Biostatistics 695 HW # 3
Jian Kang
October 3, 2007
2.7 In the United States, the estimated annual probability that a woman over the age
of 35 dies of lung cancer equals 0
.
001304 for current smokers and 0
.
000121 for
nonsmokers (M. Pagano and K. Gauvreau, Principles of Biostatistics, Duxbury
Press, Pacific Grove, CA. 1993, p. 134).
(a) Find and interpret the difference of proportions and the relative risk. Which
measure is more informative for these data? Why?
Ans:
The difference of proportion is 0
.
001304

0
.
000121 = 0
.
001183. The
relative risk is 0
.
001304
/
0
.
000121 = 10
.
7786. The relative risk is more in
formative, because the difference of proportion is so small that we might
think there is no difference. But the relative risk are more significant, which
implies that the smoker risk are about 10 times than the nonsmoker risk.
(b) Find and interpret the odds ratio. Explain why the relative risk and odds
ratio take similar values.
Ans:
The odds ratio is
0
.
001304
/
(1

0
.
001304)
0
.
000121
/
(1

0
.
000121)
= 10
.
7896
.
The relative risk and odds ratio take similar values because the risks for
smoker and nonsmoker are both quite small.
2.9 In an article about crime in the United States, Newsweek (Jan. 10, 1994) quoted
FBI statistics for 1992 stating that of blacks slain, 94% were slain by blacks, and
of whites slain, 83% were slain by whites. Let
Y
= race of victim and
X
= race
1
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of murderer. Which conditional distribution do these statistics refer to,
Y

X
, or
X

Y
? What additional information would you need to estimate the probability
that the victim was white given that a murderer was white? Find and interpret
the odds ratio.
Ans:
The conditional distribution of murderer given victim, i.e.
X

Y
’s distribu
tion refers to the statement. And we have that
Pr(
X
= B

Y
= W) = 0
.
17
Pr(
X
= W

Y
= W) = 0
.
83
Pr(
X
= B

Y
= B) = 0
.
94
Pr(
X
= W

Y
= B) = 0
.
06
Should have the prevalence of the victim was white, i.e.
P
(
Y
= W), we can
estimate the
P
(
Y
= W

X
= W) by Bayesian theorem as follow
Pr(
Y
= W

X
= W)
=
Pr(
X
= W

Y
= W) Pr(
Y
= W)
Pr(
X
= W

Y
= W) Pr(
Y
= W) + Pr(
X
= W

Y
= B) Pr(
Y
= B)
=
0
.
83
P
(
Y
= W)
0
.
83
P
(
Y
= W) + 0
.
06
P
(
Y
= B)
=
0
.
83
P
(
Y
= W)
1 + 0
.
77
P
(
Y
= W)
.
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 Spring '12
 RRJ
 Statistics, Biostatistics, Probability, Epidemiology, Medical statistics

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