Using marginal structural models to adjust for treatment drop-in when developing clinical prediction models

Clinical prediction models (CPMs) can inform decision making about treatment initiation, which requires predicted risks assuming no treatment is given. However, this is challenging since CPMs are usually derived using data sets where patients received treatment, often initiated postbaseline as "treatment drop-ins." This study proposes the use of marginal structural models (MSMs) to adjust for treatment drop-in. We illustrate the use of MSMs in the CPM framework through simulation studies that represent randomized controlled trials and real-world observational data and the example of statin initiation for cardiovascular disease prevention. The simulations include a binary treatment and a covariate, each recorded at two timepoints and having a prognostic effect on a binary outcome. The bias in predicted risk was examined in a model ignoring treatment, a model fitted on treatment-naïve patients (at baseline), a model including baseline treatment, and the MSM. In all simulation scenarios, all models except the MSM underestimated the risk of outcome given absence of treatment. These results were supported in the statin initiation example, which showed that ignoring statin initiation postbaseline resulted in models that significantly underestimated the risk of a cardiovascular disease event occurring within 10 years. Consequently, CPMs that do not acknowledge treatment drop-in can lead to underallocation of treatment. In conclusion, when developing CPMs to predict treatment-naïve risk, researchers should consider using MSMs to adjust for treatment drop-in, and also seek to exploit the ability of MSMs to allow estimation of individual treatment effects.