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# Table 1 Schematic overview of the 3-step Monte Carlo simulation model to estimate ever IDU prevalencesƗ

 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 $N ^ x k t = ∑ i = 1 n t I i k X 3 i k = 1 t with I i k = 0 , T d i < t or T l i < t 1 , T a i ≥ t or T d i ≥ t or T l i ≥ t S i ~ bern 1 - p d r i , otherwise ,$ 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 $N ^ y k t = p ^ HIV - 1 N ^ x k t − n - 1 N ^ x k t 1 − p ^ HIV p ^ HIV - 1 ,$ with $N ^ x k t$ obtained from step 2, $p ^ HIV ~ beta 21 , 620$ and n = 639.
1. Ɨ The model was run K = 1000 times.
2. * The betapert distribution is mainly used to model expert estimates and requires a minimum, most likely and maximum value. 