Styryl sulfone compounds of the invention selectively inhibit proliferation of breast and prostate tumor cells, and induce apoptosis of such tumor cells, while sparing normal cells. The compounds, which are useful in the treatment of breast or prostate cancer, have formula (II) wherein n is zero or one; R1 is selected from the group consisting of hydrogen, chlorine, fluorine and bromine; R2 is selected from the group consisting of hydrogen, chlorine, fluorine, bromine, methyl and methoxy; and R3 is selected from the group consisting of hydrogen, chlorine and fluorine; provided, R2 may not be methyl or methoxy when R1 and R3 are both hydrogen and n is zero or one; and R1, R2 and R3 may not all be hydrogen when n is one, or formula (III) wherein R1 is selected from the group consisting of hydrogen, chlorine, fluorine and bromine or formula (IV) wherein R1 is selected from the group consisting of fluorine and bromine, and R2 is selected from the group consisting of 2-chlorophenyl, 4-chlorophenyl, 4-fluorophenyl and 4-nitro.