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Quantifying the Amount of Variation in Survival Explained by Prostate-specific Antigen¹

Departments of Epidemiology and Biostatistics [D. A. V., G. H.] and Medicine [W. K. K., H. I. S.], Memorial Sloan-Kettering Cancer Center, New York, New York 10021

Purpose: Post-therapy changes in prostate-specific antigen(PSA) have been proposed as surrogates for survival in clinical trials due to observed statistical associations. However, association alone does not satisfy the conditions of surrogacy. A measure that quantifies the amount of association is important. Using a population-based approach, we explore the relationship between PSA and survival and generate a measure to demonstrate the amount of the variation in survival explained by PSA.

Experimental Design: With serial PSA measurements from 254 patients with androgen-independent prostate cancer, we use a time-dependent Cox model with a nonlinear log relative risk function to quantify the strength of the association between time-dependent PSA and survival. The nonlinear log relative risk function provides a flexible Cox model and a more accurate measure of the strength of association between PSA and survival.

Results: Among these 254 patients, there were 247 deaths (median survival time = 13.0 months). Median follow-up time for those alive or censored was 59.3 months (range, 36.8–71.3 months). An association was observed between PSA and survival (P < 0.01, two-sided test). However, time-dependent PSA explains only 17% of the variation in survival.

Conclusions: Use of this methodology demonstrates that there remains sufficient variation in survival unaccounted for by PSA measurements in this patient cohort. Other factors, perhaps unknown, exist that determine survival outcome. Consideration of PSA alone as a surrogate can produce misleading information regarding the risk of death; its use as a surrogate for survival is not warranted when designing a clinical trial in this patient population.

Commentary

Biostatistical Approaches for Modeling Longitudinal and Event Time Data

Kim-Anh Do
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