Table 1 An example of the structure of the m-th synthetic dataset, created in the data synthesis stage of MIM. In this example, \(N=7\) (\(N^*=14\)) and \(K=3\). Prior to imputing the missing outcomes, a copy of the original target covariate dataset has been assigned the treatment value zero and been vertically concatenated to the original \(\varvec{x}^{tar}\), assigned the treatment value one
Covariates (\(\varvec{x}^{\varvec{*}}\)) | Treatment (\(\varvec{t}^{\varvec{*}}\)) | Outcome \(\left( \varvec{y}^{\varvec{*}(m)}\right)\) | ||
|---|---|---|---|---|
\(x_{1,1}^{tar}\) | \(x_{1,2}^{tar}\) | \(x_{1,3}^{tar}\) | 1 | \(y^{*(m)}_1\) |
\(x_{2,1}^{tar}\) | \(x_{2,2}^{tar}\) | \(x_{2,3}^{tar}\) | 1 | \(y^{*(m)}_2\) |
\(x_{3,1}^{tar}\) | \(x_{3,2}^{tar}\) | \(x_{3,3}^{tar}\) | 1 | \(y^{*(m)}_3\) |
\(x_{4,1}^{tar}\) | \(x_{4,2}^{tar}\) | \(x_{4,3}^{tar}\) | 1 | \(y^{*(m)}_4\) |
\(x_{5,1}^{tar}\) | \(x_{5,2}^{tar}\) | \(x_{5,3}^{tar}\) | 1 | \(y^{*(m)}_5\) |
\(x_{6,1}^{tar}\) | \(x_{6,2}^{tar}\) | \(x_{6,3}^{tar}\) | 1 | \(y^{*(m)}_6\) |
\(x_{7,1}^{tar}\) | \(x_{7,2}^{tar}\) | \(x_{7,3}^{tar}\) | 1 | \(y^{*(m)}_7\) |
\(x_{1,1}^{tar}\) | \(x_{1,2}^{tar}\) | \(x_{1,3}^{tar}\) | 0 | \(y^{*(m)}_8\) |
\(x_{2,1}^{tar}\) | \(x_{2,2}^{tar}\) | \(x_{2,3}^{tar}\) | 0 | \(y^{*(m)}_9\) |
\(x_{3,1}^{tar}\) | \(x_{3,2}^{tar}\) | \(x_{3,3}^{tar}\) | 0 | \(y^{*(m)}_{10}\) |
\(x_{4,1}^{tar}\) | \(x_{4,2}^{tar}\) | \(x_{4,3}^{tar}\) | 0 | \(y^{*(m)}_{11}\) |
\(x_{5,1}^{tar}\) | \(x_{5,2}^{tar}\) | \(x_{5,3}^{tar}\) | 0 | \(y^{*(m)}_{12}\) |
\(x_{6,1}^{tar}\) | \(x_{6,2}^{tar}\) | \(x_{6,3}^{tar}\) | 0 | \(y^{*(m)}_{13}\) |
\(x_{7,1}^{tar}\) | \(x_{7,2}^{tar}\) | \(x_{7,3}^{tar}\) | 0 | \(y^{*(m)}_{14}\) |