### Statistics 227

## Homework 9

## Due Wednesday, 4 December 1996

In Homework 8, problem 3, you used logistic regression methods to analyze
data on the occurrence of heart attacks among 35 individuals with high
cholesterol levels (Table
11.17 in Selvin). The aim was to find a predictive model for the risk
of heart attack. Specifically, you were to assess the risks associated
with weight, cholesterol level, and cigarette usage. For Homework 9,
reanalyze the data using appropriate survival analysis methods, as follows:
- Construct a new variable
`heavy` which indicates
whether an individual smokes more than 20 cigarettes per day. Assess
whether heart attacks are more likely for heavy smokers than for
light smokers by constructing the Kaplan-Meier (product-limit) estimates
for the survival curves in the two groups.
- Construct a proportional-hazards regression model for survival. Is
`heavy` or `cigs` (the number of cigarettes smoked per day)
a better predictor?
- Compare the results from the logistic analysis and the Cox analysis.
Describe how the models and the conclusions differ from one another.
- One patient appears to have had a particularly high cholesterol level.
Does this affect either the logistic or the survival analysis?

**Hints and comments:**

`kapmeier T C, by(G)`

calculates the product-limit estimator of survival-time distributions
for each value of G, and plots all of the curves on the same graph. In the
command above, T is the survival-time variable, and C indicates whether
that time corresponds to a death (C=1) or censoring (C=0).
`kapmeier` has been replaced in version 5.0 of Stata. If you
are using that version, you can temporarily revert to old-style Stata
commands by giving the command `version 4.0`, after which commands
like `kapmeier` will once again be recognized.
- The proportional hazards model is often referred to as "Cox
regression," after Sir David Cox who first introduced it. A Stata command
to do this calculation looks like this:

`cox Y X1 X2 ... Xp, d(C)`

where Y is the outcome (survival time), X1 through Xp are the predictors,
and C is an indicator that is 1 if an event was observed (death, for
instance) and a 0 if the observation was censored.
- The
`cox` command also has been replaced in Stata 5.0 and later
versions.

Last updated 26-Nov-96

For questions, send mail to
r-thisted@uchicago.edu
or mcpeek@galton.uchicago.edu