In this article, we propose a new generalization of the Weibull distribution, which incorporates the exponentiated Weibull distribution introduced by Mudholkar and Srivastava (IEEE Trans. Reliab. 1993; 42:299-302) as a special case. We refer to the new family of distributions as the beta-Weibull distribution. We investigate the potential usefulness of the beta-Weibull distribution for modeling censored survival data from biomedical studies. Several other generalizations of the standard two-parameter Weibull distribution are compared with regards to maximum likelihood inference of the cumulative incidence function, under the setting of competing risks. These Weibull-based parametric models are fit to a breast cancer data set from the National Surgical Adjuvant Breast and Bowel Project. In terms of statistical significance of the treatment effect and model adequacy, all generalized models lead to similar conclusions, suggesting that the beta-Weibull family is a reasonable candidate for modeling survival data.