如果你也在 怎样代写生存模型Survival Models这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。生存模型Survival Models在许多可用于分析事件时间数据的模型中，有4个是最突出的:Kaplan Meier模型、指数模型、Weibull模型和Cox比例风险模型。
生存模型Survival Models精算师和其他应用数学家使用预测人类或其他实体(有生命或无生命)生存模式的模型，并经常使用这些模型作为相当重要的财务计算的基础。具体来说，精算师使用这些模型来计算与个人人寿保险单、养老金计划和收入损失保险相关的财务价值。人口统计学家和其他社会科学家使用生存模型对该模型适用的人口的未来构成做出预测。
statistics-lab™ 为您的留学生涯保驾护航 在代写生存模型survival model方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写生存模型survival model代写方面经验极为丰富，各种代写生存模型survival model相关的作业也就用不着说。
统计代写|生存模型代写survival model代考|Grouped Times of Death
This study design was described in Section 4.4, along with techniques for estimating a tabular survival model from such data. We are now interested in the estimation of parametric models, and we will consider the methods of maximum likelihood and least squares for this purpose.
Suppose $n$ persons are alive at $t=0$, and we observe their deaths in $k$ non-overlapping intervals of equal length. Let $d_i$ be the number of deaths observed in $(i, i+1]$. The probability of death in $(i, i+1]$ for a person alive at $t=0$ is $i \mid q_0=S(i)-S(i+1)$, so the contribution of the $(i+1)^{s t}$ interval to the likelihood is
$$
L_i=[S(i)-S(i+1)]^{d_i}
$$
The overall likelihood is
$$
L=\prod_{i=0}^{k-1}[S(i)-S(i+1)]^{d_i} .
$$
Then $S(i)-S(i+1)$ is written in terms of the unknown parameters of the chosen parametric model, and the parameters are found by maximizing $L$.
If the chosen $S(t)$ is sufficiently simple, such as a one-parameter uniform or exponential model, then convenient expressions for the MLE’s of the parameters can be found. Otherwise, as frequently occurs, the likelihood equations must be solved numerically, or the likelihood is maximized numerically without taking derivatives.
统计代写|生存模型代写survival model代考|Maximum Likelihood Approaches
As a first example, consider a sample of $n$ laboratory mice all alive at $t=0$. We observe the exact time of each death up to time $t=r$, and cease
observation at that time with some of the mice still alive. Since not all have died we have an incomplete data situation. Note that the study design is longitudinal (not cross-sectional), and those that are not observed to die are enders, not random withdrawals. In a clinical setting this type of study is said to be truncated.
The contribution of each death to the likelihood is the PDF for death at the time that death actually occurs. The contribution for each survivor at $t=r$ is simply the probability of living to $t=r$, namely $S(r)$. If there are $d$ deaths in total, out of the original sample of size $n$, then we have
$$
L=[S(r)]^{n-d} \cdot \prod_{i=1}^d f\left(t_i\right),
$$
where $t_i$ is the time of the $i^{t h}$ death.
生存模型代考
统计代写|生存模型代写survival model代考|Grouped Times of Death
本研究设计在第4.4节中描述，以及从这些数据估计表格生存模型的技术。我们现在对参数模型的估计感兴趣，我们将为此目的考虑最大似然和最小二乘的方法。
假设$n$人活在$t=0$，我们观察他们在$k$不等长的不重叠间隔内死亡。设$d_i$为$(i, i+1]$中观察到的死亡人数。一个在$t=0$活着的人在$(i, i+1]$的死亡概率是$i \mid q_0=S(i)-S(i+1)$，所以$(i+1)^{s t}$区间对可能性的贡献是
$$
L_i=[S(i)-S(i+1)]^{d_i}
$$
总的可能性是
$$
L=\prod_{i=0}^{k-1}[S(i)-S(i+1)]^{d_i} .
$$
然后将所选参数模型的未知参数写成$S(i)-S(i+1)$，通过最大化$L$求参数。
如果选择的$S(t)$足够简单，例如单参数均匀模型或指数模型，则可以找到参数的最大似然值的方便表达式。否则，如经常发生的那样，似然方程必须用数值方法求解，或者在不求导的情况下用数值方法使似然最大化。
统计代写|生存模型代写survival model代考|Maximum Likelihood Approaches
作为第一个例子，考虑一个在$t=0$存活的$n$实验室小鼠样本。我们观察每一个死亡的确切时间，直到时间$t=r$，然后停止
当时观察用的是一些还活着的老鼠。由于并非所有人都死亡，所以数据不完整。请注意，研究设计是纵向的(而不是横断面的)，那些没有观察到死亡的是终止，而不是随机退出。在临床环境中，这种类型的研究被称为被截断。
每次死亡对可能性的贡献是实际死亡发生时死亡的PDF。每个在$t=r$存活的人的贡献就是活到$t=r$的概率，也就是$S(r)$。如果在原始样本$n$中，总死亡人数为$d$，那么我们有
$$
L=[S(r)]^{n-d} \cdot \prod_{i=1}^d f\left(t_i\right),
$$
其中$t_i$是$i^{t h}$的死亡时间。
统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。