## MATH96048 survival model课程简介

It seems that you have provided a course description for a graduate-level biostatistics course focused on the analysis of right-censored survival data. The course covers various topics such as Kaplan-Meier estimation of survival curves, proportional hazards regression, accelerated failure time models, parametric modeling of survival data, model diagnostics, time-varying covariates, and delayed entry.

The course prerequisites are either BIOST 513, BIOST 515, BIOST 518, or permission of the instructor. It is offered jointly with BIOST 537, and it appears that it is offered during the Winter quarter.

## PREREQUISITES

It seems that you have provided a course description for a graduate-level biostatistics course focused on the analysis of right-censored survival data. The course covers various topics such as Kaplan-Meier estimation of survival curves, proportional hazards regression, accelerated failure time models, parametric modeling of survival data, model diagnostics, time-varying covariates, and delayed entry.

The course prerequisites are either BIOST 513, BIOST 515, BIOST 518, or permission of the instructor. It is offered jointly with BIOST 537, and it appears that it is offered during the Winter quarter.

## MATH96048 survival model HELP（EXAM HELP， ONLINE TUTOR）

Definition: The cumulative distribution function (CDF) of $T$ is
$$F(t)=\mathrm{P}(T \leq t)$$
the probability of death by age $t$.

The given definition is not entirely accurate.

The cumulative distribution function (CDF) of a random variable $T$ is defined as:

$$F(t) = \mathrm{P}(T \leq t),$$

where $F(t)$ gives the probability that $T$ takes a value less than or equal to $t$.

In the context of survival analysis, $T$ represents the time until an event of interest, such as death or failure, occurs. The CDF $F(t)$ gives the probability that the event has occurred by time $t$. In other words, $F(t)$ is the probability of survival up to time $t$.

Thus, the statement “the probability of death by age $t$” is not accurate, as the CDF can also represent the probability of other events, such as failure or recurrence.

Definition: The survivor (or reliability) function of $T$ is
$$S(t)=\mathrm{P}(T>t)=1-F(t),$$
the probability of surviving beyond age $t$.

Yes, the definition given is correct. The survivor function, also known as the reliability function or the complementary cumulative distribution function, is defined as:

$$S(t) = \mathrm{P}(T > t) = 1 – F(t),$$

where $S(t)$ gives the probability that the event of interest has not occurred by time $t$. In other words, $S(t)$ is the probability of survival beyond time $t$.

The survivor function is a fundamental concept in survival analysis, as it provides a way to estimate the survival distribution of a population. By estimating the survivor function from data, one can obtain information on the probability of survival beyond a certain time point, the median survival time, and other important aspects of the survival distribution.

## Textbooks

• An Introduction to Stochastic Modeling, Fourth Edition by Pinsky and Karlin (freely
available through the university library here)
• Essentials of Stochastic Processes, Third Edition by Durrett (freely available through
the university library here)
To reiterate, the textbooks are freely available through the university library. Note that
you must be connected to the university Wi-Fi or VPN to access the ebooks from the library
links. Furthermore, the library links take some time to populate, so do not be alarmed if
the webpage looks bare for a few seconds.

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