8.7 Exercises 141In this study, we see that the interpretation of the odds is that the
odds are 1.6 times greater that a nonsmoker who is otherwise similar
to the smoker. Odds represent the ratio of the probability of occurrence
to the probability that the disease does not occur, and the odds ratio is
just a ratio of the odds for cases divided by the odds for controls. This
is a little different from relative risk but conveys a similar message.
When the risk (probability of occurrence of the disease) is low, the odds
ratio provides a good approximation to the relative risk.
We looked at point estimates for relative risk and odds ratios, but
we did not show you how to get confi dence intervals. Confi dence inter-
vals for these estimates are found in Lachin ( 2000 , p. 24 for relative
risk). We will discuss relative risk again in the context of survival
analysis in Chapter 10.
8.7 EXERCISES
- D e fi ne the following:
(a) Chi - square test
(b) Contingency table
(c) Odds ratio
(d) Relative risk
(e) Cohort study
(f) Case - control study
(g) Test for independence in 2 × 2 table - In a survey study, subjects were asked to report their health as excellent,
good, poor, and very poor. They were also asked to answer whether or not
they had smoked at least 250 cigarettes in their lifetime. Suppose Table
8.14 represents the outcome of the survey.
Determine if there is a relationship between cigarette usage and reported
health status at the 5% signifi cance level, one sided. What is the p - value
for the chi - square test? Why is it appropriate to use the chi - square test? - For the same subjects in the survey in the above table, the subjects were
asked if they were currently smoking, had quit smoking or never smoked.
Table 8.15 shows the survey results on smoking status versus health
assessment.
Is reported health status related to smoking status? Test at the 5% level
one - sided.