Table S1. Comparison between each data point and the posterior mean estimates, for each of

Table S1. Comparison between each point and the posterior mean estimates, for each of Risk group size % Males models M1 to M4. The posterior mean deviance is shown in parentheses Data Baseline model Revised NSHPC correction correction + Hierarchical structure Current IL 3.9 4.03 (1) 4.03 (0.9) 4.13 (0.9) 4.14 (0.9) Homosexual OL 0.7 0.81 (1) 0.78 (0.9) 0.80 (1) 0.80 (0.9) GUM attenders REW 0.8 0.80 (1) 0.81 (1) 0.81 (1) 0.80 (1) Current IL 3.4 3.60 (1) 3.60 (0.9) 3.62 (1) 3.62 (1) Homosexuals OL 3.3 3.42 (1) 3.42 (1) 3.44 (1) 3.43 (1) not GUM attenders REW 1.4 1.40 (1) 1.41 (1) 1.41 (1) 1.41 (1) Past Homosexuals IL 0.9 1.16 (1)p 1.15 (1) 1.15 (1.1) 1.16 (1.1) OL 1.2 1.35 (1) 1.35 (1) 1.36 (1) 1.36 (1) REW 0.4 0.39 (1) 0.39 (1) 0.39 (1) 0.39 (1) Current IL 1.1 0.70 (1.4) 0.69 (1.4) 0.69 (1.4) 0.80 (0.8) IDUs OL 1.0 0.49 (2.9) 0.49 (2.9) 0.50 (2.9) 0.57 (1.9) REW 1.2 1.26 (1) 1.25 (1) 1.26 (1) 1.24 (0.9) Past IL 1.1 0.64 (1.7) 0.63 (1.7) 0.64 (1.7) 1.20 (0.9) IDUs OL 0.6 0.27 (2.1) 0.27 (2.1) 0.27 (2.1) 0.67 (0.9) REW 0.7 0.69 (1) 0.69 (1) 0.69 (1) 0.67 (1) GUM IL 10.1 10.20 (1) 10.1 1 (1) 10.23 (1) 10.11 (0.8) OL 7.3 7.36 (1) 7.38 (1) 7.41 (1) 7.52 (0.9) REW 5.0 5.03 (1) 5.02 (1) 5.02 (1) 5.09 (1) SSA IL 8.3 8.32 (1) 8.32 (1) 8.32 (1) 8.32 (1) OL 6.6 6.59 (1) 6.59 (1) 6.59 (1) 6.59 (1) REW 1.0 1.03 (1) 1.03 (1) 1.03 (1) 1.03 (1) Females Current IL 0.3 0.40 (0.7) 0.40 (0.6) 0.37 (0.6) 0.31 (0.3) IDUs OL 0.3 0.39 (0.7) 0.39 (0.7) 0.39 (0.7) 0.20 (0.7) REW 0.4 0.38 (0.9) 0.38 (0.9) 0.38 (0.9) 0.40 (0.9) Past IL 0.5 0.51 (0.6) 0.51 (0.7) 0.53 (0.6) 0.69 (0.8) IDUs OL 0.2 0.31 (0.7) 0.31 (0.7) 0.32 (0.7) 0.36 (0.8) REW 0.2 0.20 (0.9) 0.20 (0.9) 0.20 (0.9) 0.21 (0.9) GUM attenders IL 11.9 12.05 (0.9) 11.7 6 (0.9) 10.98 (1.2) 10.9 (1.1) OL 7.3 7.51 (1) 7.48 (1) 7.28 (1) 7.29 (0.8) REW 5.5 5.49 (1) 5.50 (1) 5.49 (1) 5.44 (1) SSA IL 9.2 9.22 (1.1) 9.21 (1) 9.21 (1) 9.21 (1) OL 7.2 7.20 (1) 7.20 (1) 7.20 (1) 7.20 (1) REW 1.0 1.03 (1) 1.03 (1) 1.03 (1) 1.03 (1) 1

Data Baseline model Revised NSHPC correction correction + Hierarchical structure Seroprevalence % Current Male IDUs IL 6.02 3.3 (3.5) 3.3 (3.4) 3.3 (3.4) 4.5 (1.4) OL 4.73 1.94 (6.2) 1.96 (6.1) 1.95 (6.2) 2.13 (5.1) REW 0.24 0.26 (0.1) 0.26 (0.1) 0.26 (0.1) 0.29 (0.6) Current Female IL 4.76 3.49 (0.7) 3.49 (0.7) 3.41 (0.7) 5.55 (0.3) IDUs OL 1.41 0.85 (0.5) 0.86 (0.5) 0.87 (0.5) 2.64 (0.7) REW 0.37 0.41 (0.1) 0.41 (0.1) 0.42 (0.1) 0.36 (0.3) Female SSA IL 2.45 3.96 (34) 3.51 (18.2) 2.43 (0.6) 2.49 (0.6) OL 2.29 3.42 (18.2) 3.02 (8.5) 2.11 (1.2) 2.15 (0.9) REW 1.56 2.94 (11.6) 2.59 (7.1) 1.67 (0.4) 1.72 (0.5) Female IL 0.09 0.15 (7.5) 0.14 (6) 0.14 (4.7) 0.14 (4.9) non-ssa OL 0.06 0.07 (1.3) 0.07 (0.6) 0.06 (0.4) 0.06 (0.4) REW 0.02 0.03 (1.2) 0.02 (0.3) 0.02 (0.4) 0.02 (0.5) All Females IL 0.39 0.50 (4.2) 0.45 (1.5) 0.43 (0.8) 0.43 (0.7) Prevalence of undiagnosed HIV % OL 0.26 0.31 (1.8) 0.28 (0.4) 0.27 (0.3) 0.26 (0.2) REW 0.04 0.06 (10.7) 0.05 (3.7) 0.04 (0.9) 0.04 (0.9) Homosexuals IL 4.57 4.68 (1) 4.68 (1) 4.68 (1) 4.67 (1) GUM attenders OL 3.51 4.02 (0.8) 4.01 (0.8) 4.05 (0.8) 4.11 (0.8) REW 1.97 1.64 (1) 1.64 (1) 1.64 (1) 1.63 (1) Male IL 0.43 0.49 (1) 0.49 (1) 0.49 (1) 0.43 (1) GUM attenders OL 0.17 0.21 (0.9) 0.21 (0.9) 0.22 (0.9) 0.26 (0.7) REW 0.09 0.08 (1) 0.08 (1) 0.08 (1) 0.08 (0.6) Female IL 0.32 0.33 (0.9) 0.33 (0.9) 0.30 (1.4) 0.33 (0.8) GUM attenders OL 0.20 0.27 (1) 0.26 (0.9) 0.25 (0.7) 0.20 (0.4) REW 0.07 0.06 (1) 0.06 (1.1) 0.06 (1) 0.06 (0.6) Proportion reported diagnosed % Male Current Il 69 68 (1.1) 68 (1.1) 68 (1.1) 66 (1.6) IDUs OL 53 51 (1.1) 51 (1.1) 51 (1.1) 56 (1.3) REW 52 51 (1) 51 (1) 51 (1) 51 (1) Female Il 60 59 (1) 59 (1) 60 (0.9) 70 (2.3) Current OL 73 72 (1) 72 (1) 72 (1) 63 (3.5) IDUs REW 56 56 (1) 56 (1) 56 (1) 57 (0.9) Female SSA IL 40, 58 59 (28.9) 68 (8.8) 59 (0.9) 59 (0.9) OL 30, 47 50 (23.7) 58 (7) 45 (1) 45 (1) REW 13, 29 39 (32.9) 45 (9.6) 33 (1.1) 32 (1) Female IL 36, 46 54 (6.5) 57 (2.8) 46 (0.6) 44 (0.6) not- SSA OL 27, 37 41 (2.6) 44 (1.1) 35 (0.6) 35 (0.6) REW 26, 38 41 (6.8) 47 (2.8) 39 (0.8) 39 (0.8) 2

Data Baseline model Revised NSHPC correction correction + Hierarchical structure SOPHID Males Fraction of cases, % Homosexual IL 81 80 (1) 80 (1) 80 (1) 81 (0.9) OL 58 57 (1) 57 (1) 57 (1) 57 (1) REW 71 71 (1) 71 (1) 71 (1) 71 (0.9) IDUs IL 15 15 (1.1) 15 (1.1) 15 (1.1) 15 (1) OL 8 8 (1.4) 8 (1.4) 8 (1.4) 8 (1.1) REW 17 17 (1) 17 (1) 17 (1) 17 (1) SSA IL 68 68 (1) 68 (1) 68 (1) 68 (1) OL 70 70 (1) 70 (1) 70 (1) 70 (0.9) REW 37 37 (1) 37 (1) 37 (1) 37 (0.9) Total cases, counts IL 6237 6244 (1) 6243 (1) 6243 (1) 6237 (1) OL 1790 1798 (1) 1798 (1) 1797 (1) 1800 (1) REW 5054 5056 (1) 5056 (1) 5056 (1) 5055 (1) Females Fraction of cases, % SSA IL 6 6 (1.1) 6 (1) 6 (1) 6 (1) OL 2.2 2 (1.1) 2 (1) 2 (1) 2 (1) REW 6 6 (1) 6 (1) 6 (1) 6 (1) IDUs IL 80 79 (1.2) 79 (1) 80 (1) 80 (1) OL 84 84 (1.1) 84 (1) 84 (1) 84 (0.9) REW 56 56 (1.3) 56 (1.1) 56 (1) 56 (1) Total cases, counts IL 2087 1981 (6.5) 2014 (3.5) 2078 (1) 2079 (0.9) OL 1441 1382 (3.5) 1407 (1.8) 1452 (1) 1446 (0.9) REW 1876 1819 (2.8) 1843 (1.6) 1872 (1) 1873 (0.9) NOTE. IL: Inner London, OL: Outer London and REW: Rest of England and Wales 3

Table S2. Posterior mean (standard deviation) of risk group size, prevalence, prevalence of undiagnosed infection and probability of diagnosis. Baseline model correction correction + Group size, % Males Male Homosexuals IL 8.8 (1.6) 8.78 (1.53) 8.90 (1.59) 8.92 (1.58) OL 5.6 (1.1) 5.56 (1.06) 5.60 (1.05) 5.59 (1.05) REW 2.6 (0.2) 2.60 (0.25) 2.60 (0.25) 2.59 (0.24) Current IL 4.1 (1.1) 4.03 (1.03) 4.13 (1.08) 4.14 (1.06) Homosexual OL 0.8 (0.4) 0.78 (0.39) 0.80 (0.41) 0.80 (0.39) GUM attenders REW 0.8 (0.1) 0.81 (0.14) 0.81 (0.14) 0.80 (0.14) Current IL 3.6 (1) 3.60 (0.98) 3.62 (1.02) 3.62 (1.02) Homosexuals OL 3.5 (0.8) 3.42 (0.83) 3.44 (0.82) 3.43 (0.82) not GUM attenders REW 1.4 (0.2) 1.41 (0.18) 1.41 (0.18) 1.41 (0.18) Past IL 1.2 (0.6) 1.15 (0.58) 1.15 (0.59) 1.16 (0.59) Homosexuals OL 1.4 (0.5) 1.35 (0.52) 1.36 (0.53) 1.36 (0.53) REW 0.4 (0.1) 0.39 (0.09) 0.39 (0.09) 0.39 (0.09) All IDUs IL 1.3 (0.5) 1.33 (0.47) 1.33 (0.47) 2.00 (0.62) OL 0.8 (0.3) 0.76 (0.31) 0.77 (0.31) 1.24 (0.41) REW 1.9 (0.2) 1.94 (0.21) 1.95 (0.21) 1.92 (0.2) Current IL 0.7 (0.3) 0.69 (0.34) 0.69 (0.33) 0.80 (0.29) IDUs OL 0.5 (0.2) 0.49 (0.23) 0.50 (0.24) 0.57 (0.22) REW 1.3 (0.2) 1.25 (0.17) 1.26 (0.17) 1.24 (0.16) Past IL 0.6 (0.3) 0.63 (0.31) 0.64 (0.31) 1.20 (0.58) IDUs OL 0.3 (0.2) 0.27 (0.16) 0.27 (0.16) 0.67 (0.36) REW 0.7 (0.1) 0.69 (0.12) 0.69 (0.13) 0.67 (0.12) GUM IL 10.2 (1.7) 10.11 (1.63) 10.2 3 (1.66) 10.11 (1.49) attenders OL 7.4 (1.2) 7.38 (1.18) 7.41 (1.18) 7.52 (1.13) REW 5.0 (0.3) 5.02 (0.33) 5.02 (0.33) 5.09 (0.33) SSA IL 8.3 (0.03) 8.32 (0.032) 11.6 9 (0.88) 11.28 (0.89) OL 6.6 (0.03) 6.59 (0.025) 9.32 (0.72) 8.99 (0.72) REW 1.0 (3) 1.03 (3) 1.50 (0.13) 1.44 (0.13) Females All IDUs IL 0.9 (0.4) 0.91 (0.44) 0.89 (0.43) 1.00 (0.42) OL 0.7 (0.4) 0.70 (0.36) 0.71 (0.37) 0.56 (0.27) REW 0.6 (0.1) 0.58 (0.11) 0.58 (0.11) 0.61 (0.11) Current IL 0.4 (0.3) 0.40 (0.29) 0.37 (0.27) 0.31 (0.16) IDUs OL 0.4 (0.3) 0.39 (0.26) 0.39 (0.26) 0.20 (0.1) REW 0.4 (0.1) 0.38 (0.09) 0.38 (0.09) 0.40 (0.09) Past IL 0.5 (0.3) 0.51 (0.33) 0.53 (0.32) 0.69 (0.42) IDUs OL 0.3 (0.2) 0.31 (0.23) 0.32 (0.23) 0.36 (0.26) REW 0.2 (0.1) 0.20 (0.07) 0.20 (0.07) 0.21 (0.07) 4

Baseline model correction correction + GUM IL 12.0 (1.7) 11.76 (1.7) 10.9 8 (1.63) 10.90 (1.46) attenders OL 7.5 (1.2) 7.48 (1.23) 7.28 (1.21) 7.29 (1.11) REW 5.5 (0.4) 5.50 (0.36) 5.49 (0.36) 5.44 (0.35) SSA IL 9.2 (0.03) 9.21 (0.033) 12.8 8 (0.95) 12.43 (0.96) OL 7.2 (0.03) 7.20 (0.026) 10.1 6 (0.77) 9.79 (0.78) REW 1.0 (3) 1.03 (3) 1.49 (0.13) 1.44 (0.13) Prevalence, % Male Homosexuals IL 12.2 (1.8) 12.2 (1.7) 12.2 (1.7) 12.2 (1.7) OL 3.9 (1.3) 3.9 (1.2) 3.9 (1.2) 4.0 (1.2) REW 2.7 (0.3) 2.7 (0.3) 2.7 (0.3) 2.7 (0.3) Current IL 15.8 (7.5) 15.9 (7.3) 14.9 (7) 15.2 (7.3) Homosexual OL 14.4 (9.4) 14.2 (9.7) 14.0 (9.6) 13.6 (7.8) GUM attenders REW 4.4 (1.9) 4.4 (1.8) 4.4 (1.9) 4.7 (1.9) Current IL 11.7 (7.8) 11.8 (7.7) 12.8 (8.1) 12.1 (8.2) Homosexuals OL 3.0 (1.8) 3.1 (1.8) 3.0 (1.8) 3.1 (1.8) not GUM attenders REW 2.3 (1) 2.3 (1.1) 2.2 (1.1) 2.1 (1.1) Past IL 3.5 (10.1) 2.8 (7.2) 2.97 (7.27) 4.09 (11.67) Homosexuals OL 1.4 (1.6) 1.3 (1.6) 1.48 (1.91) 1.39 (1.61) REW 0.6 (0.9) 0.7 (1.1) 0.72 (1.12) 0.64 (0.88) All IL 3.3 (1.1) 3.32 (1.18) 3.33 (1.16) 2.31 (0.74) IDUs OL 2.0 (0.8) 1.96 (0.78) 1.95 (0.78) 1.10 (0.39) REW 0.3 (0.04) 0.26 (0.04) 0.26 (0.04) 0.28 (0.04) Current IL 3.3 (1.1) 3.32 (1.18) 3.33 (1.16) 4.49 (1.37) IDUs OL 2.0 (0.8) 1.96 (0.78) 1.95 (0.78) 2.13 (0.77) REW 0.3 (0) 0.26 (0.04) 0.26 (0.04) 0.29 (0.09) Past IL 3.3 (1.1) 3.32 (1.18) 3.33 (1.16) 0.86 (0.76) IDUs OL 2.0 (0.8) 1.96 (0.78) 1.95 (0.78) 0.26 (0.29) REW 0.3 (0) 0.3 (0.04) 0.26 (0.04) 0.3 (0.14) GUM IL 0.9 (0.2) 0.9 (0.18) 0.92 (0.17) 0.78 (0.18) attenders OL 0.4 (0.2) 0.4 (0.18) 0.46 (0.18) 0.45 (0.16) REW 0.2 (0.1) 0.2 (0.06) 0.20 (0.06) 0.18 (0.07) SSA IL 2.9 (0.2) 2.4 (0.14) 1.56 (0.13) 1.41 (0.16) OL 2.5 (0.2) 2.1 (0.16) 1.41 (0.14) 1.19 (0.17) REW 2.4 (0.3) 2.0 (0.21) 1.22 (0.16) 0.95 (0.16) Low Risk IL 0.04 (0.029) 0.030 (0.025) OL 0.04 (0.02) 0.029 (0.018) 0.01 8 (0.02) 0.032 (0.025) 0.01 9 (0.015) 0.026 (0.017) 5

Baseline model correction correction + REW 0.02 (5) 0.014 (4) 8 (5) 0.010 (6) Female All IDUs IL 3.5 (1.8) 3.5 (1.83) 3.41 (1.76) 2.8 (1.15) OL 0.9 (0.5) 0.9 (0.53) 0.87 (0.55) 1.2 (0.6) REW 0.4 (0.1) 0.4 (0.09) 0.42 (0.1) 0.4 (0.08) Current IL 3.5 (1.8) 3.49 (1.83) 3.41 (1.76) 5.55 (1.88) IDUs OL 0.9 (0.5) 0.86 (0.53) 0.87 (0.55) 2.64 (1.04) REW 0.4 (0.1) 0.41 (0.09) 0.42 (0.1) 0.36 (0.13) Past IL 3.5 (1.8) 3.49 (1.83) 3.41 (1.76) 1.41 (1.29) IDUs OL 0.9 (0.5) 0.86 (0.53) 0.87 (0.55) 0.43 (0.54) REW 0.4 (0.1) 0.41 (0.09) 0.42 (0.1) 0.43 (0.27) GUM IL 0.6 (0.2) 0.63 (0.18) 0.65 (0.19) 0.68 (0.17) attenders OL 0.4 (0.2) 0.44 (0.17) 0.45 (0.17) 0.39 (0.14) REW 0.1 (0.1) 0.14 (0.06) 0.16 (0.06) 0.16 (0.06) SSA IL 4.0 (0.2) 3.51 (0.14) 2.43 (0.16) 2.49 (0.17) OL 3.4 (0.2) 3.02 (0.16) 2.11 (0.16) 2.15 (0.16) REW 2.9 (0.3) 2.59 (0.21) 1.67 (0.18) 1.72 (0.18) Low Risk IL 0.05 (0.03) 0.04 (0.027) 0.03 3 (0.026) 0.032 (0.024) OL 0.04 (0.019) 0.03 (0.016) 0.02 2 (0.014) 0.025 (0.014) REW 0.02 (5) 0.01 (4) 9 (4) 0.010 (4) Prevalence Undiagnosed HIV, % Male Homosexuals IL 3.15 (0.49) 3.15 (0.48) 3.17 (0.48) 3.16 (0.48) OL 1.76 (1.15) 1.70 (1.1) 1.74 (1.12) 1.76 (1.14) REW 0.92 (0.25) 0.92 (0.25) 0.91 (0.24) 0.91 (0.25) Current IL 4.68 (0.49) 4.68 (0.49) 4.68 (0.49) 4.67 (0.49) Homosexual OL 4.07 (2.34) 4.01 (2.31) 4.05 (2.35) 4.11 (2.34) GUM attenders REW 1.64 (0.32) 1.64 (0.32) 1.64 (0.32) 1.63 (0.32) Current IL 2.29 (0.59) 2.29 (0.58) 2.29 (0.59) 2.28 (0.57) Homosexuals OL 1.75 (1.3) 1.69 (1.23) 1.71 (1.24) 1.74 (1.29) not GUM attenders REW 0.71 (0.33) 0.70 (0.34) 0.70 (0.32) 0.70 (0.33) Past IL 0.50 (0.13) 0.50 (0.12) 0.50 (0.12) 0.50 (0.12) Homosexuals OL 0.44 (0.28) 0.43 (0.28) 0.44 (0.29) 0.44 (0.29) REW 0.17 (0.05) 0.17 (0.05) 0.17 (0.05) 0.17 (0.05) All IDUs IL 0.84 (0.38) 0.86 (0.39) 0.86 (0.39) 0.72 (0.27) OL 0.84 (0.38) 0.84 (0.37) 0.83 (0.38) 0.47 (0.18) REW 0.11 (0.03) 0.11 (0.03) 0.11 (0.03) 0.12 (0.03) Current IL 1.05 (0.4) 1.06 (0.41) 1.06 (0.41) 1.55 (0.51) IDUs OL 0.96 (0.4) 0.95 (0.4) 0.95 (0.4) 0.95 (0.36) 6

Baseline model correction correction + REW 0.13 (0.02) 0.13 (0.02) 0.13 (0.02) 0.14 (0.05) Past IL 0.61 (0.41) 0.63 (0.42) 0.62 (0.42) 0.16 (0.2) IDUs OL 0.61 (0.39) 0.61 (0.39) 0.61 (0.39) 0.06 (0.1) REW 0.07 (0.04) 0.07 (0.04) 0.07 (0.04) 0.08 (0.07) GUM IL 0.49 (0.09) 0.49 (0.09) 0.49 (0.09) 0.43 (0.07) attenders OL 0.21 (0.13) 0.21 (0.13) 0.22 (0.13) 0.26 (0.1) REW 0.08 (0.02) 0.08 (0.02) 0.08 (0.02) 0.08 (0.02) SSA IL 1.62 (0.16) 1.12 (0.13) 0.62 (0.11) 0.45 (0.14) OL 1.70 (0.18) 1.26 (0.15) 0.80 (0.14) 0.55 (0.16) REW 1.82 (0.28) 1.43 (0.2) 0.84 (0.15) 0.56 (0.15) Low Risk IL 0.02 (0.016) 0.013 (0.011) Female OL 0.03 (0.015) 0.018 (0.012) 0.01 REW 2 (4) 9 (3) 7 (7) 7 (8) 0.01 0 (8) 0.013 (0.011) 5 (2) 5 (3) All IDUs IL 1.12 (0.74) 1.08 (0.73) 0.94 (0.64) 0.68 (0.36) OL 0.19 (0.14) 0.19 (0.14) 0.19 (0.15) 0.42 (0.23) REW 0.15 (0.05) 0.15 (0.05) 0.16 (0.05) 0.14 (0.04) Current IL 1.46 (0.83) 1.45 (0.84) 1.36 (0.77) 1.66 (0.62) IDUs OL 0.24 (0.16) 0.24 (0.16) 0.24 (0.17) 0.98 (0.41) REW 0.18 (0.04) 0.18 (0.04) 0.18 (0.04) 0.16 (0.06) Past IL 0.82 (0.7) 0.79 (0.69) 0.64 (0.6) 0.20 (0.26) IDUs OL 0.13 (0.12) 0.13 (0.12) 0.13 (0.13) 0.09 (0.14) REW 0.10 (0.06) 0.10 (0.06) 0.10 (0.06) 0.10 (0.1) GUM IL 0.34 (0.07) 0.33 (0.06) 0.30 (0.06) 0.33 (0.05) attenders OL 0.26 (0.12) 0.26 (0.11) 0.25 (0.1) 0.20 (0.08) REW 0.06 (0.02) 0.06 (0.02) 0.06 (0.02) 0.06 (0.02) SSA IL 1.62 (0.16) 1.12 (0.13) 0.62 (0.11) 0.62 (0.11) OL 1.70 (0.18) 1.26 (0.15) 0.80 (0.14) 0.80 (0.14) REW 1.82 (0.28) 1.43 (0.2) 0.84 (0.15) 0.86 (0.16) Low Risk IL 0.02 (0.016) 0.013 (0.011) 7 (7) 6 (6) OL 0.03 (0.015) 0.018 (0.012) 0.01 0 (8) 0.011 (9) REW 0.01 (4) 9 (3) 5 (2) 5 (2) Proportion diagnosed, % Male Homosexuals IL 74 (5) 74 (4) 74 (4) 74 (4) OL 59 (15) 60 (15) 59 (14) 59 (15) REW 66 (6) 66 (6) 66 (6) 66 (6) Current IL 62 (21) 62 (21) 60 (22) 60 (22) Homosexual OL 63 (24) 62 (25) 62 (24) 62 (24) 7

Baseline model correction correction + GUM attenders REW 56 (21) 55 (21) 55 (22) 58 (21) Current IL 68 (24) 68 (24) 71 (23) 68 (24) Homosexuals OL 39 (23) 42 (24) 41 (23) 41 (23) not GUM attenders REW 61 (22) 62 (22) 61 (23) 59 (23) Past IL 50 (29) 50 (29) 50 (29) 52 (30) Homosexuals OL 48 (28) 48 (28) 49 (28) 48 (28) REW 49 (28) 49 (28) 50 (29) 49 (28) IDUs IL 74 (6) 74 (6) 75 (6) 69 (5) OL 57 (6) 57 (6) 58 (6) 58 (5) REW 60 (5) 60 (5) 60 (5) 58 (6) Current IL 68 (4) 68 (4) 68 (4) 66 (4) IDUs OL 51 (4) 51 (4) 51 (4) 56 (4) REW 51 (1) 51 (1) 51 (1) 51 (1) Past IL 82 (9) 81 (9) 82 (10) 82 (10) IDUs OL 69 (14) 69 (14) 69 (14) 77 (13) REW 75 (14) 75 (14) 75 (14) 73 (14) GUM IL 41 (13) 43 (13) 46 (11) 42 (14) attenders OL 47 (21) 49 (20) 53 (19) 40 (17) REW 49 (20) 51 (20) 57 (18) 50 (21) SSA IL 44 (3) 54 (3) 60 (5) 69 (7) OL 33 (3) 40 (3) 44 (5) 55 (7) REW 23 (3) 28 (3) 31 (4) 42 (7) Low Risk IL 43 (25) 46 (26) 49 (27) 69 (26) OL 35 (21) 38 (22) 44 (25) 50 (25) REW 29 (15) 33 (17) 41 (22) 42 (22) Female IDUs IL 69 (10) 70 (10) 73 (9) 76 (6) OL 78 (7) 78 (7) 78 (7) 67 (6) REW 63 (5) 63 (5) 63 (5) 65 (7) Current IDUs IL 59 (7) 59 (7) 60 (7) 70 (4) OL 72 (6) 72 (6) 72 (5) 63 (4) REW 56 (2) 56 (2) 56 (2) 57 (2) Past IL 77 (13) 78 (13) 82 (12) 86 (9) IDUs OL 86 (9) 86 (9) 86 (9) 81 (11) REW 77 (13) 77 (13) 77 (13) 78 (12) GUM IL 41 (17) 44 (17) 50 (17) 49 (15) attenders OL 37 (18) 38 (18) 42 (18) 45 (18) REW 47 (21) 50 (21) 53 (20) 55 (21) SSA IL 59 (2) 68 (2) 74 (4) 75 (4) OL 50 (3) 58 (3) 62 (5) 63 (5) REW 39 (4) 45 (4) 50 (5) 50 (5) 8

Baseline model correction correction + Low Risk IL 58 (25) 62 (26) 71 (25) 73 (25) OL 38 (22) 44 (23) 56 (26) 55 (25) REW 31 (15) 36 (17) 49 (22) 47 (23) 9

Table S3. Posterior means (standard deviation) of Ssupplementary parameters, ν, λ, α, ε Priors Baseline NSHPC Adjusted Both SSA corrections correction + Hierarchical structure Overall SOPHID incompleteness, ν (%) ν ~ Beta(183.9,1487.7) 9.8 (0.7) 10.2 (0.7) 11.1 (0.8) 11.1 (0.8) LOR of effective proportion diagnosed to reported diagnosed (sd), λ Log(λ) ~ Normal(0,10000) 0.73 (0.16) 0.75 (0.17) LOR effective to Census estimate Size (sd), ε Log(ε) ~ Normal(0,10000) 0.37 (0.08) 0.33 (0.09) 10