Interaction of treatment with a continuous variable: Comparison of approaches and an IPD meta-analysis to summarize results across several studies

Interactions between treatments and covariates in RCTs are a key topic. Standard methods for modeling treatment–covariate interactions with continuous covariates are categorization or linear functions. To use full information of the data spline based methods are one alternative and we have proposed to estimate a continuous treatment effect function with the multivariable fractional polynomial interaction (MFPI) procedure (R&S 2004). Four variants of MFPI, allowing varying flexibility in functional form, were suggested. MFPI is applicable to most of the popular regression models, including Cox and logistic regression.