Causal inference for N-of-1 trials

The aim of personalized medicine is to tailor treatment decisions to individuals' characteristics. N-of-1 trials are within-person crossover trials that hold the promise of targeting individual-specific effects. While the idea behind N-of-1 trials might seem simple, analyzing and interpreting N-of-1 trials is not straightforward. In particular, there exists confusion about the role of randomization in this design, the (implicit) target estimand, and the need for covariate adjustment. Here we ground N-of-1 trials in a formal causal inference framework and formalize intuitive claims from the N-of-1 trial literature. We focus on causal inference from a single N-of-1 trial and define a conditional average treatment effect (CATE) that represents a target in this setting, which we call the U-CATE. We discuss the assumptions sufficient for identification and estimation of the U-CATE under different causal models in which the treatment schedule is assigned at baseline. A simple mean difference is shown to be an unbiased, asymptotically normal estimator of the U-CATE in simple settings, such as when participants have stable conditions (e.g., chronic pain) and interventions have effects limited in time (no carryover). We also consider settings where carryover effects, trends over time, time-varying common causes of the outcome, and outcome-outcome effects are present. In these more complex settings, we show that a time-varying g-formula identifies the U-CATE under explicit assumptions. Finally, we analyze data from N-of-1 trials about acne symptoms. Using this example, we show how different assumptions about the underlying data generating process can lead to different analytical strategies in N-of-1 trials.