A study is conducted in patients with HIV. The primary outcome is CD4 cell count, which is a measure of the stage of the disease. Lower CD4 counts are associated with more advanced disease. The investigators are interested in the association between vitamin and mineral supplements and CD4 count. A multiple regression analysis is performed relating CD4 count to the use of supplements (coded as 1 = yes and 0 = no) and to the duration of HIV in years (i.e., the number of years between the diagnosis of HIV and the study date). For the analysis, y = CD4 count:    = 501.41 + 12.67 Supplements − 30.23 Duration of HIV.   What is the expected CD4 count for a patient taking supplements who has had HIV for 2.5 years? What is the expected CD4 count for a patient not taking supplements who was diagnosed with HIV at study enrollment? What is the expected CD4 count for a patient not taking supplements who has had HIV for 2.5 years?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy
Problem 2EA
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  1. A study is conducted in patients with HIV. The primary outcome is CD4 cell count, which is a measure of the stage of the disease. Lower CD4 counts are associated with more advanced disease. The investigators are interested in the association between vitamin and mineral supplements and CD4 count. A multiple regression analysis is performed relating CD4 count to the use of supplements (coded as 1 = yes and 0 = no) and to the duration of HIV in years (i.e., the number of years between the diagnosis of HIV and the study date). For the analysis, y = CD4 count:

 

 = 501.41 + 12.67 Supplements − 30.23 Duration of HIV.

 

  1. What is the expected CD4 count for a patient taking supplements who has had HIV for 2.5 years?
  2. What is the expected CD4 count for a patient not taking supplements who was diagnosed with HIV at study enrollment?
  3. What is the expected CD4 count for a patient not taking supplements who has had HIV for 2.5 years?
  4. If we compare two patients and one has had HIV for 5 years longer than the other, what is the expected difference in their CD4 counts?
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