<p>Cure fraction regression models are useful for lifetime data with long-term survivors. We propose a flexible cure rate model called the odd log-logistic exponential considering a frailty effect, which can measure possible heterogeneity or correlation in the data. The model also considers two systematic components to assess the effect of covariates on both the proportion of cured individuals and the survival time of patients. In order to examine the performance of the proposed model, simulations are presented to verify the robust aspects of this flexible class against censoring and influential observations. The potential of the new regression model to accurately predict cervical cancer data is illustrated using a real dataset.</p>