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\section*{First Mini-Project, 36-402, Spring 1998}

\subsection*{Description of the problem}

There is evidence that psychotheraputic interventions run by
professional therapists facilitate adjustment to disease among people
with cancer.  However, the costs associated with formal psychotherapy
groups preclude communities from adopting them.  Instead, community
support groups borrow some of the cognitive and behavioral principles
of psychotherapy, often focusing on providing emotional support
through peer discussion and informal support through education.  In
this study, peer discussion and education groups were examined to see
if they too help cancer patients adjust to life with the disease.

The data from this study consists of records on 312 women with Stage I
or Stage II breast cancer.  The women were divided into groups of
8--12 women each, and these groups were randomly assigned to one of
four possible interventions:  education group, peer discussion group,
combined education and peer discussion group, and control (no group
participation).  There were 7 groups for each intervention (for a
total of 28 groups).  The intervention lasted eight weeks.

Patients' quality of life was measured before the intervention,
immediately after the intervention, and six months after the
intervention.  Among the quality of life measures were
\begin{itemize}
\item {\bf PAF} A measure of the patient's positive affect (affect =
emotional expression)
\item {\bf NAF} A measure of the patient's negative affect.
\end{itemize}
PAF and NAF are based on different questionnaires, and so even though
you would expect them to be negatively correlated you wouldn't expect
the correlation to be exactly $-1$.

An extract of the data is contained in the file {\tt
http://www.stat.cmu.edu/afs-data/402/mp1/healthed.dat}, suitable for
reading into SPLUS with {\tt read.table()}.  The data looks like this:
\begin{verbatim}
group   interv  t1pa    t2pa    t1na    t2na
1       2       3.9     3.4     3.75    2.38
1       2       4       3.7     1       1.13
9       1       3.1     5       2.13    1
9       1       2.2     2.1     3.5     3.25
.
.
.
\end{verbatim}
where the meanings of the variables are:
\begin{verbatim}
group  - which of the 28 groups was the patient assigned to

interv - which intervention was this patient's group assigned to:
         1 = peer discussion
         2 = education
         3 = combined peer and education
         4 = control

t1pa   - PAF measure, taken before the intervention

t2pa   - PAF measure, taken immediately after the intervention

t1na   - NAF measure, taken before intervention

t2na   - NAF measure, taken immediately after intervention
\end{verbatim}
Note that there is some missing data, denoted by NA's in the data
file.

\subsection*{Your mission}

Your mission is to explore and analyze these data, and write up a
report of your conclusions.  Some issues to keep in mind include:
\begin{itemize}
\item {\bf Coding the factors.} Part of the problem looks like a
two-way ANOVA for the factors ``peer discussion'' and ``education''.
But the {\tt interv} variable isn't the right variable to think about
for this kind of analysis; you will have to create new variable(s)
that do what you want for this.
\item {\bf Groups.} Since ``education'' and ``peer discussion'' takes
place in classes, the patients coudn't be ``treated'' individually,
but rather had to be ``treated in groups or classes of 8--12 patients
each.  Can the groups be ignored in the analysis?  If not, how should
they enter into the problem?
\item {\bf What are the study units?}  Normally we would think of
individual patients as the units of study (the individual
observations).  We can do that here too, if we can convince ourselves
that the groups do not affect the outcomes.  However, it seems
plausible that individual responses are correlated with other
responses from the same group.  Does that mean the groups should be
the study units, so perhaps we should use group averages as the ``raw
data''?  If we do this, it feels like we've averaged away some
potentially important information about individuals.  Is there a
compromise between these two?
\item {\bf What is the response variable? Or perhaps there is more
than one\ldots} You might take just one measure, such as {\tt t2na},
as your outcome measure.  The trouble is, this is a measure of both
how much effect the treatment had, and how much negative affect the
patient had anyway, even before the treatment; that is why {\tt t1na}
was also collected.  Some possible ways to handle this include:
\begin{itemize}
\item let the response be $y$ $=$ {\tt t2na - t1na}
\item let the response be $y$ $=$ {\tt t2na}, but include {\tt t1na} as a
(continuous) predictor in the model
\end{itemize}
The second method above is called ANCOVA (Analysis of Covariance); an
ANCOVA model is simply an ANOVA model that also includes one or more
continuous predictors of some kind.  The reason for putting the
continuous predictor in the model is similar to why we include the
blocks in the model in a randomized blocks experiment: we try to pull
variation due to the continuous predictor out of the error sum of
squares, to make $F$ tests for factors in the model more powerful
(because, presumably, we will have lowered the error sum of squares).

Which of these two works better in this problem?  Why?  And what do we
do about the other variables, {\tt t1pa} and {\tt t2pa}?
\end{itemize}
The above are a few technical issues that will influence the kinds of
analysis you do for your final report; there are other technical
issues to think about too, like equality of variability of residuals
throughout the range of data, normality assumptions, existence of
outliers, and all of the other usual things that you think about with
linear models and ANOVA.

Of course, when all is said and done, the main questions you are
trying to answer are:
\begin{itemize}
\item Did any of the interventions (treatments) have an effect on PA
or NA scores?
\item If so, what would you recommend to new patients seeking
community-based support (education, peer discussion, or both), based
on the evidence of this study.
\end{itemize}
Your answers should be clearly-stated, sensible, and well justified by
the data above and the methods you use.

You may find that the methods presented in class are adequate to
answer these questions, and that's fine.  Or you may feel you need to
learn more; if you do you, may find it helpful to look at Chapters 7
and 10 of Venables and Ripley, or you may want to search the Web or
consult one of the textbooks I have been using in class (Box, Hunter
and Hunter, or Neter, Wasserman and Kutner), or other books in the
library (E\&S or Hunt).

\subsection*{On Writeups}

A good generic outline for project reports is:
\begin{enumerate}\parsep=0pt\parskip=0pt\itemsep=0pt\setcounter{enumi}{-1}
\item Executive summary (state background, problem, and conclusions in
one page or less);
\item Description of problem, problem background, and data;
\item Summary of analyses performed (what, why, how, results);
\item Conclusions;
\item Technical Appendices;
\item Bibliography and Credits
\end{enumerate}
Parts 1--3 should have as little technical material as you can
possibly get away with: a few well-chosen graphs, the names of the
techniques you applied and what parts of the data were used, and
perhaps one or two parameter estimates or $p$-values is the most you
should think about.  Part 4 should contain the ``story'' of your
technical analyses.  However, it should be possible to understand what
you've done from parts 1--3, without looking at part 4 at all.

If I were doing this, I would write part 4 first, as a sort of edited
``diary'' of my work as I learn about the problem (maybe not too
different from the handouts I prepare for class).  Then I would write
parts 2 and 3, using the highlights of my ``diary'', and finally I
would write parts 0 and 1, summarizing my work.  I expect part 1 would
be short, since you don't know anymore about the problem than I've
told you.

You are welcome to discuss this problem with each other, but I would
like a list of people you discussed this with (in and out of class),
as well as a list of any outside sources you consulted (books, Web
pages, etc.) in Part 5 of your report.

\subsection*{Timeline, Deadines}

I would like this to be a ``miniproject'', not a full-blown project.
So I would like to discuss with you your progress after one week,
probably in class, and then I would like you to hand in your final
reports one week later.  So the deadlines are:
\begin{itemize}
\item {\em Tue Feb 17.} I will take questions in class on the data,
the project, etc.
\item {\em Thu Feb 19.} Bring a draft of Part 4 of your report to
class for me to check, in class.
\item {\em Thu Feb 26.} Bring your final reports to class.
\end{itemize}
I may be willing to negotiate these deadlines a little, as long as the
whole class can agree on new ones.

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