  Clone-censor-weighting (CCW) is an analytic method for studying treatment
regimens that are indistinguishable from one another at baseline without
relying on landmark dates or creating immortal person time. One particularly
interesting CCW application is estimating outcomes when starting treatment
within specific time windows in observational data (e.g., starting a treatment
within 30 days of hospitalization). In such cases, CCW estimates something
fairly complex. We show how using CCW to study a regimen such as "start
treatment prior to day 30" estimates the potential outcome of a hypothetical
intervention where A) prior to day 30, everyone follows the treatment start
distribution of the study population and B) everyone who has not initiated by
day 30 initiates on day 30. As a result, the distribution of treatment
initiation timings provides essential context for the results of CCW studies.
We also show that if the exposure effect varies over time, ignoring exposure
history when estimating inverse probability of censoring weights (IPCW)
estimates the risk under an impossible intervention and can create selection
bias. Finally, we examine some simplifying assumptions that can make this
complex treatment effect more interpretable and allow everyone to contribute to
IPCW.
