3. (Kaplan-Meier and Nelson-Aalen estimators) Consider the following censored lifetime data: 12 23 13 23+ 25 14+ 15+ 16+ 18 25 26 26 ktk 1 2 3 4 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. d 18 19 21 22+ 26+ 27+ 29 30 Yk 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 t,= (t), A = A(t), while SKM and SNA are respectively Kaplan-Meier and Nelson-Aalen estimates of S (tk). Please complete the table in your assignment submission. (b) Use R to plot estimated cumulative hazard rate Ã(t) and survival probability S(t). (c) It is known that the estimated variance Var(SNA (1)) of the estimate SNA(t) of survival probability S(t) for the Nelson-Aalen estimator is given by Var(SNA (1)) = [SNA (1)]² Σ de (yx — de) 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). JL 1

Q: 7z^2 = 252 z = and z = (both answers of z are required)

A:

Q: secA + tanA is equal to

A: Given:  To Find: To simplify the given expression.

Q: 13. GEOMETRY Two angles are supplementary if the sum of their measures is 180°. The two angles shown…

A:

Q: у" + 5у 3D 0

A: Given the differential equation y" + 5y = 0 Auxiliary equation of the given differential equation is…

Q: Solve (y- 8)“ = 144 . Use a comma to separate your two answers. y = Simplify radicals as needed.

A:

Q: Explain the three basic concepts used to derive the Kriging equation.

A: The kriging technique is employed basically to fits the surface to three-D analysis. kriging…

Q: dx -5 V4 x

A:

Q: I can't understand your handwriting and it's blurrry. Can you send a clearer one.Thanks

A: Given that                          We have to conduct hypothesis testing for the claim that the…

Q: Describe a model that represents 3/3x4/4

A: Like we can easily see that 3/3 is 1 whole and  4/4 is 1 whole

Q: What is outliner?

A: Hi, In statistics there is no word outliner. You might have meant the word outlier. So, here goes…

Q: Integrate. 3 sc²x CSC x + xp

A: Given

Q: 10) [ 5x (2 + 3x²)® dx

A: ∫5x2+3x28 dx Using Substitution u  =2+3x2du=6x dx⇒x dx=du6 ∫5x2+3x28 dx=∫5du6u8…

Q: Ve dx

A:

Q: dx 36-12x2

A:

Q: Use the equation (x-1)^2+(y+3)^2=12 find the radius and show steps

A:

Q: Can you please help me solve in detail. Thank you.

A:

Q: Explain why dii= 3 and not dii = 1.

A:

Q: Entegrate. your reark dx 4+25,2

A:

Q: 15p' x 4p Simplify 12p³

A:

Q: Explain how to simplify VVr.

A:

Q: 4 4x2 + dx

A:

Q: Calculate (3+j6)19 in rectangular format. Please show all your steps.

A: By using De moivres theorem the answer is given as follows :

Q: Can you show me how you drawn that and how you got your numb

A: For the give differential equation, check the slope at different points and draw the lines with the…

Q: Express 2e3+in6 in rectangular form.

A:

Q: please explain in clear format

A:

Q: Use the diagram below to answer the following questions: h = 3x^2 + 6x - 4 ; b = 4x Area of the…

A: