From: Should Men who have sex with Men be allowed to donate blood in Israel?
The total expected number of transmission acquired HIV cases is = BLOOD x T x (A + B + C + D) |
Where A is the number of infected donors, who donate despite knowing they are HIV+ A = POP x PREV x INFDON x (1-(1-((1-S_{NAT}) x (1-S_{EIA})))) |
Where B is the number of infected donors during the windows period where neither the Nucleic Acid Test nor ELISA test can detect HIV. B = PSC x W_{NAT}/(365.25 x YRS_{PS}) PSC = POP x INC x YRS_{PS} x DON |
Where C is the number of infected donors, who were asymptomatic and were not detected due to false-negative screening results resulting from the period where only the Nucleic Acid Test (but not the ELISA) can detect HIV (C_{1}) and the period where both NAT and ELISA can detect HIV (C_{2}). C = C_{1} + C_{2} C_{1} = PSC x (1-S_{NAT}) *(W_{NAT-}W_{EIA})/(365.25 x YRS_{PS})) C_{2} = PSC x (YRS_{PS}-W_{EIA}/365.25)/YRS_{PS} x (1-S_{NAT}) x (1-S_{EIA}) |
Where D is the number of infected donors who are correctly detected but whose blood nevertheless is allowed to be donated due to laboratory misclassification errors. D = (PSC + (POP x PREV x INFDON)- 2 (A + B + C)) x LAB BLOOD = the average number of persons who become infected via transfusions from a single infected donor T = Probability that recipient of infected blood donation will become infected (%) POP = numbers aged 18–69 in group. DON = Percentage of people in group who donate blood (%) INFDON = Percentage of people who know they are HIV+ but nevertheless donate. PREV = Prevalence rate INC = Incidence rate per annum YRS_{PS} = Pre-symptomatic period: average length of time from infection to symptoms (years) based on weighted average of first-time to repeat donors over the 10 year period PSC = Number of pre-symptomatic donors B_{1} = number of infected donors during the window period of the Nucleic Acid Test. B_{2} = number of infected donors during period when the Nucleic Acid Test is working but EIS is still in window period S_{NAT} = Sensitivity of the Nucleic Acid Test W_{NAT} = Duration of the Nucleic Acid Test window period (days) S_{EIA} = Sensitivity of the anti-HIV test W_{EIA} = Duration of the anti-HIV window period (days) LAB = Laboratory misclassification error rate (%) |