Table 1.
Simulation results comparing the proposed two-step approach with shared random effects model, and generalized linear mixed model for different settings of parameter values, with 7 designed observations per subject.a
| Parameterb | True | SREM | GLMM | Two-step |
|---|---|---|---|---|
|
| ||||
| Bias (coverage %)c | Bias (coverage %) | Bias (coverage %) | ||
| σb = 1.5, σc = 1, ρ = −0.2 (weak nonignorability) | ||||
|
|
||||
| β0 | −1.0 | −0.001 (94.6) | −0.007 (94.8) | −0.012 (94.9) |
| β1 | 1.0 | 0.001 (94.0) | −0.010 (93.3) | 0.005 (93.8) |
| β2 | 0.8 | 0.001 (94.3) | −0.024 (92.6) | 0.009 (94.4) |
| β3 | −0.2 | 0.000 (95.1) | −0.007 (93.4) | 0.000 (95.2) |
|
| ||||
| γ0 | 3.5 | 0.004 (94.7) | - | 0.004 (94.7) |
| γ1 | −0.6 | −0.001 (95.3) | - | −0.001 (95.2) |
| γ2 | −1.2 | 0.000 (95.8) | - | 0.000 (95.7) |
| γ3 | −0.5 | 0.000 (95.3) | - | 0.000 (95.2) |
|
| ||||
| σb | 1.5 | −0.005 (95.2) | −0.006 (94.8) | - |
| σc | 1.0 | −0.002 (96.4) | - | −0.003 (96.1) |
| ρ | −0.2 | −0.003 (94.2) | - | - |
|
| ||||
| σb = 1.5, σc = 1, ρ = −0.6 (strong nonignorability) | ||||
|
|
||||
| β0 | −1.0 | −0.003 (94.5) | −0.015 (94.6) | −0.031 (93.6) |
| β1 | 1.0 | 0.000 (94.1) | −0.037 (93.2) | 0.007 (93.3) |
| β2 | 0.8 | 0.000 (94.3) | −0.079 (79.4) | 0.014 (93.2) |
| β3 | −0.2 | 0.000 (94.6) | −0.023 (83.9) | 0.000 (94.6) |
|
| ||||
| γ0 | 3.5 | 0.007 (95.1) | - | 0.007 (95.2) |
| γ1 | −0.6 | 0.000 (95.2) | - | 0.000 (95.2) |
| γ2 | −1.2 | 0.000 (94.6) | - | 0.000 (94.7) |
| γ3 | −0.5 | −0.001 (94.9) | - | −0.001 (95.2) |
|
| ||||
| σb | 1.5 | −0.004 (95.2) | −0.027 (92.5) | - |
| σc | 1.0 | −0.001 (94.7) | - | −0.002 (94.7) |
| ρ | −0.6 | −0.001 (95.9) | - | - |
|
| ||||
| σb = 2.5, σc = 2, ρ = −0.2 (weak nonignorability) | ||||
|
|
||||
| β0 | −1.0 | 0.000 (94.6) | −0.059 (94.7) | −0.038 (95.6) |
| β1 | 1.0 | −0.003 (94.4) | −0.028 (94.5) | 0.012 (94.4) |
| β2 | 0.8 | 0.000 (93.8) | −0.054 (91.0) | 0.028 (93.5) |
| β3 | −0.2 | 0.000 (95.0) | −0.010 (92.8) | 0.000 (95.0) |
|
| ||||
| γ0 | 3.5 | 0.013 (95.4) | - | 0.013 (95.6) |
| γ1 | −0.6 | −0.001 (95.3) | - | −0.001 (95.5) |
| γ2 | −1.2 | −0.001 (94.3) | - | −0.001 (94.3) |
| γ3 | −0.5 | −0.002 (95.1) | - | −0.002 (95.0) |
|
| ||||
| σb | 2.5 | −0.006 (94.0) | −0.006 (93.9) | - |
| σc | 2.0 | 0.002 (94.8) | - | 0.002 (95.0) |
| ρ | −0.2 | −0.001 (94.3) | - | - |
|
| ||||
| σb = 2.5, σc = 2, ρ = −0.6 (strong nonignorability) | ||||
|
|
||||
| β0 | −1.0 | 0.003 (94.7) | −0.142 (86.7) | −0.086 (89.7) |
| β1 | 1.0 | −0.004 (94.4) | −0.088 (91.2) | 0.027 (91.7) |
| β2 | 0.8 | −0.002 (93.8) | −0.180 (57.5) | 0.058 (89.4) |
| β3 | −0.2 | −0.001 (95.1) | −0.033 (73.8) | −0.001 (95.2) |
|
| ||||
| γ0 | 3.5 | 0.007 (94.5) | - | 0.007 (94.7) |
| γ1 | −0.6 | 0.004 (94.4) | - | 0.004 (94.8) |
| γ2 | −1.2 | −0.001 (93.7) | - | −0.001 (94.3) |
| γ3 | −0.5 | −0.001 (94.8) | - | −0.001 (94.9) |
|
| ||||
| σb | 2.5 | −0.011 (95.4) | −0.107 (84.5) | - |
| σc | 2.0 | 0.000 (94.5) | - | 0.001 (94.3) |
| ρ | −0.6 | 0.001 (93.8) | - | - |
Abbreviations: GLMM, generalized linear mixed model; SREM, shared random effects model.
a
Designed number of observations is 7.
b
Parameters are defined in Equations (5)-(6).
c
Bias is calculated as the difference between the estimated parameters over 1000 simulations and their true values. Coverage percentage is calculated as the percentage of simulations in which the 95% confidence interval covers the true parameter value.