Instructor: Professor Eric Slud,  Statistics Program, Math Dept.
                                       Rm 2314, x5-5469,  evs@math.umd.edu

Office hours: M 1-2, W 11-12, Th 1-2 (initially), or by appointment.

SAMPLE  PROBLEMS  FOR  IN-CLASS  TEST Old and New.
NOTE changed date for test, which is now Friday April 11.

For Syllabus click here for lecture Handouts click here, and
      here for Statistical Computing handouts.
For Homework, click here.

The topic of the course is the statistical analysis of data on lifetimes or durations.
Such data often have the feature of being right-censored, where subjects may
leave the study at random times and those who have not died at the ending time of
the study are simply recorded as being still alive, or truncated, where subjects enter
the study only if they meet some criterion which may involve an age-variable or
time since diagnosis or other preliminary event.  Such data arise frequently in
clinical trials, epidemiologic studies, reliability tests, and insurance. We first
present parameterizations of survival distributions, in terms of hazard intensities,
which lend themselves to the formulation of parametric models, including
regression-type models which relate failure-time distributions to auxiliary
biomedical predictors. The special features of truncation or censoring present
unique challenges in the formulation of likelihoods and efficient estimation and
testing in settings where the distributions of arrival-times and withdrawal-times
are unknown and not parametrically modelled. This statistical topic has achieved
great prominence in the theoretical statistical literature because it is a particularly
good arena for the introduction of techniques of estimating and testing finite-
dimensional parameter values --- such as a treatment- effectiveness parameter
in clinical studies --- in the presence of infinite-dimensional unknown
parameters. Such problems are referred to as Semiparametric.

Prerequisites: The presentation will be geared to second-year Stat grad students.
Minimum background is Stat 410 and Stat 700.

Required Text:  The required text is:

Klein, J. and Moeschberger, M. (2003) Survival Analysis: Techniques for
Censored and Truncated Data, 2nd ed. Springer-Verlag ISBN: 038795399X

Data:

Datasets contained in Appendix A of the Kalbfleisch & Prentice book, except
for Dataset V, can be downloaded in Excel format from the public ftp site,
linked here .     Two of the datasets (Datasets I and V) are available in ASCII format,
as rectangular tables, here.

Recommended Text(s):

The book which we used last time this course was taught will serve as a useful reference,
but the explanations given there are harder, less straightforward and often more intuitive.

Kalbfleisch, J. and Prentice, R. (2002) The Statistical Analysis of Failure Time Data,
2nd ed. John Wiley ISBN: 0-471-36357-X

Another very useful recommended text (a 1980 book reissued as a paperback)

R. Miller, Jr. (1980) Survival Analysis. Wiley-Interscience 1998, ISBN: 0471255483

and, for the more mathematically inclined, a primarily theoretical text by two
former Maryland students:

Fleming, T. and Harrington, D. (1991) Counting Processes and Survival Analysis.
ISBN: 047152218X

Coverage of the Klein & Moeschberger book will be Chapters 1-9, plus a few
miscellaneous topics. The main topics are:

Klein & Moeschberger is a very methods-oriented book, and will be covered along
with R software implementation with real-data examples. The Miller book explains things
well and gives good background and literature references. For additional mathematical
justifications, including the connection with counting processes and martingales, I will draw
additional material from Fleming and Harrington and the research literature. Other data
examples, and more sophisticated data analyses, can be found in the Kalbfleisch and
Prentice book.

Grading:  The course grade will be based 50% on 7 homework problem sets,
25% on an in-class test, and 25% on a course project or paper at the end. The homework
problems will be a mixture of theoretical problems at Stat 410/Stat 700 level, and of
computational or data-analysis problems. The in-class test will be designed to test
(i) definitions (of models and distributions and statistics),
(ii) ability to use model definitions to construct likelihoods (and partial likelihoods) and
derive statistics from them, and
(iii) basic properties of estimators and test-statistics studied in class.
The course project will be either a paper on a topic not fully covered in class, with
illustrative data analysis, or an extended and coherent data analysis and writeup (of about
10 pages, not including computer output).
Note: homework problem assignments will be due approximately every 2 weeks.
The problem sets and due dates will be posted to this web-page and announced in
class. The problems will be due on the dates announced and will be graded down for
lateness unless you have a VERY good excuse.

Computing in the course can be done with Splus, R, SAS, or any other package you
are familiar with which also has preprogrammed Survival Analysis modules. However,
Splus and R are the best choices if you want guidance and/or help from me. R is also
the best choice in accommodating the newest methods from the research literature. Various
datasets can be explored and accessed within existing R packages and libraries, e.g. by
issuing the command
       > data()        after        > library(survival)
Whatever package you choose, you can get computing help, datasets, and further links at
StatLib.  All of the datasets for the Klein and Moeschberger book, including its exercises,
can be found here . As mentioned above, all of the datasets in (the Appendix of) the
Kalbfleisch and Prentice text are freely available for download, and Datasets I and V can
be found in ASCII format here . As an indication of how the datasets were imported using
R into the format given, see the following linked script.

See Handouts section below for link to "Rbasics" file connected with the data analysis tasks
needed for Homeworks. For the systematic Introduction to R and R reference manual
distributed with the R software, either download from the R website or simply invoke
the command

> help.start()

from within R. For a slightly less extensive introductory tutorial in R, click here .

Lecture Note and Slides Handouts:

Statistical Computing Handouts:

The following material and handouts were produced in previous terms
when the course was given using Splus as the computing platform. They
are mostly still usable, since R and Splus are syntactically the same and
share many older functions, but these handouts will be updated and
converted to R as the term progresses.

NOTE: to get started using survival-related functions in R, you need to "load" the
R survival package, which is accomplished by the command:

> library(survival)

Handouts can be found at linked pages for each of the following topics:

(0) Basics on R commands for data entry and life table estimates

(1) Nelson-Aalen & Kaplan Meier calculation         (converted to R)

(2) Illustrative R Script for Survival Curves, Hazards, Medians, and SE's.

(3) Nelson-Aalen calculation for left-truncated right-censored data.     (converted)

(4) Script and Illustrative Picture on model fitting of VA Lung-Cancer data in R.
This Script and picture also contain material about fitting and plotting the Cox Model
for the same dataset and comparing the results to the previous accelerated failure time
parametric regression model.

 (5) R calculations for weighted logrank (2-sample) test statistics.

 (6) Splus log on Stratified Analyses (Survival Curves & Weighted
        Logrank & Cox Models).

 (7) New illustration of Stratified versus interaction-term tests of difference between
coefficients in subgroups of a survival dataset. This R script and picture explain in the
example of a Mayo lung-cancer study that there are actual differences between the
coefficient for a baseline health index ("Karnofsky score") for the two sexes in the study,
but that these differences are obscured if an assumption of common baseline hazard for
both sexes is made.

(8) Log of Splus analyses related to Cox model and comparison
with exponential regression model, along with some pictures.

(9) Handout containing R Log on Self-Consistency Property of Kaplan-Meier Estimator
and Redistribute-to-the-Right Algorithm and Coding for Turnbull (1974) self-consistent estimator
of survival-distribution in double-censored survival data.

(10) Splus algorithm of Turnbull for interval-censored data.

 (10) Splus computations for kernel-smoothed Nelson-Aalen estimator.

(11) R Script for Time-dependent Cox-Model fitting, illustrated with data analysis
       of Mayo-Clinic Lung Cancer Data.

(12) R script for calculating Partial Likelihoods in (non-time-dependent) Cox-model.
       This includes calculations with risk-groups. The script will later be augmented
       to include the calculation of score statistics for individual coefficients.

Syllabus.

Chapter 1. Introduction: Terminology, data structures & examples.    1 class,   1/28

Chapter 2. Failure Time models.           4   classes,   1/30 - 2/6

Chapter 3. Censored-Data Parametric Inference & Likelihoods.    3   classes,    2/8 - 2/13

Chapter 4. Nonparametric survival-curve estimation.    3   classes,    2/15 - 2/20

Chapter 6. Other estimation techniques.            3   classes,    2/27 - 3/3

Chapter 7. Rank statistics for 1- and 2-sample Tests.     5 classes,     3/5 - 3/14

Chapter 8. Relative Risk Regression Models     5 classes,     3/24 - 4/2