WEEK 8 PROBLEMS30 POINTS 15 points each. Place answers within the Word document below. 1. A study is conducted to estimate survival in patients following kidney transplant. Key factors that adversely affect success of the transplant include advanced age and diabetes. This study involves 25 participants who are 65 years of age and older and all have diabetes. Following transplant, each participant is followed for up to 10 years. The following are times to death, in years, or the time to last contact (at which time the participant was known to be alive). Deaths: Alive: 1.2, 2.5, 4.3, 5.6, 6.7, 7.3 and 8.1 years 3.4, 4.1, 4.2, 5.7, 5.9, 6.3, 6.4, 6.5, 7.3, 8.2, 8.6, 8.9, 9.4, 9.5, 10, 10, 10, and 10 years Use the life table approach to estimate the survival function. Use years intervals of 0-2; 2-4; Complete the table below. Interval in Years Number At Risk During Interval, Average Number At Risk During Interval, Number of Deaths During Interval, Lost to FollowUp, Ct Proportion Dying qt = Dt/Nt* Proportion Surviving pt = 1-qt Survival Probability St = pt*St-1 Nt Nt* =Nt-Ct /2 Dt 0-2 25 25 1 0 0.0400 0.9600 0.9600 2-4 24 23.5 1 1 0.0426 0.9574 0.9191 4-6 22 20 2 4 0.1000 0.9000 0.8272 6-8 16 14 2 4 0.1429 0.8571 0.7091 8-10 10 5.5 1 9 0.1818 0.8182 0.5801 Use the Kaplan-Meier approach to estimate the survival function. Complete the table below Time, Years 0 1.2 2.5 3.4 4.1 4.2 4.3 5.6 5.7 5.9 6.3 6.4 6.5 6.7 7.3 8.1 8.2 8.6 8.9 9.4 9.5 10.0 Number at Risk Nt 25 25 24 23 22 21 20 19 18 17 16 15 14 13 12 10 9 8 7 6 5 4 Number of Deaths Dt Number Censored Ct 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 Survival Probability St+1 = St*((Nt-Dt)/Nt) 1 0.96 0.92 0.92 0.92 0.92 0.874 0.828 0.828 0.828 0.828 0.828 0.828 0.764 0.701 0.631 0.631 0.631 0.631 0.631 0.631 0.631 Referring to the graph above: What is the probability of surviving 6.5 years? A. 0.35 B. 0.15 C. 0.99 D. 0.90 Patients have an 85% chance of surviving how many years? A. B. C. D. 6.0 4.25 3.2 5.5