Lecture 2
Event Time Data
Censoring & Truncation
More Examples on Event History Analysis
Medical field
Death, Relapse, Occurrence of symptoms, disease onset
Reliability
Machine breakdown, Machine repair
Business/Economics
Bankruptcy, Duration of l
Topic 4:
Assessment and Development of
the Cox Proportional Hazard Model
In the last chapter, we saw some of the mechanics of the Cox model. We
covered its derivation, how to fit it, how to compare hazard ratios, how
to test if a covariate has an effect a
Topic 4-2: A further method for assessing the
PHM
4.5.1 Motivation for extending the PHM
The use of time-dependent covariates allows us to relax the proportional
hazards assumption as well as gives us a framework for testing the
adequacy of the proportion
R-Implementation:
1. Read Data in R
2. #reads the file dataset.dat from the working directory:
> read.table("dataset.dat")
#reads the file dataset.dat from web page:
read.table("http:/./dataset.dat")
#reads the file dataset.dat from the directory mydata o
Topic 3-1: Coxs proportional hazards
model
(Time-independent Covariates)
1. The Proportional Hazards Model
2. Partial Likelihood Formulation
3. Treatments for Tied Event Times
300+ papers or books
advisor to government
knighted for contribution to science
Lecture 4
Kaplan-Meier Estimate of S(t)
=
= ( > ) for continuous
Life Table
At the dawn of modern statistics, in the 17th century, John
Graunt and William Petty pioneered the study of mortality
The construction of life tables dates back to 18th century
Topic 2-3: Hypothesis Test
1. Log-Rank Test
2. Weighted Log-Rank Test
3. K-Sample Comparison
4. Trend Test
5. Stratified Log-Rank Test
1. Log-Rank Test
1|P a g e
In many biomedical researches, one is interested in comparing
the survival functions between
Topic 3-2: Coxs proportional hazards
model
(Time-independent Covariates)
4. Inference for Regression Parameter
5. Estimation of Survival Function
1
4. Inference for Regression Parameter
Estimation of Regression Parameter
In this section, we illustrate the
Topic 5
Stratified and Extended Proportional Hazards Model
The proportional hazards model has the following advantages:
Nice interpretation
Theoretical properties have been studied extensively
Software widely available
Likelihood surface is easy to wo
Topic 1
Xiaoli Gao
1
Introduction
Survival analysis is a collection of various methods for analyzing the time
to a certain event, it is often a common practice in biomedical study
Time to death
Time of HIV incubation period (HIVAIDS)
Relapse of breast
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