Design and Analysis of Clinical Study Odds ratio and relative risk Dr. Tuan V. Nguyen Garvan Institute of Medical Research Sydney, Australia.

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