Design and Analysis of Clinical Study Odds ratio and relative risk
Dr. Tuan V. Nguyen
Garvan Institute of Medical Research
Sydney, Australia
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
Overview
• Distinction of research studies• Incidence and prevalence• Odds ratio• Relative risk
Distinction of studies
time
PAST PRESENT FUTURE
Cohort study, RCT
(longitudinal, prospective)
Case-control study
Cross-sectional study
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
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
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
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
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
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
Effect of the incidence on RR and OR
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%]
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
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
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 = ?
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
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
Type I and Type II errors
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
Clinical relevance and statistical significance
• 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