Exponential decay nonlinear regression analysis of patient survival curves: preliminary assessment in non-small cell...

For processes that follow first order kinetics, exponential decay nonlinear regression analysis (EDNRA) may delineate curve characteristics and suggest processes affecting curve shape. We conducted a preliminary feasibility assessment of EDNRA of patient survival curves.

EDNRA was performed on Kaplan-Meier overall survival (OS) and time to relapse (TTR) curves for 323 patients with resected NSCLC and on OS and progression-free survival (PFS) curves from selected publications.

In our resected patients, TTR curves were triphasic with a "cured" fraction of 60.7% (half-life [t1/2] >100,000 months), a rapidly relapsing group (7.4%, t1/2=5.9 months) and a slowly relapsing group (31.9%, t1/2=23.6 months). OS was uniphasic (t1/2=74.3 months), suggesting an impact of co-morbidities; hence, tumor molecular characteristics would more likely predict TTR than OS. Of 172 published curves analyzed, 72 (42%) were uniphasic, 92 (53%) were biphasic, 8 (5%) were triphasic. With first-line chemotherapy in advanced NSCLC, 87.5% of curves from 2 to 3 drug regimens were uniphasic vs. only 20% of those with best supportive care or 1 drug (p<0.001). 54% of curves from 2 to 3 drug regimens had convex rapid-decay phases vs. 0% with fewer agents (p<0.001). Curve convexities suggest that discontinuing chemotherapy after 3-6 cycles "synchronizes" patient progression and death. With postoperative adjuvant chemotherapy, the PFS rapid-decay phase accounted for a smaller proportion of the population than in controls (p=0.02) with no significant difference in rapid-decay t1/2, suggesting adjuvant chemotherapy may move a subpopulation of patients with sensitive tumors from the relapsing group to the cured group, with minimal impact on time to relapse for a larger group of patients with resistant tumors. In untreated patients, the proportion of patients in the rapid-decay phase increased (p=0.04) while rapid-decay t1/2 decreased (p=0.0004) with increasing stage, suggesting that higher stage may be associated with tumor cells that both grow more rapidly and have a higher probability of surviving metastatic processes than in early stage tumors. This preliminary assessment of EDNRA suggests that it may be worth exploring this approach further using more sophisticated, statistically rigorous nonlinear modelling approaches. Using such approaches to supplement standard survival analyses could suggest or support specific testable hypotheses.