Multi-cancer early detection tests are precipitating a re-examination of potential short-term endpoints for cancer screening trials. A reduction in advanced stage incidence is a prime candidate, and stage-shift models that substitute early-stage for late-stage survival have been used to predict mortality reduction due to screening. However, standard stage-shift models often ignore prognostic subtypes, effectively implying that cancers detected early also have an associated subtype shift. To illustrate the differences between mortality predictions from stage-shift models that ignore versus preserve prognostic subtype, we use ovarian cancer partitioned by histologic subtype and prostate cancer partitioned by grade. We infer general conditions under which stage-shift models that preserve prognostic subtype are likely to predict mortality reductions that differ from those that ignore subtype and examine the implications for short-term endpoints based on stage in cancer screening trials.