Absolute measures• Measures to be discussed
– Attributable risk (AR) – aka risk/rate difference (RD)– Attributable risk percent (AR%)– Population attributable risk (PAR)– Population attributable risk percent (PAR%)
Absolute measures• Attributable risk (AR) – aka risk/rate difference (RD)• “Risk” in attributable risk used generically to include risk
or rate• Provides information about absolute association
between an exposure and a disease, or the excess risk or rate of disease in the exposed
• AR = Rexposed – Runexposed• Where R indicates either risk or rate – (i.e., CI
(cumulative incidence) or ID (incidence density))
Absolute measures• Interpretations of AR:• Difference in risk/rate of disease between the exposed
and unexposed• Excess risk/rate of disease in the exposed compared
with the unexposed
• AR has same units as the incidence measure used (risk (dimensionless) if CI; rate (1/time) if ID)
Absolute measures
Szklo Figure 3-1
Absolute measures• Example: study of oral contraceptive (OC) use and
bacteriuria among women 16-49 yrsover 1 year
• AR = ?• How do we compare cumulative incidence to estimate
AR?
Absolute measures
• Take difference to estimate AR• AR = CIe – CIu =• AR = (27/482)–(77/1908) = 0.01566• Women who use OCs have 0.01566 higher risk of
bacteriuria compared with women who do not use OCs over 1 year
• Can multiply by a population size to facilitate interpretation: 0.01566x100,000 = 1566/100,000
• Among every 100,000 women who use OCs there are 1566 excess cases of bacteriuria compared with women who do not use OCs over 1 year
Absolute measures• Attributable risk percent (AR%)• Provides information about the excess incidence in the
exposed (AR) as a percentage of incidence in the exposed population
• AR% = (Rexposed – Runexposed) / Rexposed x 100• AR% = AR/ Rexposed x 100
Absolute measures• Interpretations of AR%:• Percentage of all disease incidence among the exposed
that is associated with the exposure• Percentage of disease incidence in the exposed that is
in excess of the incidence in the unexposed
Absolute measures
Szklo Figure 3-1
100% of incidence in the exposed population AR% - percentage of
disease incidence in the exposed that is in excess of the incidence in the unexposed
Absolute measures• AR% = ?• AR% = (CIe – CIu)/CIe x 100• AR% = (27/482)–(77/1908)/(27/482) x 100 = 28%• Of the bacteriuria incidence among women who use
OCs, 28% is in excess of the incidence in women who do not use OCs
Absolute measures• Attributable risk percent (AR%) is analogous to efficacy
for an intervention (e.g., vaccine, other treatment)• The control group is considered “exposed”• The treatment group is considered “unexposed”
• AR% = (Rexposed – Runexposed) / Rexposed x 100
• Efficacy% = (Rcontrol – Rtreatment) / Rcontrol x 100
• Percentage of disease incidence in the control group that is in excess of the incidence in the treatment group
Absolute measures
• Population attributable risk (PAR)• Provides information about the excess risk or rate of
disease in the entire population (not just among the exposed as with AR)– Sometimes the AR is called the “attributable risk among the
exposed” to make this distinction clear• PAR = Rtotal – Runexposed• Alternative formulation:• PAR = (AR)(Pe)
– Pe = prevalence of the exposure in the total population– See extra slides for derivation
• Alternative formulation useful if estimating PAR for a total population other than your study population for which you have an estimate of Pe
Absolute measures• Interpretations of PAR:• Excess risk/rate of disease in the total population
compared with the unexposed
• If association is believed to be causal, PAR can be used to estimate the impact of an exposure on the health of a population of interest
• PAR will never be larger than AR in a given population• PAR has same units as the incidence measure used
(risk (dimensionless) if CI; rate (1/time) if ID)
Absolute measures• PAR = ?• PAR = CIt – CIu=• PAR = (104/2390)–(77/1908) = 0.00316• In the total population of women there is 0.00316 higher
risk of bacteriuria compared with women who do not use OCs
• Can multiply by a population size to facilitate interpretation: 0.00316x100,000 = 316/100,000
• There are 316 excess cases of bacteriuria for every 100,000 women in the total population compared with women who do not use OCs
JC: review NNT
Absolute measures• Comparison of AR and PAR• AR = 1566/100,000• PAR = 316/100,000• PAR < AR
• Why is this the case?
Absolute measures• Population attributable risk percent (PAR%)• Provides information about the excess incidence in the
total population (PAR) as a percentage of incidence in the total population
• PAR% = (Rtotal – Runexposed) / Rtotal x 100• PAR% = (PAR / Rtotal) x 100
Absolute measures• PAR% = ?• PAR% = (CIt – CIu)/CIt x 100• PAR% = (104/2390)–(77/1908)/(104/2390) x 100 =
7.3%• Of the bacteriuria incidence in the total population of
women, 7% is in excess of the incidence in women who do not use OCs
Absolute measures• Comparison of AR% and PAR%• AR% = 28%• PAR% = 7%• PAR% < AR%
• Why is this the case?
Absolute measures
Szklo Figure 3-2
Exposure uncommon in total population
Exposure common in total population
Absolute measures• AR versus PAR
– The AR depends only on the strength of the relation between the exposure and the disease
– The PAR depends both on the strength of the relation and the prevalence of the exposure
Absolute measures••
AR = Rexposed – Runexposed
PAR = Rtotal – Runexposed• Think of Rtotal (risk/rate in total population) as a weighted
average of the risk/rate among the exposed and unexposed
• Weighted by the prevalence of the exposure (Pe):– Rt = (Pe)Re + (Pu)Ru
– Rt = (Pe)Re + (1-Pe)Ru
– When Pe is close to 1 (and 1- Pe is close to 0), Rt is close to Re
and thus PAR is close to AR– When Pe is close to 0 (and 1- Pe is close to 1), Rt is close to Ru
(not Re) and thus PAR is much smaller than AR
Absolute measures
Szklo Figure 3-2
Prevalence of exposure not depicted here, but reflected in different magnitudes of PAR
Pe is close to 0, Rt is close to Ru (not Re) and thus PAR is much smaller than AR
Pe is close to 1, Rt is close to Re and thus PAR is close to AR
– An exposure with a large AR can have a low PAR if the exposure is uncommon
– Example: extremely carcinogenic but rare chemical
• Removing an exposure with a large AR but a small PAR would not improve the overall health of the population appreciably
Absolute measures
Absolute measures• There are some study designs (case-control) for which
measures of disease cannot be estimated – only the odds ratio (OR), a relative measure, can be calculated (more in study design)
• For these studies, there are alternative formulas for the absolute measures that can be applied – they require making some assumptions and/or bringing in outside information
Absolute measures• Alternative formulation for AR%• Additional information/assumptions
– OR estimates risk/rate ratio• AR% = [(OR – 1) / OR] x 100• Alternative formula is a simple algebraic transformation
of original formula– Dividing (Re – Ru) / Re by Ru
– ((Re/Ru)-(Ru/Ru)) / (Re/Ru)– (RR-1)/RR– RR estimated by OR*
– *How well OR estimates risk or rate ratio depends on design of case-control study and on how common disease is for cumulative case-control
Absolute measures• Alternative formulation for PAR%• Additional information/assumptions
– OR estimates risk/rate ratio– Prevalence of exposure in the total population can be estimated as the proportion of
non-diseased individuals exposed, or from another source: Pe
• – PAR% = [((Pe)(OR-1)) / ((Pe)(OR-1) + 1)] x 100
• Note Miettinen 1974 other formulation– PAR% = AR% x (proportion exposed among diseased)– Will provide a different estimate than formulation above
Absolute measures• Derivation of alternative formula for PAR%• Think of Rtotal (risk/rate in total population) as a weighted
average of the risk/rate among the exposed and unexposed
• Weighted by the prevalence of the exposure:– Rt = (Re)(Pe) + (Ru)(1-Pe)
• Substitute into original equation– PAR% = (Rt – Ru)/ Rt
– PAR% = ((Re)(Pe) + (Ru)(1-Pe) – Ru)/ (Re)(Pe) + (Ru)(1-Pe)– PAR% = ((Re)(Pe) + (Ru)-(RuPe) – Ru)/ (Re)(Pe) + (Ru)-(RuPe)
Absolute measures• Divide numerator and denominator by Ru
– PAR% = ((Re)(Pe)/Ru + 1 - Pe–1)/ (Re)(Pe)/Ru + 1-Pe
– PAR% = ((Re)(Pe)/Ru - Pe)/ (Re)(Pe)/Ru - Pe+ 1– PAR% = (Pe(Re/Ru - 1)/ Pe(Re/Ru – 1) + 1
• Note that RR = Re / Ru therefore if OR estimates RR– PAR% = [(Pe)(OR-1)] / [(Pe)(OR-1) + 1]
Absolute measures• Alternative formulation for AR, PAR• Additional information/assumptions
– OR estimates risk/rate ratio– Prevalence of exposure in the total population can be estimated
as the proportion of non-diseased individuals exposed, or from an outside source: Pe
– Risk/rate for the total population can be estimated, usually from an outside source: Rt
• Ru = (Rt) / ((OR)(Pe) + (1- Pe))• Re = (OR)(Ru)• AR = Re-Ru
• PAR = Rt-Ru
Absolute measures• Derivation of alternative formulas for AR and PAR• Think of Rtotal (risk/rate in total population) as a weighted
average of the risk/rate among the exposed and unexposed
• Weighted by the prevalence of the exposure:– Rt = (Re)(Pe) + (Ru)(1- Pe)
• Note that RR = Re / Ru therefore if OR estimates RR– Re = (OR)(Ru)– Rt = (OR)(Ru)(Pe) + (Ru)(1- Pe)
• Solve for Ru
– Ru = (Rt) / ((OR)(Pe) + (1- Pe))– Re = (OR)(Ru)
Absolute measures• Formula review
– AR = Rexposed – Runexposed
– AR% = [(Rexposed – Runexposed) / Rexposed] x 100– PAR = Rtotal – Runexposed– PAR = (AR)(Pe)– PAR% = [(Rtotal – Runexposed) / Rtotal] x 100
– AR% = [(OR – 1) / OR] x 100– PAR% = [((Pe)(OR-1)) / ((Pe)(OR-1) + 1)] x 100– AR = (OR)(Ru) - (Rt / [(OR)(Pe) + (1- Pe)])– PAR = Rt - [(Rt)/ ((OR)(Pe) + (1- Pe))]
