数据统计作业代写 STAT 6227代写 r语言代写 SAS代写

STAT 6227, Assignment #1

数据统计作业代写 1. Distribution functions and hazard functions: Let T ∈ T be a time-to-event random variable within the time range T on (0, ∞) with probability

1. 数据统计作业代写

Distribution functions and hazard functions: Let T ∈ T be a time-to-event random variable within the time range T on (0, ∞) with probability CDF F(t) = P(T ≤ t) and survival function S(t) = 1 − F(t) at t ∈ T , λ(t) be the hazard rate, and Λ(t) the cumulative hazard. Let m(t) be the mean residual life function.

1.1 If T has an exponential(λ) distribution, what are the expressions of S(t), λ(t), Λ(t) and m(t)?

1.2 If T has a uniform(0, a) distribution, what are the expressions of S(t), λ(t), Λ(t) and m(t)?

1.3 If T has geometric distribution with θ, i.e. P(T = i) = θ(1 − θ)ⁱ⁻¹ for any interger i = 1, 2, . . ., what are the expressions of S(t), λ(t), Λ(t) and m(t)?

1.4 Suppose that λ(t) follows the parametric model λ(t) = ab(bt)^a−1 exp[(bt)^a ] for some (a, b). What are the expressions of Λ(t), F(t) and S(t)?

1.5 Show that the expected value of T is

2. 数据统计作业代写

Application to the IMRAW-IST data: This dataset has been used in Sloand et al. (2008). You may use either SAS or R to do the computation and show your results in graphs.

2.1 Calculate the KM estimate and its 95% pointwise confidence interval of S(t) for time to death of the IST patients.

2.2 Calculate the KM estimate and its 95% pointwise confidence interval of S(t) for time to AML or death of the IST patients.

2.3 Repeat (2.1) and (2.2) for men and women separately.

2.4 Repeat (2.1) and (2.2) for patients with “IPSS high” and not “IPSS high” separately.

2.5 Calculate the KM estimate and its 95% pointwise confidence interval of S(t) for time to death of the IMRAW patients.

2.6 Calculate the KM estimate and its 95% pointwise confidence interval of S(t) for time to AML or death of the IMRAW patients.

2.7 Repeat (2.5) and (2.6) for men and women separately.

2.8 Repeat (2.5) and (2.6) for patients with “IPSS high” and not “IPSS high” separately.

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