Statistical Methods in Medical Research: Regression Analysis, Relative Risk, and Incidence Calculations

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Statistical Methods in Medical Research: Regression Analysis, Relative Risk, and Incidence Calculations1) An open label study (where participant are aware of the treatment they are taking) is conducted toassess the time relief followingtreatment in patients with arthritis. The following linear regressionequations are estimated relating time to pain relief measured in minutes (dependent variable) toparticipant’s age (in years) gender (coded 1 for males and 0 for females) and severity of diseases (a scoreranging from 0 t0 100 with higher scores indicative of more severe arthritis.Time to pain Relief =-24.2 +0.9 AgeTime to pain Relief= 11.8 +19.3 male GenderTime to pain Relief= 3.8 +0.4 severityTime to pain Relief =-19.8 +0.50 Age +10.9 male Gender +0.2 severityA)What is expected time to pain relief for a male following treatment?11.8 + 19.3 = 31.1B)What is the expected time to pain relief for a participant aged 50 following treatment-24.2 + 0.9 * 50 = 20.82) A study is conducted in patients with HIV. The primary outcome is CD4 cell count which is a measureof the stage of the disease. Lower CD4 counts are associated with more advanced disease. Theinvestigators are interested in the association between vitamins and mineral supplements and CD4count. A multiple regression analysis is performed relating CD4 count to use of supplements ( coded as1=yes, 0=no) and to duration of HIV in years ( i.e. the number of years between the diagnosis of HIV andthe study date) for the analysis, y=CD4 count.Y=302 +15.1 supplements-18.6 duration of HIV.A) What is the expected CD4 count for a patient taking supplements who has had HIV for 2.5 years.302 + 15.1 * 1-18.6 * 2.5 = 270.6B) What is the expected CD4 count for a patient not taking supplement who was diagnosed with HIVat study enrollment?302 + 15.1 * 0-18.6 * 0 = 302C) What is the expected CD4 count for a patient not taking supplements who has had HIV for 2.5 years302 + 15.1 * 0-18.6 * 2.5 = 255.53) A randomized trial is conducted to evaluate the efficacy of a new cholesterol lowering medication.The primary outcome is incident coronary artery disease. Participants are free of coronary artery diseaseat the start of the study and randomized to receive either the new medication or a placebo. Participantsare followed for a maximum of 10 years for the development of coronary artery disease.

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