Time-fixed vs time-varying causal diagrams for immortal time bias.

Abstract

We thank Shrier and Suissa1 for their interest in our editorial2 on causal diagrams3–7 for immortal time bias (ITB) and for their detailed analysis of our causal diagrams. They proposed a time-varying approach for these diagrams and concluded that the structure of ITB for both exposure misclassification and exclusion scenarios is selection (collider-stratification) bias. We chose to use simpler causal diagrams in our editorial in order to explain the key concepts without confusing the readers who might be less familiar with these diagrams, but we welcome the chance now to consider the more detailed analysis of ITB using time-varying diagrams. Here, we first explain why we believe that our time-fixed causal diagrams are correct. Then we will demonstrate that Shrier and Suissa’s presentation and interpretation of time-varying causal diagrams for ITB are incorrect, and also provide the correct time-varying diagrams that are actually equivalent to the time-fixed diagrams originally presented in our editorial.