Since carcinogenicity bioassays are time-consuming, costly, and use animal resources, structure-activity relationship equations which model toxicological end-points have been developed to make available alternative methods which approximate the results that could be obtained from bioassays but which are less expensive and time-consuming and use fewer, if any, animals. These equations are based on sets of bioassay results and explain the end-point under consideration in terms of substructural and other parameters which describe the chemical entities. The resulting equations--or models--can then be used to estimate--or predict--the end-point for new structures. The estimation is followed by validation procedures.