This work proposes a frailty model that accounts for non-random treatment assignment in survival analysis. Using Monte Carlo simulation, we found that estimated treatment parameters from our proposed endogenous selection survival model (esSurv) closely parallel the consistent two-stage residual inclusion (2SRI) results, while offering computational and interpretive advantages. The esSurv method greatly enhances computational speed relative to 2SRI by eliminating the need for bootstrapped standard errors and generally results in smaller standard errors than those estimated by 2SRI. In addition, esSurv explicitly estimates the correlation of unobservable factors contributing to both treatment assignment and the outcome of interest, providing an interpretive advantage over the residual parameter estimate in the 2SRI method. Comparisons with commonly used propensity score methods and with a model that does not account for non-random treatment assignment show clear bias in these methods, which is not mitigated by increased sample size. We illustrate using actual dialysis patient data comparing mortality of patients with mature arteriovenous grafts for venous access to mortality of patients with grafts placed but not yet ready for use at the initiation of dialysis. We find strong evidence of endogeneity (with estimate of correlation in unobserved factors ρ^=0.55) and estimate a mature-graft hazard ratio of 0.197 in our proposed method, with a similar 0.173 hazard ratio using 2SRI. The 0.630 hazard ratio from a frailty model without a correction for the non-random nature of treatment assignment illustrates the importance of accounting for endogeneity.