Multilevel model of main effects and cross-level interactions predicting overdose outcomes
| Conditional effects | Repeat non-fatal overdose n=24 031 | Drug-related death n=23 463 | Any death n=24 031 | |||||||||
| B (SE) | OR | CI | P value | B (SE) | OR | CI | P value | B (SE) | OR | CI | P value | |
| Between-patient (L1) | ||||||||||||
| Race (White) | −0.46 (0.14) | 0.68 | (0.49 to 0.96) | <0.001 | −0.31 (0.27) | 0.73 | (0.30 to 1.79) | 0.255 | −0.12 (0.15) | 0.81 | (0.54 to 1.22) | 0.432 |
| Sex (male) | −0.15 (0.04) | 0.86 | (0.75 to 1.00) | <0.001 | −0.15 (0.09) | 0.86 | (0.64 to 1.16) | 0.102 | −0.09 (0.06) | 0.92 | (0.76 to 1.11) | 0.133 |
| 25–34 (15–24) | 0.01 (0.06) | 1.01 | (0.84 to 1.22) | 0.835 | 0.18 (0.13) | 1.20 | (0.79 to 1.83) | 0.148 | 0.24 (0.12) | 1.27 | (0.85 to 1.91) | 0.051 |
| 35–44 (15–24) | −0.28 (0.07) | 0.75 | (0.60 to 0.94) | <0.001 | −0.001 (0.14) | 1.00 | (0.62 to 1.60) | 0.992 | 0.40 (0.13) | 1.50 | (0.97 to 2.31) | 0.002 |
| 45–54 (15–24) | −0.52 (0.08) | 0.60 | (0.46 to 0.77) | <0.001 | 0.14 (0.15) | 1.15 | (0.70 to 1.91) | 0.357 | 1.29 (0.13) | 3.65 | (2.41 to 5.53) | <0.001 |
| 55–64 (15–24) | −0.56 (0.09) | 0.57 | (0.43 to 0.76) | <0.001 | −0.54 (0.19) | 0.58 | (0.31 to 1.10) | 0.005 | 1.66 (0.12) | 5.28 | (3.94 to 7.99) | <0.001 |
| 65–74 (15–24) | −1.29 (0.15) | 0.27 | (0.17 to 0.44) | <0.001 | −2.95 (0.71) | 0.06 | (<0.01 to 0.53) | <0.001 | 2.16 (0.13) | 8.69 | (5.58 to 13.55) | <0.001 |
| 75–84 (15–24) | −1.54 (0.21) | 0.21 | (0.11 to 0.42) | <0.001 | −2.23 (0.58) | 0.11 | (0.01 to 0.73) | <0.001 | 2.64 (0.14) | 14.08 | (8.78 to 22.58) | <0.001 |
| 85 plus (15–24) | −2.13 (0.34) | 0.12 | (0.04 to 0.36) | <0.001 | – | – | – | – | 3.09 (0.16) | 21.92 | (13.09 to 36.69) | <0.001 |
| Time at risk | <0.01 (<0.01) | 1.00 | (1.00 to 1.00) | <0.001 | −0.003 (<0.01) | 1.00 | (1.00 to 1.00) | <0.001 | −0.004 (<0.01) | 1.00 | (1.00 to 1.00) | <0.001 |
| Repeat non-fatal overdose (no) | – | – | – | – | 1.30 (0.10) | 3.68 | (2.62 to 5.18) | <0.001 | 1.04 (0.09) | 2.82 | (2.18 to 3.75) | <0.001 |
| Between-county (L2) | ||||||||||||
| Opioid prescribing rate | −0.01 (0.08) | 0.99 | (0.84 to 1.16) | 0.866 | 0.08 (0.09) | 1.08 | (0.91 to 1.29) | 0.382 | −0.08 (0.08) | 0.92 | (0.79 to 1.08) | 0.339 |
| Medical doctor rate | −0.07 (0.09) | 0.93 | (0.78 to 1.12) | 0.469 | −0.05 (0.11) | 0.95 | (0.77 to 1.17) | 0.626 | −0.05 (0.09) | 0.95 | (0.80 to 1.14) | 0.587 |
| Rural (urban) | 0.02 (0.18) | 1.02 | (0.72 to 1.44) | 0.916 | 0.21 (0.22) | 1.24 | (0.81 to 1.90) | 0.331 | 0.14 (0.17) | 1.15 | (0.82 to 1.60) | 0.423 |
| Percentage Black | 0.06 (0.09) | 1.06 | (0.88 to 1.27) | 0.541 | 0.10 (0.10) | 1.11 | (0.91 to 1.34) | 0.294 | −0.02 (0.09) | 0.98 | (0.82 to 1.16) | 0.804 |
| Percentage Hispanic | −0.06 (0.09) | 0.94 | (0.80 to 1.11) | 0.492 | −0.10 (0.10) | 0.91 | (0.74 to 1.11) | 0.336 | −0.005 (0.08) | 0.99 | (0.85 to 1.17) | 0.953 |
| Percentage male | −0.10 (0.08) | 0.90 | (0.77 to 1.06) | 0.207 | −0.06 (0.10) | 0.94 | (0.77 to 1.14) | 0.522 | −0.05 (0.08) | 0.95 | (0.82 to 1.11) | 0.521 |
| Percentage over 65 | −0.03 (0.10) | 0.97 | (0.80 to 1.17) | 0.732 | −0.03 (0.11) | 0.97 | (0.77 to 1.20) | 0.757 | 0.08 (0.09) | 1.09 | (0.91 to 1.30) | 0.371 |
| Poverty rate | −0.16 (0.10) | 0.86 | (0.71 to 1.03) | 0.108 | −0.27 (0.11) | 0.76 | (0.62 to 0.95) | 0.016 | 0.08 (0.09) | 1.09 | (0.91 to 1.30) | 0.345 |
| Percentage < high school education | −0.01 (0.09) | 0.99 | (0.84 to 1.17) | 0.913 | −0.09 (0.11) | 0.91 | (0.73 to 1.14) | 0.404 | 0.11 (0.08) | 1.12 | (0.96 to 1.32) | 0.159 |
| Unemployment | 0.14 (0.11) | 1.16 | (0.94 to 1.43) | 0.176 | 0.19 (0.13) | 1.21 | (0.93 to 1.57) | 0.157 | −0.18 (0.10) | 0.84 | (0.68 to 1.02) | 0.086 |
| Halfway house provider rate | 0.16 (0.08) | 1.17 | (1.01 to 1.37) | 0.044 | 0.25 (0.08) | 1.29 | (1.11 to 1.50) | 0.001 | 0.20 (0.07) | 1.23 | (1.06 to 1.41) | 0.007 |
| Buprenorphine provider rate | −0.03 (0.09) | 0.97 | (0.81 to 1.15) | 0.713 | −0.19 (0.10) | 0.83 | (0.68 to 1.01) | 0.073 | −0.20 (0.09) | 0.82 | (0.69 to 0.97) | 0.028 |
| Naltrexone provider rate | 0.07 (0.08) | 1.08 | (0.92 to 1.26) | 0.369 | 0.25 (0.09) | 1.28 | (1.07 to 1.54) | 0.008 | 0.17 (0.08) | 1.19 | (1.02 to 1.38) | 0.028 |
| Cross-level interactions | ||||||||||||
| Halfway house provider rate × race (White) | 0.15 (0.09) | 1.16 | (0.98 to 1.37) | 0.087 | −0.12 (0.18) | 0.89 | (0.62 to 1.27) | 0.510 | 0.04 (0.10) | 1.04 | (0.85 to 1.27) | 0.719 |
| Buprenorphine provider rate × race (White) | −0.04 (0.18) | 0.96 | (0.68 to 1.36) | 0.816 | 0.11 (0.34) | 1.12 | (0.57 to 2.19) | 0.741 | −0.17 (0.22) | 0.84 | (0.54 to 1.30) | 0.436 |
| Naltrexone provider rate × race (White) | −0.17 (0.27) | 0.84 | (0.49 to 1.44) | 0.531 | −0.08 (0.48) | 0.92 | (0.36 to 2.35) | 0.868 | 0.54 (0.23) | 1.73 | (1.09 to 2.73) | 0.019 |
| Random effects | ||||||||||||
| Between-county residual variability | 0.30 (0.06) | – | – | <0.001 | 0.20 (0.82) | – | – | 0.007 | 0.25 (0.07) | – | – | <0.001 |
| Between-patient residual variability | 0.97 (0.01) | – | – | <0.001 | 0.97 (0.01) | – | – | <0.001 | 1.16 (0.01) | – | – | <0.001 |
CI refers to 99.9% confidence interval for L1 effects and 95% confidence interval for L2 effects. To facilitate cross-variable comparison, L2 coefficients are standardised. For categorical variables, reference categories are listed in parentheses. For fatal overdose, adults aged 85 plus were removed from the final model due to no instances of fatal overdose in that age group
L1, level 1; L2, level 2.