Leukocyte telomere length (LTL) is a marker of biological aging. Statistical methods to differentiate the effect of LTL from the effect of chronological aging on incident stroke are not established. We conduct research among participants of the Strong Heart Study (n=5,835), who were assessed during a clinic visit and followed for stroke events through 2018. To study the association between LTL and stroke, we used frailty models based on the proportional hazards that account for family relatedness. The correlation between LTL and age was addressed using Studentized residuals of a linear model. There were 428 (7.34%) stroke cases over a mean follow-up time of 17 years. We found a non-linear relationship. After adjusting for covariates, the hazard ratios for the 2nd, 3rd, and 4th quartile vs. those in the shortest LTL quartile are 0.8 (95%CI: 0.6-1.1; p value=0.71), 0.6 (95% CI: 0.4, 0.9; p-value: 0.005), and 0.9 (95%CI: 0.7-1.2; p-value=0.4). Participants in the 3rd LTL quartile had significantly lower risk of developing stroke. The current report provides an application of methods to analyze highly correlated variables in frailty models of unbalanced family clusters.