Simulated Treatment Comparison Protocol

Simulated Treatment Comparison (STC) is a modification of covariate adjustment,²¹ which fits an outcome model using the IPD in the $AB$ trial:
$g\left({\mu }_{t(AB)}\left(\mathit{X}\right)\right)={\beta }_0+{\mathit{\beta }}_1^T\mathit{X}+({\beta }_B+{\mathit{\beta }}_2^T{\mathit{X}}^{EM})I(t=B),$
where ${\beta }_0$ is an intercept term, ${\mathit{\beta }}_1$ is a vector of coefficients for prognostic variables, ${\beta }_B$ is the relative effect of treatment $B$ compared to $A$ at $\mathit{X}=0$ , ${\mathit{\beta }}_2$ is a vector of coefficients for effect modifiers ${\mathit{X}}^{EM}$ (a subvector of the full covariate vector $\mathit{X}$ ), and ${\mu }_{t(AB)}\left(\mathit{X}\right)$ is the expected outcome of an individual assigned treatment $t$ with covariate values $\mathit{X}$ , which is transformed onto a chosen linear predictor scale with link function $g(·)$ .
The model in equation (8) is a more general form of that given by Ishak et al.^{7 (link)}, which does not include any effect modifier terms. The STC literature advocates forming indirect comparisons directly on the natural outcome scale with $g(·)$ the identity link in equation (4) or (5); however, this leads to scale conflicts¹⁰ if the same link is not used in the outcome model (8) (see the following section on the importance of scale). ${\hat{Y}}_{A(AC)}$ and ${\hat{Y}}_{B(AC)}$ may be predicted from the outcome regression by substituting in mean covariate values to obtain ${\hat{Y}}_{A(AC)}=g^{-1}({\hat{\beta }}_0+{\hat{\mathit{\beta }}}_1^T{\overline{\mathit{X}}}_{(AC)})$ and ${\hat{Y}}_{B(AC)}=g^{-1}({\hat{\beta }}_0+{\hat{\mathit{\beta }}}_1^T{\overline{\mathit{X}}}_{(AC)}+{\hat{\mathit{\beta }}}_B+{\hat{\mathit{\beta }}}_2^T{\overline{\mathit{X}}}_{(AC)}^{EM})$ . These estimators are systematically biased whenever $g(·)$ is not the identity function, because the mean outcome depends on the full distribution of the covariates and not just their mean.^{7 (link)} Instead of substituting in mean covariate values in this case, Ishak et al. suggest that estimates are obtained by first drawing samples from the joint covariate distribution in the $AC$ trial and then averaging over the predicted outcomes based on the regression model. This simulation approach, however, inflates uncertainty of the relative effect estimates.
Standard tools for model checking (such as AIC/DIC, examining residuals, among others) may be used when constructing the outcome model in the $AB$ trial; however (as with MAIC), additional assumptions are required to predict absolute outcomes in the $AC$ population, which are difficult to test with the limited data available.