TABLE 1.
Simulation results for the general test-and-treat case for the equal and unequal reward loss for sub-optimal treatment options: two intervention stages, three treatment options at each stage nested within the exam at each stage with 500 replications, and n=1000 or 2000. opt% show the empirical mean and standard deviation (SD) of the percentage of subjects correctly classified to their underlying true optimal treatments, estimated by the proposed method when (a) the conditional mean model and the propensity score model are both correctly specified, (b) the conditional mean model is mis-specified and the propensity score model is correctly specified, and (c) the conditional mean model is correctly specified and the propensity score model is mis-specified. Scenarios 1,2 and 3, correspond to the cases when the true ratios of preference for having the exam v.s. not having the exam among all patients are 1:1, 2:1 and 1:2.
| Sub-optiomal | Scenario 1 (1:1) | Scenario 2 (2:1) | Scenario 3 (1:2) | ||
|---|---|---|---|---|---|
| Reward | opt% | opt% | opt% | ||
|
| |||||
| N=1000 | Equal Loss | (a) | 90.1(7.4) | 86.1(9.2) | 91.9(6.3) |
| (b) | 84.7(7.5) | 81.0(7.9) | 86.9(6.4) | ||
| (c) | 90.1(7.6) | 86.3(9.3) | 92.1(6.4) | ||
|
| |||||
| Unequal Loss | (a) | 96.2(3.8) | 96.3(4.0) | 97.7(2.0) | |
| (b) | 92.0(6.1) | 87.5(12.5) | 94.7(4.1) | ||
| (c) | 96.0(4.1) | 96.2(4.4) | 97.6(2.2) | ||
|
| |||||
| N=2000 | Equal Loss | (a) | 91.2(7.5) | 86.8(9.3) | 93.2(6.4) |
| (b) | 85.8(6.6) | 81.9(6.3) | 88.2(6.1) | ||
| (c) | 91.1(7.5) | 86.9(9.3) | 93.2(6.4) | ||
|
| |||||
| Unequal Loss | (a) | 96.9(3.4) | 97.7(2.7) | 98.2(1.8) | |
| (b) | 96.6(3.6) | 93.8(8.8) | 97.7(1.7) | ||
| (c) | 96.9(3.4) | 97.7(2.6) | 98.1(1.8) | ||