Replication-competent adenovirus vectors specific for cells which allow a probasin transcriptional response element (PB-TRE) to function, such as cells which express the androgen receptor (AR), and methods of use of such viruses are provided. These viruses comprise an adenoviral gene under control of a transcriptional regulatory portion of a PB-TRE, which is in turn dependent upon AR expression. The gene can be, for example, a gene required for viral replication or the adenovirus death protein gene (ADP). The viruses can also comprise at least one additional adenoviral gene under control of at least one additional prostate-specific transcriptional response element, such as that controlling prostate-specific antigen expression (PSA-TRE). Thus, virus replication can be restricted to target cells exhibiting prostate-specific gene expression, particularly prostate carcinoma cells.