
2 x 2 table
Risk Disease No disease
Presence a d
Absence b c
cb
da
dbca
OR
68.1
19515
9855
OR
ba
aySensitivit
dc
cySpecificit
da
aPPV
25.020
5ySensitivit
83.01180
985OR
025.0200
5PPV
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Overview
• Distinction of research studies• Incidence and prevalence• Odds ratio• Relative risk
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Distinction of studies
time
PAST PRESENT FUTURE
Cohort study, RCT
(longitudinal, prospective)
Case-control study
Cross-sectional study
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Measure of disease frequency
Study Estimate
Case-control Association odds ratio
Cross-sectional Prevalence Prevalence ratio
Prospective (longitudinal) Incidence Relative risk, Hazards ratio odds ratio
RCT Incidence Hazards ratio, odds ratio
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Fracture(b)
No fracture(d)
Smoking(a)
No smoking(c)
Risk factors Outcome
Fracture(b)
No fracture(d)
Smoking(a)
No smoking(c)
Risk factors Outcome
Longitudinal study Case-control study
Measure of association: Relative risk =
a/(a+b)c/(c+d) Odds ratio
=
a*db*c
Longitudinal and case-control studies
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Measure of disease frequency
Risk factor Cases Controls
Presence a b
Absence c d
Total N1 N2
Case-control study
N1 and N2 are pre-determined (fixed)
Risk factor at baseline
Disease No disease Total
Presence a b N1
Absence c d N2
Prospective study
N1 and N2 are fixed at baseline
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Risk factor
Cases Controls
Presence a b
Absence c d
Total N1 N2
Odds ratio (OR) and relative risk (RR)
Case-control study
Risk factor at baseline
Disease No disease
Total
Presence a b N1
Absence c d N2
Prospective study
cb
da
dbca
OR
bac
dca
dcc
baa
RR
ORbc
daRR
When a and c are very small
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OR and RR: an example
BMD Total Fracture No-fracture
Incidence
Low 200 5 195 0.025
High 1000 15 985 0.015
Prospective study
68.119515
9855
OR
67.1015.0
025.0RR
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OR and RR: an example
BMD Total Fracture No-fracture
Incidence
Low 200 20 180 0.10
High 1000 50 950 0.05
Prospective study
11.250180
95020
OR
0.205.0
10.0RR
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Effect of the incidence on RR and OR
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Translating measures of association
Incidence of fracture in women = 3%
Incidence of fracture in men = 1.5%
– “Incidence in women was 2 times that in men.”
– “Incidence in women was 2 times as great as in men.”
– “Incidence in women was 100% greater than incidence in men.” [(3.0 – 1.5) / 1.5 = 100%]
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Prognosis (prospective cohort study)
• Baseline: 1287 women recruited in 1989-1992– Bone mineral density (osteoporosis, non-osteoporosis)
• Follow-up: 1989 2005– Fracture
Total Fracture No-fracture
Osteoporosis 345 137 208
Non-osteoporosis 942 191 751
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Prognosis (prospective cohort study)
Total Fracture No-fracture
Osteoporosis 345 137 208
Non-osteoporosis 942 191 751
42.0191137
137|
FractureOsteoPySensitivit
78.0208751
751|
fractureNoosteoNonPySpecificit
40.0208137
137|
OsteoFracturePPPV
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Diagnostic study
• Gold standard : biopsy• Test: mammography
• Result of biopsy: cancer, no cancer• Result of mammography: +ve, -ve
Mammography result
Biopsy result
Cancer No cancer
+ve a c
-ve b d
Sensitivity = a / (a+b)Specificity = d / (c+d)PPV = ?
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Diagnosis – cohort study
• RANDOMLY selected 1000 individuals• Biopsy • Mammography
Mammography result
Biopsy result
Cancer No cancer
+ve 8 50
-ve 2 940
Total 10 990
Sensitivity = 8 / (8+2)= 0.80Specificity = 940 / (940 + 50) = 0.95PPV = 8/(8+50) = 0.14
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Diagnosis – validation study
• Select 100 women with cancer• Select 100 women without breast cancer• Perform mammography test on the 200 women
Mammography result
Biopsy result
Cancer No cancer
+ve 90 15
-ve 10 85
Total 100 100
Sensitivity = 90 / 100 = 0.90Specificity = 85 / 100 = 0.85PPV = not estimable
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Type I and Type II errors
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TRUTH STATISTICAL TEST Not significant
Effect
Effect
No effect
No effect
Significant (p<0.05)
Not significant (p>0.05)
Significant (p<0.05)
Not significant (p>0.05)
OK (1-)
Type II error ()
Type I error ()
OK
: significance level1- : power
Risks of Inference
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Clinical relevance and statistical significance
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• Two studies: – Study 1: group 1 = group 2 = 15 subjects
– Study 2: group 1 = group 2 = 1500 subjects
n Group 1
(mean±SD)
Group 2
(mean±SD)
Difference (95% CI) P value
15 135 ± 8.5 144 ± 12.0 9 (1.0 -12.0) 0.09
1500 139.4 ± 8.3 140.2 ± 10.1 0.8 (0.3 -1.8) 0.0235
Clinical relevance and statistical significance