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Problem 1 (Problems 7.10 – 7.14 in the book)
Suppose the incidence rato of MI (myocardial infarction) per year was 5 per 1000among 45- to 54-year-old men in 1990. To look at changes over time, 5000 45- to54-year old men were followed for 1 year staring in 2000. Fifteen new cases of MIwere found.
a) Test the hypothesis that incidence rates of MI changed from 1990 to 2000.
Suppose that 25% of MI cases in 1990 died within 24 hours. This proportion is calledthe 24-hour case-fatality rate.
b) Of the 15 new MI cases in the preceding study, 5 dies within 24 hours. Test if
the 24-hour case-fatality rate changed from 1990 to 2000.
1. Suppose we eventually plan to accumulate 50 MI cases during the period
2000–2005. Assume that the 24-hour case-fatality rate is truly 20% duringthis period. How much power would such a study have in distinguishingbetween case-fatality rates in 1990 and 2000–2005 if a two-sided test withsignificance level .05 is planned?
2. How large a sample is needed to achieve 90% power?
Suppose we identify fifty women 50 to 54 years old who have both a mother and asister with a history of breast cancer. Five of these women themselves have developedbreast cancer at some time in their lives. If we assume the expected prevalence rateof breast cancer in women whose mothers have had breast cancer is 4%, does havinga sister with the disease add to the risk?
The probability of bearing twins in the United States is approximately 1 in 90. Thisproportion is thought to be affected by a number of factors, including age, race, and
parity. To study the effect of age, hospital records are abstracted. Of 538 deliveriesfor women under 20, 2 resulted in twins. What can be said about the effect ofmaternal age on having twins?
Refer to the data set nifed.txt. The file is on the CD-ROM that came with thebook, use read.csv to read in the comma separated file. The format of the file isexplained on page 157 in the book.
Use hypothesis-testing methods to assess if either treatment affects blood pressureor heart rate in patients with severe angina.
Problem 5 (Problems 7.73 – 7.75 in the book)
A combination of photochemotherapy with oral methoxsalen (psoralen) and ultra-violet A radiation (called PUVA treatment) is an effective treatment for psoriasis.
However, PUVA is mutagenic, increase the risk of squamous-cell skin cancer, and cancause irregular, pigmented skin lesions. Stern et al.1 performed a study to assess theincidence of melanoma among patients treated with PUVA. The study identified 1380patients with psoriasis who were first treated with PUVA in 1975 ot 1976. Patientswere subdivided according to the total number of treatments received (< 250 or ≥ 250from 1975 to 1996). Within each group, the observed number of melanomas was de-termined from 1975 to 1996 and compared with the expected number of melanomasas determined by published U.S. age- and sex-specific melanoma incidence rates. Theresults were as in table 7.6.
Table 7.6: Relationship of PUVA treatment to incidence of
1. Suppose we want to compare the observed and expected number of events among
the group with < 250 treatments. Perform an appropriate hypothesis test.
2. Provide a 95% confidence interval for the expected number of events in the group
3. Interpret the results in 1. and 2.
1Stern, R.S., Nichols, K.J., & Vakeva, L.H. (1997). Malignant melanoma in patients treated for psoriasis
with methoxsalen (Psoralen) and ultraviolet A radiation (PUVA). The PUVA follow-up study. NewEngland Journal of Medicine, 322(3), 1041–1045.
Problem 6 (Problems 7.81 – 7.82 in the book)
An investigator wants to test a new eye drop that is supposed to prevent ocular itchingduring allergy season. To study the drug she uses a contralateral design whereby foreach participant one eye is randomized to get active drug (A) whereas the other eyegets placebo (P). Ten participants are randomized into the study. The randomizationassignment is given in Table 7.8.
1. What is the principal advantage of the contralateral design?
2. More left eyes seem to be assigned to A than to P, and the investigator wonders
if the assignments are really random. Perform a hypothesis test to assess howwell the randomization is working.
Problem 7 (Problems 8.1 – 8.3 in the book)
Twenty volunteers adopt a low-cholesterol diet for 3 months. The mean ±1 sd ofchange (baseline – 3 months) in serum cholesterol over the 3-month period was 20.0 ±35.0 mg/dL.
a) Test for significant changes in mean cholesterol over 3 months.
An important component of cholesterol is HDL cholesterol, which is widely believedto have a beneficial effect on heart disease. The mean ±1 sd of change (baseline –3 months) in HDL cholesterol over the 3-month period was 3.0 ± 12.0 mg/dL. Themean ±1 sd of weight loss over the 3-month period was 5.2 ± 8.0 lb.
1. Test for significant changes in mean HDL cholesterol over 3 months.
2. Test for significant changes in mean weight over 3 months.
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