This disclosure provides a method of preventing, alleviating or treating a condition (i.e., neutropenia) in a subject in need thereof, the condition characterized by compromised white blood cell production in the subject. The method includes administering to the subject a therapeutically effective amount of a protein complex on the same day as a chemotherapy regimen, wherein the protein complex is a modified human granulocyte-colony stimulating factor (hG-CSF) covalently linked to an immunoglobulin Fc region via a non-peptidyl polymer. The non-peptidyl polymer is site-specifically linked to an N-terminus of the immunoglobulin Fc region, and the modified hG-CSF comprises substitutions in at least one of Cys17 and Pro65.