Table 3.
Posterior Results from Bayesian Joint Hierarchical Models
| Joint Hierarchical Models | |||
|---|---|---|---|
| Model 1: All Subjects (n=1793) |
Model 2: Male (n=1306) |
Model 3: Female (n=487) |
|
| Weibull PH with Frailty Model | Posterior Median Hazard Ratio (HR) (95% Credible Interval) |
||
| Demographicsz | |||
| Gender (Ref: Female) | 0.99 (0.60, 1.67) | -- | -- |
| Age at Enrollment | 0.99 (0.98, 1.01) | 1.00 (0.98, 1.01) | -- |
| Age at First Use | 1.10 (1.07, 1.12)*** | 1.09 (1.06, 1.11)*** | 1.09 (1.03, 1.17)*** |
| Ethnicity (Ref: Hispanic & Others) |
|||
| White | 1.09 (0.85, 1.37) | 1.11 (0.86, 1.40) | 1.02 (0.35, 3.26) |
| Black | 0.60 (0.41, 0.87)* | 0.62 (0.43, 0.90)* | 0.70 (0.19, 9.23) |
| Primary Drug Group | |||
| Cocaine to Heroin | 0.46 (0.24, 0.79)* | 0.63 (0.27, 1.23) | 0.12 (0.03, 0.44) ** |
| Meth to Heroin | 0.28 (0.13, 0.62)*** | 0.14 (0.03, 0.49)* | 0.40 (0.11, 1.46) |
| Meth to Cocaine | 0.62 (0.27, 1.57) | 0.22 (0.05, 0.90)* | 3.37 (0.68, 17.5) |
| %Usage | |||
| Substance | 2.69 (1.80, 4.16)*** | 2.79 (1.82, 4.32)*** | 1.17 (0.17, 9.23) |
| Alcohol | 1.12 (0.81, 1.57) | 1.03 (0.74, 1.47) | 3.42 (1.06, 13.2)* |
| Kendall's τ | 0.07 (0.003, 0.34) | 0.08 (0.002, 0.71) | 0.17 (0.008, 0.63) |
| Mixed-Effects Models | Posterior Median (95% Credible Interval) |
||
| Overall % Substance Usage | |||
| Cocaine – Heroin | -6.70 (-11.2, -2.10)** | -7.30 (-14.2, -0.60)* | -5.70 (-11.6, 0.20) |
| Methamphetamine – Heroin | -7.60 (-12.8, -2.00)* | -8.70 (-16.6, -0.10)* | -6.60 (-14.1, 0.70) |
| Intra-Class Correlation (ICC) | 0.40 (0.21, 0.72) | 0.39 (0.19, 0.72) | 0.57 (0.29, 0.87) |
| Overall % Alcohol Usage | |||
| Cocaine – Heroin | 4.00 (-2.20, 10.2) | 3.10 (-5.20, 11.5) | 7.20 (-2.30, 17.3) |
| Methamphetamine – Heroin | 5.50 (-1.90, 12.6) | 7.80 (-2.20, 18.0) | 2.90 (-8.70, 15.6) |
| Intra-Class Correlation (ICC) | 0.33 (0.15, 0.66) | 0.34 (0.16, 0.68) | 0.36 (0.14, 0.81) |
*
P < 0.05,
**
P < 0.001,
***
P < 0.0001.
Note: In the survival models, P represents the posterior probability of a value less than one (or > 1) for the hazard ratio. In the mixed-effects models, P represents the posterior probability of a value less than zero (or > 0) for the regression coefficient. The posterior probability can be used in place of the frequentist's p-value.