STEP 1: Imputation by Chained Equations: missing risk factor information Missing risk factor information was imputed using Imputation by Chained Equations. The imputation model contains the variables: injecting drug use, sex, nationality, year at registration and age at registration. The imputation results in one complete dataset X k , containing original and imputed values. STEP 2: Stochastic Mortality Modeling: lacking follow-up of the HIV + /AIDS – cases For a complete dataset k, the number of registered HIV-cases for whom injecting drug use was the most probable route of transmission and who were alive at time t is calculated as ${\stackrel{^}{N}}_{x}^{k}\left(t\right)=\sum _{i=1}^{{n}_{t}}\left({I}_{i}^{k}\left|{X}_{3\phantom{\rule{0.2em}{0ex}}i}^{k}=1\right\right)\left(t\right)\phantom{\rule{0.6em}{0ex}}\mathit{with}\phantom{\rule{0.6em}{0ex}}{I}_{i}^{k}=\left\{\begin{array}{l}0,\phantom{\rule{0.5em}{0ex}}{T}_{d\phantom{\rule{0.2em}{0ex}}i} where I i indicates the ‘vital’ status with I i  = 1 if person i is still alive and living in Belgium and I i  = 0 otherwise, where r i is the number of years since HIV registration or r i  = t − t hi and where p d is the annual non-AIDS mortality rate among seropositive IDUs with p d  ~ betapert*(0.58%, 1.08%, 1.58%). STEP 3: Benchmark-multiplier method: population size estimation The number of ever-injecting drug users being alive at time t is given by ${\stackrel{^}{N}}_{y}^{k}\left(t\right)={\stackrel{^}{p}}_{\mathit{HIV}}^{-1}{\stackrel{^}{N}}_{x}^{k}\left(t\right)-{n}^{-1}{\stackrel{^}{N}}_{x}^{k}\left(t\right)\left(1-{\stackrel{^}{p}}_{\mathit{HIV}}\right){\stackrel{^}{p}}_{\mathit{HIV}}^{-1},$ with ${\stackrel{^}{N}}_{x}^{k}\left(t\right)$ obtained from step 2, ${\stackrel{^}{p}}_{\mathit{HIV}}~\mathit{beta}\left(21,620\right)$ and n = 639. 