This invention is directed to a therapeutic strategy, involving (1) identification of alternative alleles of genes coding for proteins vital for cell viability or cell growth and the loss of one of these alleles in cancer cells due to loss of heterozygosity (LOH) and (2) the development of inhibitors with high specificity for the single remaining alternative allele of the vital gene retained by the cancer cell after LOH. The inhibitors of this invention are specific for one alternative allele of a gene that codes for a protein vital to cell viability or cell growth. The targeted gene has two alternative alleles in which the inhibitors of this invention block only the one alternative allele still present in the cancer cells. Exposure to the inhibitor inhibits or kills cancer cells which have undergone LOH. Protein is still capable of being expressed in the normal cells exposed to the inhibitor by the unblocked alternative allele. This differential effect of the inhibitor on cancer cells and normal cells accounts for the high therapeutic index of the inhibitors of this invention when used as antineoplastic agents.