Simulated Treatment Comparison (STC) is a modification of covariate adjustment,21 which fits an outcome model using the IPD in the trial:
where is an intercept term, is a vector of coefficients for prognostic variables, is the relative effect of treatment compared to at , is a vector of coefficients for effect modifiers (a subvector of the full covariate vector ), and is the expected outcome of an individual assigned treatment with covariate values , which is transformed onto a chosen linear predictor scale with link function .
The model inequation (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 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). and may be predicted from the outcome regression by substituting in mean covariate values to obtain and . These estimators are systematically biased whenever 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 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 trial; however (as with MAIC), additional assumptions are required to predict absolute outcomes in the population, which are difficult to test with the limited data available.
where is an intercept term, is a vector of coefficients for prognostic variables, is the relative effect of treatment compared to at , is a vector of coefficients for effect modifiers (a subvector of the full covariate vector ), and is the expected outcome of an individual assigned treatment with covariate values , which is transformed onto a chosen linear predictor scale with link function .
The model in
Standard tools for model checking (such as AIC/DIC, examining residuals, among others) may be used when constructing the outcome model in the trial; however (as with MAIC), additional assumptions are required to predict absolute outcomes in the population, which are difficult to test with the limited data available.
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