noun. A congenital or acquired deficiency of gamma globulins in the blood.

noun. A condition in which gammaglobulins such as immunoglobulins are absent from the blood, or present only in low concentrations

noun. a rare immunological disorder characterized by the virtual absence of gamma globulin in the blood and consequent susceptibility to infection

"Too little Btk causes a disease called Bruton's agammaglobulinemia, in which the B-lymphocytes fail to mature and produce antibodies, leading to infections."

agammaglobulinemic  

immunodeficiency