On the causal interpretation of rate-change methods:the prior event rate ratio and rate difference

A growing number of studies use data before and after treatment initiation in groups exposed to different treatment strategies to estimate "causal effects" using a ratio measure called the prior event rate ratio (PERR). Here, we offer a causal interpretation for PERR and its additive scale analog, the prior event rate difference (PERD). We show that causal interpretation of these measures requires untestable rate-change assumptions about the relationship between (1) the change of the counterfactual ratebefore and after treatment initiation in the treated group under hypothetical intervention to implement the control treatment; and (2) the change of the factual rate before and after treatment initiation in the control group. The rate-change assumption is on the multiplicative scale for PERR, but on the additive scale for PERD; the two assumptions hold simultaneously under testable, but unlikely, conditions. Even if investigators can pick the most appropriate scale, the relevant rate-change assumption may not hold exactly, so we describe sensitivity analysis methods to examine how assumption violations of different magnitudes would affect study results. We illustrate the methods using data from a published study of proton pump inhibitors and pneumonia.