Prevalence (proportion) 1. 1991 23.8 2. 1960 52 85 2477 310 cross sectional study prevalence Time referent: prevalence 1985 40 45 prevalence 0.5 80 85 43 Time referent 1985 time referent Risk and Cumulative incidence Risk Cumulative incidence 1. 8 1 12.5 2. 100 3. 0 1
4. I 5 35 Prevalence risk/cumulative incidence point 11 1 100 1 1 A 10 12 B 12 12.565 12.5 65 0 65 12.5 (or cumulative incidence: CI) cohort study t-year C = cohort study Framingham Heart Study* 30 39 789 12 40 12 cumulative incidence 40/789 = 5% *Framingham cohort study 40 1000 2
Incidence rate (variable time at entry) (loss to follow-up) person-time 90 91 92 93 94 95 96 97 98 99 00 10 2 8 3 6 4 6.5 5 2 6 3.5 7 3 8 10 9 9 10 4 62 person-years 3 incidence rate = 3 /62 person-years 10,100,,,10,000 1 100 =48.4/1,000 person-years rate rate person-time cumulative incidence rate, prevalence rate rate prevalence, cumulative incidence 0 1 (0 100%) Rate (proportion) Incidence rate = ()/(person-time ) 1975 Framingham study 35 5000 General Motors 2500 1990 50 15 3
cumulative incidence 1% 5 Harvard School of Public Health 2500 100 CI Loss of follow up bias incidence rate Competing risks cumulative incidence risk Q Q 2 2 Q cumulative incidence incidence rate person-year (mouse year?) competing risks Q incidence rate cumulative incidence cumulative incidence incidence rate competing risks cumulative incidence incidence rate (IR) IR cumulative incidence 4
loss of follow-up, competing risks incidence rate 5
Incidence rate Cumulative incidence Incidence rate Cumulative incidence IR CI 20 T year C = 1 exp.{- I j T j } 50 20 50-5 4 55-5 9 60-6 4 65-6 9 Incidence rate I j T j (1983-7) T j 221.1/100,000 PY 5 1105.5/100,000 PY 272.1/100,000 PY 5 1360.5/100,000 PY 334.8/100,000 PY 5 1674.0/100,000 PY 392.3/100,000 PY 5 1961.5/100,000 PY 20 year C = 1 exp.{- I j T j } = 5.9% 50 70 6 incidence rate t-year C = 1 - exp.{- IT} 65 5 69 incidence rate 20-year C = 1 - exp.{- 0.003923 x 5}=1.94% I j T j < 0.1 t year C = I j T j I IT<0.1 t-year C = IT 6
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Incidence rate Prevalence Incidence rate (I), Prevalence (P), Duration (D) P = ID / (1 + ID) ID (P < 0.1) Or P/(1 P) = I x D (odds of disease) (prevalence) P/(1 P) P incidence rate P ID (P < 0.1) Prevalence incidence rate duration Incidence rate Duration (D) Prevalence (P) (I) 3/100,000 PY 25 years 75/100,000 40/100,000 PY 1 years 40/100,000 10,000/100,000 PY 3 days 82/100,000 incidence rate incidence rate prevalence 10 I prevalence 8
Difference measure Risk difference (RD) = Ce Cu = attributable risk ( ) Ce: cumulative incidence of exposed group, Cu: cumulative incidence of unexposed group -1 < RD < +1 RD 12 7 19 14 16 30 C 12/14 7/16 RD = 12/14 7/16 = 42% 42 Rate difference (RD) = Ie Iu Ie: incidence rate of exposed group, Iu: incidence rate of unexposed group - < RD < + RD 41 15 Person-years 28,010 19,017 IR 41/28,010 15/19,017 RD = 6.71 / 10,000 PY Ratio measure Risk ratio (RR) = Ce / Cu = relative risk RD RR 12 7 19 9
14 16 30 C 12/14 7/16 RR = (12/14) / (7/16) = 1.96 RR 96 RR 2 10 49 {RR 0.51} incidence rate incidence rate ratio (RR) = Ie / Iu relative risk 41 15 Person-years 28,010 19,017 IR 41/28,010 15/19,017 RD = {41 28,010PY}/{15/19,017} = 1.85 2 85 RR RD 0 RR RD PY 1970 vinyl chloride 1,000 10 20 3.33/10 8 PYRD = 1000 x 3.3/10 8 PY - 3.3/10 8 PY= 3.297 / 10 5 PY RD vinyl chloride vinyl chloride 10
Incidence rate / 10 5 person-years RD/ 10 5 PY RR (21-39 cig/day) 55-64 501 969 468 1.93 65-74 1,015 1,710 695 1.68 RD RR RD RR RD effect modification Incidence rate / 10 5 person-years RD/ 10 5 PY RR (21-39 cig/day) 55-64 40 400 360 10 65-74 80 720 640 9 RD 10 RR RD effect modification RD RR RD RR 11
Attributable risk (rate) & population attributable risk (rate) Attributable risk risk difference (RD) AR = RD = [C exposed C unexposed ] 0.86 0.44 risk difference (attributable risk) 0.42 42 Population attributable risk (PAR) PAR = Pr (E) x [C exposed C unexposed ] 25 0.25 x 0.42 = 0.105 (10.5%) Attributable risk percent (AR%) = etiologic fraction, relative excess incidence, attributable proportion AR% = [C exposed C unexposed ]/ C exposed x 100 = [RR - 1]/ RR x 100 = [OR - 1]/ OR x 100 (65-74 ) AR% = (9 1) / 9 x 100 = 89% (65-74 ) AR% = (1.68 1) / 1.68 x 100 = 40% 90 40 Population attributable risk percent (PAR%) exposure PAR% AR% PAR% = AR% x Pr (E=1/D=1) AR% RR=1.96, 19 12 APR% = [(1.96 1)/1.96] x 12/19 = 0.31 1/3 12
Q incidence prevalence (duration) Q2: prevalence incidence rate Incidence rate incidence rate prevalence Q3:65 1000 100 10 200 prevalence 100/1000 = 0.10 cumulative incidence 100 200 / 900 = 0.22 Q4 100 5 20 Cumulative incidence 1 1 incidence rate cumulative incidence Q5: 5 270 18500 21500 Person-years = 5 x [(18500 + 21500) / 2] = 100,000 person-years Incidence rate = 270 / 100,000 = 27 / 10,000 Q6 10 person-year 1 3 0 2 6 2 3 2 1 4 4 2 13
5 4 1 6 8 2 7 4 1 8 5 3 9 5 2 10 3 0 14 / 44 person-months x 12 months = 3.82 /person-year Q7: 500 100 16 40 a. Relative risk (RR) RR = (40/100) / (16/400) = 10 b. AR = RD = (40/100) - (16/400) = 0.36 c. AR% = (C 1 C 0 )/C 1 = (0.4 0.04) / 0.4 = 0.90 AR% = (RR 1)/RR = (10 1) / 10 = 0.90 9 1 d. PAR = Pr (E) x AR = (100/500) x AR = 0.072 100 7.2 36 e. PAR% = Pr(E) x AR% = (40/56) x 0.90 = 0.64 2/3 14