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Statistical Methods in Medical Research: Survival Analysis and Clinical Trial Evaluation

This document discusses statistical methods used in medical research, particularly survival analysis and clinical trial evaluation techniques.

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    HLTH 501 Page 1 of 7 Statistical Methods in Medical Research: Survival Analysis and Clinical Trial Evaluation W EEK 8 P ROBLEMS — 30 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: 1.2, 2.5, 4.3, 5.6, 6.7, 7.3 and 8.1 years Alive: 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, N t Average Number At Risk During Interval, N t* =Nt - C t /2 Number of Deaths During Interval, D t Lost to Follow - Up, C t Proportion Dying q t = D t /N t* Proportion Surviving pt = 1 - qt Survival Probability S t = pt*S t - 1 0 – 2 25 25 1 0 0.04 0.96 0.96 2 – 4 24 23.5 1 0 0.0425531 0.9574468 0.919148936 4 – 6 23 22.5 2 0 0.08888888 0.91111111 0.837446809 6 – 8 21 20 2 0 0.1 0.9 0.753702128 8 – 10 19 18 1 0 0.05555555 0.94444444 0.711829787 Use the Kaplan - Meier approach to estimate the survival function. Complete the table below Time, Years Number at Risk Nt Number of Deaths Dt Number Censored Ct Survival Probability S t+1 = S t *((N t - D t )/N t ) 0 25 0 0 1 1.2 25 1 0 0.96 2.5 24 1 0 0.92 3.4 23 0 1 0.92

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    HLTH 501 Page 2 of 7 4.1 22 0 1 0.92 4.2 21 0 1 0.92 4.3 20 1 0 0.874 5.6 19 1 0 0.828 5.7 18 0 1 0.828 5.9 17 0 1 0.828 6.3 16 0 1 0.828 6.4 15 0 1 0.828 6.5 14 0 1 0.828 6.7 13 1 0 0.7643076 92 7.3 12 1 1 0.7006153 85 8.1 11 1 0 0.6369230 77 8.2 9 0 1 0.6369230 77 8.6 8 0 1 0.6369230 77 8.9 7 0 1 0.6369230 77 9.4 6 0 1 0.6369230 77 9.5 5 0 1 0.6369230 77 10 4 0 4 0.6369230 77

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