Table 2 A summary of fifteen simulated scenarios
From: Accounting for treatment use when validating a prognostic model: a simulation study
Scenario | Specification | ||||||
|---|---|---|---|---|---|---|---|
Data generating models (development and validation sets)† | Sample size of data sets | % outcome (before treatment) | Baseline risk in the absence of treatment (Risk) | Treatment allocation model | % treated in validation set | Treatment effect model | |
1 (Default) | logit(Y) = −1.50 + 1*X1 + 1*X2 + 0*U | 1000 | 20 | 1 / (1 + exp.(1.50–1*X1–1*X2–0*U)) | P(Tr) = 1 / (1 + exp. (1.95–10*Risk)) | 50 | ORTr = 0.5 |
2 | - | - | - | - | P(Tr) = 0.50 | - | - |
3 | - | - | - | - | - | - | ORTr = 1 / (1 + exp.(−1 + 5*Risk)) |
4 | - | - | - | - | P(Tr) = 1 / (1 + exp. (18–100*Risk)) | - | - |
5 | - | - | - | - | P(Tr) = 1 / (1 + exp. (3.30–10*Risk)) | 25 | ORTr = 0.3 |
6 | - | - | - | - | P(Tr) = 1 / (1 + exp. (3.30–10*Risk)) | 25 | - |
7 | - | - | - | - | P(Tr) = 1 / (1 + exp. (3.30–10*Risk)) | 25 | ORTr = 0.8 |
8 | - | - | - | - | - | - | ORTr = 0.3 |
9 | - | - | - | - | - | - | ORTr = 0.8 |
10 | - | - | - | - | P(Tr) = 1 / (1 + exp. (0.70–10*Risk)) | 75 | ORTr = 0.3 |
11 | - | - | - | - | P(Tr) = 1 / (1 + exp. (0.70–10*Risk)) | 75 | - |
12 | - | - | - | - | P(Tr) = 1 / (1 + exp. (0.70–10*Risk)) | 75 | ORTr = 0.8 |
13 | logit(Y) = −1.55 + 1*X1 + 1*X2 + 1*U | - | - | 1 / (1 + exp.(1.55–1*X1–1*X2–1*U)) | P(Tr) = 1 / (1 + exp. (1.90–10*Risk)) | - | - |
14 | logit(Y) = −1.70 + 1*X1 + 1*X2 + 2*U | - | - | 1 / (1 + exp.(1.70–1*X1–1*X2–2*U)) | P(Tr) = 1 / (1 + exp. (1.80–10*Risk)) | - | - |
15 | logit(Y) = −2.15 + 1*X1 + 1*X2 + 4*U | - | - | 1 / (1 + exp.(2.15–1*X1–1*X2–4*U)) | P(Tr) = 1 / (1 + exp. (1.55–10*Risk)) | - | - |