An approach is presented for fitting the accelerated failure time model to interval censored data that does not involve computing the nonparametric maximum likelihood estimate of the distribution function at the residuals. The approach involves estimating equations computed with the examination times from the same individual treated as if they had actually been obtained from different individuals. The dependence between different measurements obtained from the same individual is then accounted for in the calculation of the standard error of the regression coefficients. The approach is applicable to interval censored data in settings in which examinations continue to occur regardless of whether the failure time has occurred. Simulations are presented to assess the behaviour of the approach, and the methodology is illustrated through an application to data from an clinical trial.