Table 4.
Estimated optimal values and error rates of sequential advantage selection (SAS), S-score and LASSO methods for the scenarios with the first choice of β (eight important prescriptive variables: X1, X9, X10, X20, X22, X30, X35 and X40). True value Q(gopt) is the mean response following the true optimal treatment regime gopt, while Q(ĝopt) is the mean response following the estimated optimal treatment regime ĝopt of the three methods. The mean response of each optimal treatment regime is obtained by the average outcome of Monte Carlo simulation using the true model with 10,000 replicates. Err.rate stands for error rate of the estimated optimal treatment regime, which is the proportion of individuals with misspecified optimal treatment following the estimated optimal treatment regime. The quantity in parenthesis is standard deviation of corresponding value.
| Setting | True Value | SAS | S Score | LASSO | |||
|---|---|---|---|---|---|---|---|
| Q(gopt) | Q(ĝopt) | Err.rate | Q(ĝopt) | Err.rate | Q(ĝopt) | Err.rate | |
| Randomized Study | |||||||
| Model I, ρ = 0.2 | 2.94 | 2.86(0.09) | 0.072 | 2.60(0.16) | 0.168 | 2.58(0.14) | 0.454 |
| Model I, ρ = 0.5 | 2.94 | 2.87(0.06) | 0.072 | 2.65(0.15) | 0.156 | 2.64(0.12) | 0.462 |
| Model I, ρ = 0.8 | 2.90 | 2.86(0.04) | 0.058 | 2.49(0.06) | 0.205 | 2.64(0.10) | 0.468 |
| Model II, ρ = 0.2 | 3.35 | 3.25(0.07) | 0.089 | 3.08(0.15) | 0.150 | 3.04(0.12) | 0.462 |
| Model II, ρ = 0.5 | 3.25 | 3.18(0.04) | 0.075 | 2.98(0.14) | 0.151 | 2.98(0.12) | 0.468 |
| Model II, ρ = 0.8 | 3.05 | 3.01(0.03) | 0.056 | 2.63(0.06) | 0.207 | 2.80(0.10) | 0.471 |
| Model III, ρ = 0.2 | 3.93 | 3.75(0.15) | 0.117 | 3.58(0.18) | 0.169 | 3.56(0.14) | 0.452 |
| Model III, ρ = 0.5 | 3.88 | 3.73(0.11) | 0.105 | 3.58(0.17) | 0.155 | 3.54(0.14) | 0.457 |
| Model III, ρ = 0.8 | 3.60 | 3.52(0.08) | 0.076 | 3.19(0.07) | 0.201 | 3.30(0.11) | 0.466 |
|
| |||||||
| Observational Study | |||||||
| Model I, ρ = 0.2 | 2.94 | 2.89(0.04) | 0.061 | 2.70(0.12) | 0.137 | 2.77(0.06) | 0.313 |
| Model I, ρ = 0.5 | 2.94 | 2.88(0.03) | 0.066 | 2.73(0.11) | 0.132 | 2.82(0.05) | 0.305 |
| Model I, ρ = 0.8 | 2.90 | 2.86(0.02) | 0.057 | 2.50(0.06) | 0.202 | 2.81(0.05) | 0.300 |
| Model II, ρ = 0.2 | 3.35 | 3.26(0.07) | 0.089 | 3.16(0.09) | 0.129 | 3.22(0.06) | 0.301 |
| Model II, ρ = 0.5 | 3.25 | 3.18(0.04) | 0.077 | 3.05(0.11) | 0.131 | 3.13(0.05) | 0.299 |
| Model II, ρ = 0.8 | 3.05 | 3.01(0.02) | 0.056 | 2.63(0.05) | 0.206 | 2.95(0.05) | 0.299 |
| Model III, ρ = 0.2 | 3.93 | 3.79(0.10) | 0.106 | 3.67(0.13) | 0.144 | 3.77(0.07) | 0.306 |
| Model III, ρ = 0.5 | 3.88 | 3.73(0.09) | 0.107 | 3.65(0.13) | 0.137 | 3.74(0.06) | 0.304 |
| Model III, ρ = 0.8 | 3.60 | 3.53(0.04) | 0.076 | 3.21(0.07) | 0.195 | 3.48(0.05) | 0.303 |