<p>The semiparametric accelerated failure time and additive hazards models are commonly used alternatives to the proportional hazards model. For independent samples of right-censored or left-truncated right-censored failure time data, estimating equation based procedures are used to derive estimators for the unknown model parameters. In various applications, a sample data set can consist of multiple types of partially observed failure time data through the use of multiple sampling schemes or combination of multiple data sets. We propose three different estimation methodologies for estimating the unknown regression parameters in the accelerated failure time and additive hazards models using combined right-censored and left-truncated right-censored failure time data. These three methods are based on averaging the parametric estimators of the two samples, determining the zero-crossing of the summation of the two samples’ estimating equations and determining the zero-crossing of a single estimating equation based on the combination of the two samples. We assess the performance of the estimators through extensive simulation studies and use the estimators to model the factors affecting African lion mortality.</p>