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Number needed to treet

1/(PoP1) = 1/RD


Utility of Risk Risk Difference

RD can have more clinical/public health meaning since is characterizes absolute risk


RR vs. RD

RR is less dependent upon the underlying population.
RD provides incidence information. No methods to do multivariate RD. 

2 reasons to use OR

1) Logistic regression for fixed (defined) cohort studies.
2) Casecontrol estimates 

OR can estimate RR if

D is infrequent in both E+ and E
min(Po,P1)<0.1 (10%) 

Major problems with risk, incidence, and odds information

They do not measure the health "impact" of a particular exposure.


Attributal fraction

Proportion of the disease occurence that would be eliminated if exposure to the risk factor were prevented


Attributable fraction: Synonyms

Etiologic fraction
attributable proportion attributable risk population attributable risk (percent) 

Who is the Attrubutable fraction calculated for?

1) E+ group
2) Entire population 

Attributable fraction for the exposed (discription)

Proportion of cases in the E+ group attributable to E.
Eg. Among NSAID users, what proportion of peptic ulcers are caused by NSAIDS? 

Attributable fraction for the exposed (Eqn)

(P1Po)/P1 (risk data)
(I1Io)/I1 (rate data) (RR1)/RR (risk data) (IRR1)/IRR (rate data) (OR1)/OR (rare disease assumption) 

Attributable fraction for Population (disc)

Proportion of cases in the population attributable to E.
Eg. For a given patient population, what proportion of peptic ulcers are caused by NSAIDS? (need strength of the association between E and D and prevalence of E+) 

Attributable fraction for Population (eqns)

(PPo)/P (risk)
(IIo)/I (rate) ¶(RR1)/[1+¶(RR1)] (risk) ¶(IRR1)/[1+¶(IRR1)] (rate) ¶c(OR1)/OR (Odds) 

Attributable Fraction for population (¶ and ¶c)

¶ = N1/N (proportion exposed in cohort for risk data)
¶ = T1/T (Proportion exposed for persontime for rates) ¶c = a/(a+b) (exposure prevalence in D+ for rare D) 

Attributable fraction for exposed (protective exposures) (disc)

Also called prevented fraction or effictiveness.
Often used in vaccine studies 

Attributable fraction for exposed (protective exposures)(eqn)

1)(PoP1)/P1
1)1RR 

Marginal costeffecitiveness

(Difference in cost)/(Events prevented)
See 812 