OBJECTIVES: Copulas provide an elegant approach to model the association of paired survival times and have been used in oncology studies to analyze patient-level correlation between time to progression and overall survival (OS), where dependence is positive. Here, we aim to determine and test a representative set of candidate copulas for modelling the association of time to investigator-assessed complete or partial response (TTCPR) and OS, where the dependence is negative, which poses some specific challenges.

METHODS: We conducted a literature review to identify suitable survival copulas that allow for negative dependence characterized by a single coupling parameter. We applied a candidate set of parametric bivariate survival models based on the selected copula functions to a synthetic dataset designed to mimic some features of TTCPR-OS outcomes for avelumab plus axitinib versus sunitinib in advanced renal cell carcinoma from the JAVELIN Renal-101 study, where the respective treatment arms correspond to regimes of higher and lower durability of response.

RESULTS: Correlation coefficient estimates from the six selected copulas were found to be moderately sensitive to the choice of copula. The Frank, Plackett, Clayton, and Gaussian copulas allow for perfect positive association and hence can represent TTPCR-OS correlation even when response is highly durable. However, these copulas differ in their associated clinical assumptions and in their tail behavior, leading to minor variations in predicted OS and TTCPR. The Gumbel-Barnett and Cooray copulas can only accommodate weak and weak to moderate negative dependence, respectively, so are appropriate only when durability of response is relatively low.

CONCLUSIONS: Copulas provide a rigorous method to calculate clinically interpretable quantities that measure the dependence of OS on TTCPR, such as rank correlation coefficients and OS curves conditioned on maximum response times. Collectively, the copulas identified here exhibit diverse characteristics, and therefore constitute a suitable candidate set for modelling TTCPR-OS correlation in oncology.