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# EPI Qual Formulas by Course.pdf

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Harvard University

Epidemiology

Epidemiology EPI202-01

Murray Mittleman

Fall

Description

EPI Qual Formulas by Course (Methods)
EPI 201
Measures
o Population risk difference (PRD) = R – R = RD * Prev(exposure) =
t unexp
excess incidence in total study population due to exposure
EPI 202
*see roadmap and derivations sheet for most formulas*
Measures
o Prevalence (binomial): # existing cases of a disease / total study population @
a given point
Point
Period: point prevalence + CI over period of time
o t-year Cumulative incidence (binomial): # events that occur between t and t0/ 1
# subjects at risk at time 0 during a certain period of time
o survival = 1 – risk (binomial)
o IR (poisson) = # new cases arising during a given time period / total person-
time of observation at risk and units!
Relationships between measures
o T-year CI = 1-exp{-∑ I ΔT}j j
When IR is constant over Δt, then t-year CI = 1-exp{-I*t}
When IΔt is small (i.e. < 0.1) , C ~ I*t
o P = (I*D) / (1+I*D) where D = average disease duration, P = prevalence
Equivalently, P / (1-P) = I*D
P = I*D for small prevalence (P<0.1)
o Risk difference (function of two binomial) = attributable risk among the
exposed = C –eC non_exp
o Rate difference (function of two poisson) = I – Ie non_expunits of person-time
o Risk Ratio = C / Ce non_exp perform inferences on log scale
o Rate Ratio = I / e non_exp log scale
o NNT (number needed to treat to prevent 1 adverse event) = 1 / RD
Attributable risks
o AR = RD
o AR% = excess fxn = (C – C e non_exp / Ce* 100 = (RR – 1) / RR * 100
o PAR = C – CT non-exp Prev(exposure in population) * AR
o PAR% = (C – C T non_exp / CT= AR% * Prev(exposed|diseased)
o Same for attributable rates, but Pr(E) = prevalence of person-time in the
exposed.
OR = [C /11-C )1 / [C /01-C )]0= [C (11C )] 0 [C (10C )],1where C / C1= CI0. So
when the CI ≠ 1, then the OR > CIR. OR ~ CIR in rare disease.
Sampling fraction = x /1T f1wh1re f /f i1 0he sampling fraction.
x0 T0f 0
o If the controls are sampled independently of exposure, the same fraction is
taken from the exposed and unexposed person-time pools (i.e. controls
represent exposure person-time in study base) so sampling fraction = 1.
1 If binomial distribution:
o Mean = np; variance = npq
o If a proportion: mean = p; variance = [p(1-p)]/n
Matched case-control analysis (using matched data layout)
o Relative efficiency compared to infinite controls = R =EM / (M+1);
M=matching ratio
o OR MH = McNemar’s estimator = f / 10= b01
o RGB variance of the log(OR MH ) = 1/10+ 1/f01 1/b + 1/c
o McNemar’s hypothesis test
H : there is no association
0
Ha: there is an association
Z = [f10 01 ~ Χ 12
f +f
10 01
EPI 203
Power = 1-β = Pr(reject H 0false H 0
o Determined by: effect size, prev(exposure), sample size
β = Pr(accept H 0false H 0 type II error false negative
α = Pr(reject H0| true H0) type I error false positive
Takehome: whether they got treatment is independent of covariates at specific PS.
o PS and treatment modeled separately:
PS = linear combination of covariates
Pr(treatment) = PS + linear combination of other variables
EPI 204
Delta method: Var[G(x)] = Var(X) * [G’(μ)]^2 where X = random variable; μ = mean
of X
Binomial random variable: mean = np (n = M ; p1= Prev(E) = N /T) 1 var = npq
(a/fN1) / (b/f0 )
EPI 289
Sharp causal null: Y a=1= Y a=0
Causal null hypothesis: Pr[Y a=1= 1] = Pr[Y a=0= 1]
No association = independence: Pr[Y=1|A=1] = Pr[Y=1|A=0] ~ A indep. Y ~ Y indep.
A.
o Conditional independence: Y indep. A|B=b for all b.
Confounding: Pr[Y = 1] is NOT equal to Pr[Y=1|A=a]
a
Associational RR: Pr[Y=1|A=1] / Pr[Y=1|A=0]
Causal RR: Pr[Y a=1= 1] / Pr[Ya=0 = 1]
Exchangeability: Y iadep. A for all a (i.e. Pr[Y a1|A=a] = Pr[Y =a])
o Conditional exchangeability: Y inaep. A|L=l for all a
2 Consistency: Pr[Y=1|A=a] = [Y =1|a=a]
Standardization/IPW: ∑ PrlY=1|L=l, A=a]Pr[L=1] = ∑ Pr[Y =1lL=l]Pa[L=1] =
Pr[Y a 1] weight in standard population of interest
PS = Pr[A=1|L]; under conditional exchangeability given L, there is conditional
exchangeability given PS
o A and L are conditionally independent given PS
o Given PS, L doesn’t provide any info about the probability of the subject
being exposed.
o IPW is a PS method
IPW weight = unstabilized weight = W = 1 / f[A|L]
Stabilized weight (better for modeling and dynamic regimes) = SW = f[A] / f[A|L]
IV estimator: average effect of A on Y = effect of Z on Y / effect of Z on A
E[Y a=1] – E[Y a=0 {E[Y|Z=1] – E[Y|Z=0]} / {E[A|Z=1] – E[A|Z-0]}
To solve selection bias issue, we must assume conditional exchangeability between
censored and uncensored: Y incep. C|A=a, L=l for c=0 (not censored) – b/c using
uncensored data to represent censored people.
o W* = 1 / Pr[C=0|A,L]
To adjust for confounding and selection bias, multiply W x W*
Hazard = Pr[Y =t+1 =0]1i.e. hazard at t1 = Pr[Y =1]1 hazard at t2 = Pr[Y =1|2 =0] 1
Using sta

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Related notes for Epidemiology EPI202-01