In a randomized trial of tamoxifen therapy for breast cancer, women can experience tumor recurrence or die from competing causes. One goal of analysis is to describe the effect of tamoxifen on the probabilities of recurrence or death from other causes. To this end, we propose a semi-parametric transformation model for the crude failure probabilities of a competing risk, conditional on covariates. The model is developed as an extension of the standard approach to survival data with independent right censoring. Estimation of the regression coefficients is achieved with a rank-based least squares criterion. Simulations show that the procedure works well with practical sample sizes. A separate estimating function is developed for the baseline parameter. Prediction of covariate-adjusted failure probabilities is considered. The methodology is motivated and illustrated with data from the tamoxifen trial.