1) An open label study (where participant are aware of the treatment they are taking) is conducted to assess the time relief following treatment in patients with arthritis. The following linear regression equations are estimated relating time to pain relief measured in minutes (dependent variable) to participant's age (in years) gender (coded 1 for males and 0 for females) and severity of diseases (a score ranging from 0 t0 100 with higher scores indicative of more severe arthritis. Time to pain Relief = - 24.2 +0.9 Age Time to pain Relief= 11.8 +19.3 male Gender Time to pain Relief= 3.8 +0.4 severity Time to pain Relief = -19.8 +0.50 Age +10.9 male Gender +0.2 severity A) What is expected time to pain relief for a male following treatment? B) What is the expected time to pain relief for a participant aged 50 following treatment 2) 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 vitamins and mineral supplements and CD4 count. A multiple regression analysis is performed relating CD4 count to use of supplements ( coded as 1=yes, 0=no) and to 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. 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. B) What is the expected CD4 count for a patient not taking supplement who was diagnosed with HIV at study enrollment? C) What is the expected CD4 count for a patient not taking supplements who has had HIV for 2.5 years 3) 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 disease at the start of the study and randomized to receive either the new medication or a placebo. Participants are followed for a maximum of 10 years for the development of coronary artery disease. The following data are: Number participants Cholesterol medication Placebo 400 400 number with coronary artery disease 28 42 A) Compute the Relative Risk of coronary artery disease in patients receiving the new medication as compared to placebo. Relative Risk = B) Compute the Odd ratio of coronary artery disease in patients receiving the new medications as compared to placebo Odds Ratio = 4) A national survey is conducted to assess the association between hypertension and stroke in persons over 75 years of age with a family history of stroke. Development of stroke is monitored over a 5 years follow up period. The data are summarized below and the numbers are in millions. Developed stroke did not develop stroke Hypertension 12 37 No Hypertension 4 26 A) Compute the cumulative incidence of stroke in persons over 75 years of age Cumulative Incidence= B) Compute the Relative Risk of stroke in hypertensive as compared to non- hypertensive persons Relative Risk= C) Compute the Odds Ratio of stroke in hypertensive as compared to non- hypertensive persons Odds Ratio = 5) A small cohort study is conducted in 13 patients with an aggressive cellular disorder linked cancer. The clinical courses of the patients are depicted graphically below. A) Compute the prevalence of cancer at 12 months Prevalence = B Compute the cumulative Incidence of cancer at 12 months Cumulative incidence 12 mths = C) Compute the incidence rate (per month) of death Incidence Rate = --------------per 1,000 person months