### Homework 5 (due on Wednesday, April 19)

• Problems will be added until the last class before the due date.
• No electronic submission unless explicitly allowed.
• Use your own words when answering questions. Copying from other sources (including textbooks, handouts, my blog) is strongly discouraged, because it often indicates you don't understand your answer.

1. In the data, there are three variables. For each subject, `treatment` indicates treatment (an experimental drug) or placebo, `obstime` is the days observed after treatment, and `status` is an indicator variable for whether the time observation was censored or not. Graph the survival curves for those patients that received the placebo, and those that received the experimental drug. Did the drug improve the survival? [Note: In Stata, use `stset obstime, failure(status)` to declare the outcome variables. You also may need to generate an indicator variable for treatment.]
2. A common symptom of otitis media in young children is the prolonged presence of fluid in the middle ear, known as middle-ear effusion. The presence of fluid may result in temporary hearing loss and interfere with normal learning skills in the first two years of life. One hypothesis is that babies who are breast-fed for at least 1 month build up some immunity against the effects of the disease and have less prolonged effusion than do bottle-fed babies. A small study of 24 pairs of babies is set up, where the babies are matched on a one-to-one basis according to age, sex, socioeconomic status, and type of medications taken. One member of the matched pair is a breast-fed baby, and the other member is a bottle–fed baby. The outcome variable is the duration of middle-ear effusion (in days) after the first episode of otitis media. The results are here.
• Why might a nonparametric test be useful here? Which nonparametric test should be used here?
• Test the hypothesis that the duration of effusion is different among breast-fed babies than among bottle-fed babies using a nonparametric test.
3. A dietary survey was mailed to 537 students on two separate occasions, several months apart, including questions on many food items. Consider the red meat consumption responses listed below:
 Survey 2 Survey 1 < 1 serving/wk > 1 serving/wk Total < 1 serving/wk 136 92 228 > 1 serving/wk 69 240 309 Total 205 332 537
Examine the reproducibility of the survey using the Kappa statistic. Interpret your outcome.

Topic revision: r5 - 30 Oct 2006, ChunLi

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