The present invention relates to molecules having a variant Fc region, wherein said variant Fc region comprises at least one amino acid modification relative to a wild-type Fc region. These modified molecules confer an effector function to a molecule, where the parent molecule does not detectably exhibit this effector function. In particular, the molecules of the invention have an increased effector cell function mediated by a Fc.gamma.R, such as, but not limited to, ADCC. In one embodiment, the variant Fc region binds Fc.gamma.RIIIA and/or Fc.gamma.RIIA with a greater affinity, relative to a comparable molecule comprising the wild-type Fc region. The molecules of the invention have particular utility in treatment, prevention or management of a disease or disorder, such as cancer, in a sub-population of patients, wherein the target antigen is expressed at low levels in the target cell population, in particular, in patients refractory to treatment with an existing therapeutic antibody due to the low level of target antigen expression on the cancer or associated cells.