 # Survival Analysis - Models

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 Analaysis

• 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

Log-Rank Test

• 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](https://www.dropbox.com/s/2gvdoq69e3vj4e6/Parametric%20Survival%20Analysis.pdf?dl=0)

• 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.