Table 1.
Simulation results for various estimators of model parameters (regression coefficients ψ, β, γ and log hazard ratio ϕ) using profile, partial, weighted martingale equations jointly with the logistic estimation equation for ψ. True β and γ are 1 and 0, respectively. Both the true and the fitted models use covariate (Z)-dependent misattribution. The log-odds ratio of misattribution in the true model is −1.7 + 0.5Z. The sample sizes of the survival and external data sets are n = 500 and nr = 150, respectively. True log hazards ratio ϕ = 0.7 in the time-independent case (PH) and ϕ = 2T in the time-varying case (non-PH). The sample standard deviations (SSD) and average of the standard error estimates (SEE) are presented in parenthesis.
| Assumed Model/Method, Estimating Equations | Martingale Weights | Baseline Hazard(s) | Finite-dim Parameters | True model used in simulations | |
|---|---|---|---|---|---|
| constant ϕ | time-varying ϕ | ||||
| Logistic (Misattribution), External data, (20) | – | – |
ψ0 ψ1 |
−1.771 (.371,.367) 0.533 (.300,.300) |
−1.776 (.371,.358) 0.531 (.333,.315) |
|
Profile, (10) PH, Const ϕ |
PH-based (11), (18) |
Ĥ1(t), (12) |
ϕF βF γF |
0.693 (.229,.229) 0.999 (.097,.093) 0.006 (.114,.114) |
0.802 (.233,.228) 1.089 (.097,.094) −0.068 (.112,.115) |
|
Partial, (13) PH, Const ϕ |
PH-based (11), (18) |
Ĥ1(t)eϕ̂ → Ĥ2(t) (14) |
ϕP βP γP |
0.695 (.238,.236) 1.000 (.102,.097) 0.007 (.116,.116) |
0.652 (.227,.233) 1.011 (.093,.095) −0.001 (.124,.120) |
|
Weighted Martingale, (9) |
PH-based (11), (18) |
Ĥ1 (t), Ĥ2(t) (15) with (11) |
ϕW βW γW |
0.692 (.236,.235) 0.999 (.101,.097) 0.007 (.115,.116) |
0.636 (.220,.229) 1.001 (.091,.093) 0.002 (.123,.119) |
|
Unweighted Martingale, (16) |
Const |
Ĥ1(t), Ĥ2(t) (17) |
βC γC |
1.003 (.107,.102) 0.004 (.119,.120) |
1.005 (.094,.097) −0.002 (.126,.123) |