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Unformatted text preview: 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- . 000121 = 0 . 001183. The relative risk is 0 . 001304 / . 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 . 001304 / (1- . 001304) . 000121 / (1- . 000121) = 10 . 7896 . The relative risk and odds ratio take similar values because the risks for smoker and non-smoker 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 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...
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