Many times a "side effect" of a medication is altering a lab value (making it higher or lower than the norm). You also have to look at the patients disease processes. Do they have cancer? COPD, are they pregnant, do they have diabetes, PVD, s/p CVA etc. Take a look at the patients lifestyle, do they smoke, drink, overeat, undereat..are they stressed out? Things like that. There isn't always a clear cut reason one or several values are out of wack, you have to play detective and take a look at the big picture.
Here is a great link that I used during school, it gives the common reasons doctors will order certain labs (its set up for a lay person to understand) it also gives the "normal" value ranges and common causes/reasons for higher/lower values. Hope it helps: http://www.labtestsonline.org/
By the way here are several reasons the neutrophils are elevated: cigarette smoking, stress, infection, acute kidney failure, cancer, preeclampsia, hemolytic amemia, polycythemia anemia, certain medications and the list goes on and on.
The above was for ELEVATED NEUTROPHILS..SORRY.
Here are some reasons for low neutrophil count:
typhoid fever and brucelosis and many viral diseases, including hepatitis, influenza, rubella, rubeola, and mumps, decrease the neutrophil count. An overwhelming infection can also deplete the bone marrow of neutrophils and produce neutropenia. Many antineoplastic drugs used to treat cancer produce bone marrow depression and can significantly lower the neutrophil count. Types of drugs that can produce neutropenia include some antibiotics, the psychotropic drug lithium, phenothiazines, and tricyclic antidepressants