On quantifying heterogeneous treatment effects with regression‐based individualized treatment rules: Loss function families and bounds on estimation error

SummaryHeterogeneity in response to treatment is a pervasive problem in medicine. Many researchers have proposed individualized treatment rule methods for this problem, which personalize treatment recommendations based on an individual's recorded covariates. A challenge with using these methods in practice is that they determine a treatment rule, rather than quantify treatment benefit. This can be problematic, as a recommended treatment could be burdensome and have negligible improvements in outcome for some individuals. With the aim of helping practitioners make informed modelling choices, we identify two families of loss functions to use with individualized treatment rule methods. Under the assumption of correct model specification, estimation with a loss function from one family ensures that the model's treatment recommendations can be interpreted in terms of the risk difference, while the other family of loss functions ensures that the model's treatment recommendations can be interpreted in terms of the risk ratio. We also derive two upper bounds for a model's error in risk difference and risk ratio estimation. Each upper bound can be calculated using observed data and can provide insight to practitioners regarding model error in estimating treatment effects. We illustrate our contributions with simulation studies as well as with data from the ACTG‐175 AIDS study.