Title: Causal Inference with Two Versions of Treatment,
Abstract: Causal effects are commonly defined as comparisons of the potential outcomes
under treatment and control, but this definition is threatened by the
possibility that the treatment or control condition is not well-defined,
existing instead in more than one version. A simple, widely applicable analysis
is proposed to address the possibility that the treatment or control condition
exists in two versions with two different treatment effects. This analysis
loses no power in the main comparison of treatment and control, provides
additional information about version effects, and controls the family-wise
error rate in several comparisons. The method is motivated and illustrated
using an on-going study of the possibility that repeated head trauma in high
school football causes an increase in risk of early on-set dementia.