2. Relation Between Incidence and Prevalence
Prevalent number of
cases
Incident number of
cases
average Duration in
disease state
= x
Pn = In x D
3. Disease No disease Person-time Baseline Population
Exposed a b PT1 N1
Not exposed c d PT2 N2
Where,
a = number of persons exposed and with disease
b = number of persons exposed but without disease
c = number of persons unexposed but with disease
d = number of persons unexposed: and without disease
a+c = total number of persons with disease
b+d = total number of persons without disease
4. Risk ratio
A risk ratio (RR), also called relative risk, compares the risk of a health event
(disease, injury, risk factor, or death) among one group with the risk among
another group.
• Risk ratio= RR = “cumulative incidence ratio” = CIR
• = (Risk of disease among exposed)/(Risk of disease among non-exposed)
• = [a/(a+b)]/[c/(c+d)]
• A risk ratio of 1.0 indicates identical risk among the two groups.
• A risk ratio greater than 1.0 indicates an increased risk for the group in the
numerator, usually the exposed group.
• A risk ratio less than 1.0 indicates a decreased risk for the exposed group,
indicating that perhaps exposure actually protects against disease
occurrence.
5. • Risk Ratio
• The risk ratio of 4.99 (about 5) indicates that
risk in the exposed group is 5-times that of the
non-exposed group.
6. Rate ratio
• A rate ratio compares the incidence rates, person-time rates, or mortality
rates of two groups.
• The rate for the group of primary interest is divided by the rate for the
comparison group.
• Rate ratio= RR = “incidence density ratio” = IDR
• = (Rate of disease among exposed)/(Rate of disease among non-exposed)
• = (a/T1)/(c/T2)
7. Risk difference
Risk difference = RD
= (Risk of disease among exposed)-(Risk of disease among non-exposed)
= [a/(a+b)]-[c/(c+d)]
8. Odds Ratio
(Exposure) Odds ratio = OR = EOR
• = (Odds of exposure among diseased )/(Odds of exposure among non-
diseased)
• = (a/c)/(b/d)
• = ad/bc
(Disease) Odds ratio = OR = DOR
• = (Odds of disease among exposed)/(Odds of disease among non-exposed)
• = (a/b)/(c/d)
= ad/bc
• *** Odds ratio is symmetric: EOR = DOR
• *** 1 > Risk Ratio > Rate Ratio > Odds Ratio (Approximate one another when
size of pop at risk declines slowly [i.e. rare disease assumption])
9. OR Interpretation
• OR = measure of the strength of association
between risk factor and outcome
• - OR= 2.0:
– Those exposed to the risk factor have twice the
odds of disease compared to unexposed
10. OR Interpretation
• OR= 0.5: those exposed to the risk factor have
half the odds of disease compared to
unexposed
– Rare diseases: OR is very similar numerically to
the RR
– Common diseases: measure that OR estimates
depends on how controls are sampled
11. We are interested in effects but we measure
associations.
OK to use the effect word when you
describe aims/hypotheses, but not when you
describe actual findings
12. • We compare frequencies of diseases or
states of health (usually prevalence or
incidence) in populations
• Most measures of associations are relative
or absolute for example relative risks or
risk differences
13. • Why is the P-value not a good measure of
association?
P-value quantifies the probability that the
result is due to chance. It does not measure
how big the association or the difference is.
14. • Correlations (associations) can be
generated by the design, the conduct of
the study, the data you use, other
correlated factors (confounders), chance
or by causation.
15. Closed population, no loss to follow-up
Exposure N D Obs time/person years
No
Yes
90,000
10,000
900
500
89,550
9,750
RR = Rexp = 500/10,000 = 5.0
Rnot exp 900/90,000
IRR = IRexp = 500/9750years = 5.1
IRnot exp 900/89,550years
16. Closed population, no loss to follow-up, cont.
RD = Rexp – Rnot exp = 500/10,000 – 900/90,000 = 0.040
IRD = IRexp – IRnot exp = 500/9750 years – 900/89,550years = 0.041 years
-1
• For statistical reasons associations are often
measured as odds ratios (OR).
• The odds ratio is a ratio between 2 odds
