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

SmokingFractureNo-fracture Yes5195 No x 2 table RiskDiseaseNo disease Presencead Absencebc

Overview Distinction of research studies Incidence and prevalence Odds ratio Relative risk

Distinction of studies time PAST PRESENTFUTURE Cohort study, RCT (longitudinal, prospective) Case-control study Cross- sectional study

Measure of disease frequency StudyEstimate Case-controlAssociation  odds ratio Cross-sectionalPrevalence  Prevalence ratio Prospective (longitudinal)Incidence  Relative risk, Hazards ratio odds ratio RCTIncidence  Hazards ratio, odds ratio

Fracture (b) No fracture (d) Smoking (a) No smoking (c) Risk factorsOutcome Fracture (b) No fracture (d) Smoking (a) No smoking (c) Risk factorsOutcome Longitudinal study Case-control study Measure of association: Relative risk = a/(a+b) c/(c+d) Odds ratio = a*d b*c Longitudinal and case-control studies

Measure of disease frequency Risk factorCasesControls Presenceab Absencecd TotalN1N2 Case-control study N1 and N2 are pre-determined (fixed) Risk factor at baseline DiseaseNo diseaseTotal PresenceabN1 AbsencecdN2 Prospective study N1 and N2 are fixed at baseline

Risk factor CasesControls Presenceab Absencecd TotalN1N2 Odds ratio (OR) and relative risk (RR) Case-control study Risk factor at baseline DiseaseNo disease Total PresenceabN1 AbsencecdN2 Prospective study When a and c are very small

OR and RR: an example BMDTotalFractureNo- fracture Incidence Low High Prospective study

OR and RR: an example BMDTotalFractureNo- fracture Incidence Low High Prospective study

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 –Bone mineral density (osteoporosis, non-osteoporosis) Follow-up: 1989  2005 –Fracture TotalFractureNo- fracture Osteoporosis Non-osteoporosis

Prognosis (prospective cohort study) TotalFractureNo-fracture Osteoporosis Non-osteoporosis

Diagnostic study Gold standard : biopsy Test: mammography Result of biopsy: cancer, no cancer Result of mammography: +ve, -ve Mammography result Biopsy result CancerNo cancer +veac -vebd Sensitivity = a / (a+b) Specificity = d / (c+d) PPV = ?

Diagnosis – cohort study RANDOMLY selected 1000 individuals Biopsy Mammography Mammography result Biopsy result CancerNo cancer +ve850 -ve2940 Total10990 Sensitivity = 8 / (8+2)= 0.80 Specificity = 940 / ( ) = 0.95 PPV = 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 CancerNo cancer +ve9015 -ve1085 Total100 Sensitivity = 90 / 100 = 0.90 Specificity = 85 / 100 = 0.85 PPV = not estimable

Type I and Type II errors

TRUTHSTATISTICAL TESTNot significant 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 level 1-  : 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 nGroup 1 (mean±SD) Group 2 (mean±SD) Difference(95% CI)P value ± ± ( ) ± ± ( ) Clinical relevance and statistical significance