  Survival is poor for patients with metastatic cancer, and it is vital to
examine new biomarkers that can improve patient prognostication and identify
those who would benefit from more aggressive therapy. In metastatic prostate
cancer, two new assays have become available: one that quantifies the number of
cancer cells circulating in the peripheral blood, and the other a marker of the
aggressiveness of the disease. It is critical to determine the magnitude of the
effect of these biomarkers on the discrimination of a model-based risk score.
To do so, most analysts frequently consider the discrimination of two separate
survival models: one that includes both the new and standard factors and a
second that includes the standard factors alone. However, this analysis is
ultimately incorrect for many of the scale-transformation models ubiquitous in
survival, as the reduced model is misspecified if the full model is specified
correctly. To circumvent this issue, we developed a projection-based approach
to estimate the impact of the two prostate cancer biomarkers. The results
indicate that the new biomarkers can influence model discrimination and justify
their inclusion in the risk model; however, the hunt remains for an applicable
model to risk-stratify patients with metastatic prostate cancer.
