Simulated treatment comparison (STC) is an established method for performing population adjustment for the indirect comparison of two treatments, where individual patient data (IPD) are available for one trial but only aggregate level information is available for the other. The most commonly used method is what we call 'standard STC'. Here we fit an outcome model using data from the trial with IPD, and then substitute mean covariate values from the trial where only aggregate level data are available, to predict what the first of these trial's outcomes would have been if its population had been the same as the second. However, this type of STC methodology does not involve simulation and can result in bias when the link function used in the outcome model is non-linear. An alternative approach is to use the fitted outcome model to simulate patient profiles in the trial for which IPD are available, but in the other trial's population. This stochastic alternative presents additional challenges. We examine the history of STC and propose two new simulation-based methods that resolve many of the difficulties associated with the current stochastic approach. A virtue of the simulation-based STC methods is that the marginal estimands are then clearly targeted. We illustrate all methods using a numerical example and explore their use in a simulation study.