## Survival Analysis

The main ideas of the
course are to develop a critical approach to the analysis of survival data
often encountered in health and actuarial sciences research. This process will
include gaining some technical insight (mechanics of the statistical
methodology behind the ideas) as well as applications of these methods in
survival time related data. One of the main objective of this course isto gain
experience in survival data analysis using statistical software packages (MS
Excel,SPSS, STATA and Mathematica etc.)

Introduction to Survival
Analysis

Recognize or describe the type of problem
addressed by a survival analysis.

Define what is meant by censored data.

Give reasons why data may be censored.

Define survivor function.

Define a hazard function.

Describe the relationship between a survivor
function and a hazard function.

Identify the basic data layout for the
computer; in particular, put a given set of survival data into this layout.

Construction of actuarial life tables

Kaplan-Meier Survival
Curves and the Log-Rank Test

Compute Kaplan-Meier probabilities of
survival, given survival time and failure status information on a sample of
subjects.

Interpret a graph of KM curves that compare
two or more groups

Draw conclusions as the whether or not two or
more survival curves are the same based on

Computer results that provide a log-rank test.

Draw conclusions as to whether or not two or
more survival curves are the same based on computer results that provide a
breslow test

Decide whether the log-rank test or the
Breslow test is more appropriate for a given set of survival data.

The Cox Proportional
Hazard Model and its Characteristics

State the general form of the Cox proportional
hazard model.

State specific form of a Cox PH model
appropriate for analysis, given a survival analysis scenario involving one or
more explanatory variables.

State or recognize the form and properties of
the baseline hazard function in the Cox PH model.

Give at least three reasons for the popularity
of the Cox PH model.

State the meaning of the PH assumption

Given a computer printout involving one or
more fitted Cox PH models;

Compute any hazard ratio of interest

Carry out and interpret a designated test of
hypothesis

Evaluate interaction and confounding involving
one or more covariates.

Evaluating the Proportional Hazard Assumption

State three general approaches for evaluating
the PH assumption.

Summarize how log-log survival curves may be
used to assess the PH assumption.

Summarize how observed versus expected plots
may be used to assess the PH assumption.

Summarize how GOF tests may be used to assess
the PH assumption.

Describe given survival data or computer
output form a survival analysis that uses a Cox PH model, how to assess the PH
assumption for one or more variables in the model using

Graphical approach

The GOF approach

An extended Cox model with time dependent
covariates

The Stratified Cox Procedure

Explain a computer printout for a stratified
Cox procedure.

State the hazard form of a stratified Cox
model for a given survival analysis scenario and /or a given set of computer
results for such a model

Evaluate the effect of a predictor of interest
base on computer results form a stratified Cox procedure.

For a given survival analysis scenario and/or
a given set of computer results involving a stratified Cox model

State the no-interaction assumption for the
given model

Describe and/or carry out a test of the
no-interaction assumption

Describe and/or carry out an analysis when the
no-interaction assumption is not satisfied.

Extension of the Cox
Proportional Hazard Model for the Time-Dependent Variables

State the general form of the Cox model
extended for the time dependent variables.

State the specific form of an extended Cox
model appropriate for the analysis, given a survival analysis scenario
involving one or more time-dependent variables.

State the formula for a designated hazard
ratio of interest, given scenario describing a survival analysis using an
extended Cox model.

State the formula for an extended Cox model
that provides a method for checking the PH assumption for one more of the time
independent variables in the model, given a scenario describing a survival
analysis.

State the formula for the hazard ratio during
different time interval categories specified by the heavy side functions.

Parametric Survival Analysis Exponential
Distribution

Weibul Distribution

Gamma Fitting

Exponetial Fitting

**Case Studies:** Breast Cancer Survival Heart Transplant

**Recomended Books:**

Kleinbaum, D. (2002). Survival Data Analysis:
A self learning text, Second Edition, Springer Varlag

Elisa T. Lee (1998) Introduction to Survival
time Data, Second Edition, Wiley.