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3. (Kaplan-Meier and Nelson-Aalen estimators) Consider the following censored lifetime data: 12 23 13 14+ 15+ 16+ 18 23+ 25 25 26 26 Recall that the + sign corresponds to censoring: for e.g., 14+ means exit by censoring at age 14. (a) Find estimates of mortality rate (t), cumulative mortality rate A(t), and the survival probability (Nelson-Aalen and Kaplan-Meier) S (t). Provide your answers in 4 decimal digits. ktk dx 22+ 18 19 21 26+ 27+ 29 30 Ук λx Ak SKM SNA where to denotes event times, d, the number of exit by the event at t, y the num- ber of individuals at risk at tk,= (t), A = A(t), while SKM and SNA are respectively Kaplan-Meier and Nelson-Aalen estimates of S (tk).

3. (Kaplan-Meier and Nelson-Aalen estimators) Consider the following censored lifetime data: 12 23 13 14+ 15+ 16+ 18 23+ 25 25 26 26 Recall that the + sign corresponds to censoring: for e.g., 14+ means exit by censoring at age 14. (a) Find estimates of mortality rate (t), cumulative mortality rate A(t), and the survival probability (Nelson-Aalen and Kaplan-Meier) S (t). Provide your answers in 4 decimal digits. ktk dx 22+ 18 19 21 26+ 27+ 29 30 Ук λx Ak SKM SNA where to denotes event times, d, the number of exit by the event at t, y the num- ber of individuals at risk at tk,= (t), A = A(t), while SKM and SNA are respectively Kaplan-Meier and Nelson-Aalen estimates of S (tk).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please do 3a with handwritten working out. 

 

Please do 3b, 3c and 3d with R code

3. (Kaplan-Meier and Nelson-Aalen estimators) Consider the following censored lifetime data: 12 13 23 ktk Recall that the + sign corresponds to censoring: for e.g., 14+ means exit by censoring at age 14. 1234 (a) Find estimates of mortality rate (t), cumulative mortality rate A(t), and the survival probability (Nelson-Aalen and Kaplan-Meier) S (t). Provide your answers in 4 decimal digits. 2 3 14+ 15+ 16+ 18 26 25 26 23+ 25 4 dx 21 22+ 18 19 26+ 27+ 29 30 λx Ak SKM SNA where to denotes event times, d, the number of exit by the event at t, y the num- ber of individuals at risk at tk, = (t), A = A(t), while SKM and SNA are respectively Kaplan-Meier and Nelson-Aalen estimates of S (t). Please complete the table in your assignment submission. (b) Use R to plot estimated cumulative hazard rate A(t) and survival probability S(t). (c) It is known that the estimated variance Var(SNA (t)) of the estimate SNA(1) of survival probability S(t) for the Nelson-Aalen estimator is given by dk (yk - dk) Var(SNA (t)) = [SNA (1)]² Σ Yk kast Use the formula to estimate the variance of S (t) at age t = 18. (d) Derive a 95% confidence interval for S (t) aged t = 18 using SNA (1).
Transcribed Image Text:3. (Kaplan-Meier and Nelson-Aalen estimators) Consider the following censored lifetime data: 12 13 23 ktk Recall that the + sign corresponds to censoring: for e.g., 14+ means exit by censoring at age 14. 1234 (a) Find estimates of mortality rate (t), cumulative mortality rate A(t), and the survival probability (Nelson-Aalen and Kaplan-Meier) S (t). Provide your answers in 4 decimal digits. 2 3 14+ 15+ 16+ 18 26 25 26 23+ 25 4 dx 21 22+ 18 19 26+ 27+ 29 30 λx Ak SKM SNA where to denotes event times, d, the number of exit by the event at t, y the num- ber of individuals at risk at tk, = (t), A = A(t), while SKM and SNA are respectively Kaplan-Meier and Nelson-Aalen estimates of S (t). Please complete the table in your assignment submission. (b) Use R to plot estimated cumulative hazard rate A(t) and survival probability S(t). (c) It is known that the estimated variance Var(SNA (t)) of the estimate SNA(1) of survival probability S(t) for the Nelson-Aalen estimator is given by dk (yk - dk) Var(SNA (t)) = [SNA (1)]² Σ Yk kast Use the formula to estimate the variance of S (t) at age t = 18. (d) Derive a 95% confidence interval for S (t) aged t = 18 using SNA (1).
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