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Various Hypothesis Testing Problems

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Diabetes
The insulin pump is a device that delivers insulin to a diabetic patient at regular intervals. It presumably regulates insulin better than standard injections. However, data to establish this point are few, especially in children. The following study was set up to assess the effect of use of the insulin pump on HgbA1c, which is a long-term marker of compliance with insulin protocols. In general, a normal range for HgbA1c is < 7%. Data were collected on 256 diabetic patients for 1 year before and after using the insulin pump. A subset of the data for 10 diabetic patients is given in Table 8.40 (see attachment).

8.163 What test can be used to compare the mean HgbA1c 1 year before vs. mean HgbA1c 1 year after use of the insulin pump?
8.164 Perform the test in Problem 8.163, and report a two-tailed p- value.
8.165 Provide a 95% CI for the mean difference in HgbA1c before minus the mean HgbA1c after use of the insulin pump.

Cardiology
Example31: Cardiovascular Disease The Physicians' Health Study was a randomized clinical trial, one goal of which was to assess the effect of aspirin in preventing myocardial infarction (MI). Participants were 22,000 male physicians ages 40- 84 and free of cardiovascular disease in 1982. The physicians were randomized to either active aspirin (one white pill containing 325 mg of aspirin taken every other day) or aspirin placebo (one white placebo pill taken every other day). As the study progressed, it was estimated from self- report that 10% of the participants in the aspirin group were not complying (that is, were not taking their study [aspirin] capsules). Thus the dropout rate was 10%. Also, it was estimated from self- report that 5% of the participants in the placebo group were taking aspirin regularly on their own outside the study protocol. Thus the drop- in rate was 5%. The issue is: How does this lack of compliance affect the sample size and power estimates for the study?
(No need to answer anything here. Ex 31 is provided because Ex 32 refers to it)
Example 32: Refer to Example 10.31. Suppose we assume that the incidence of MI is .005 per year among participants who actually take placebo and that aspirin prevents 20% of MIs (i. e., relative risk = p 1 / p 2 = 0.8). We also assume that the duration of the study is 5 years and that the dropout rate in the aspirin group = 10% and the drop- in rate in the placebo group = 5%. How many participants need to be enrolled in each group to achieve 80% power using a two- sided test with significance level = .05?
(No need to answer anything here. Ex 32 is provided because problem 10.1 refers to it)
Consider the Physicians' Health Study data presented in Example 10.32.

10.1 How many participants need to be enrolled in each group to have a 90% chance of detecting a significant difference using a two- sided test with a = .05 if compliance is perfect?

Pulmonary Disease
One important aspect of medical diagnosis is its reproducibility. Suppose that two different doctors examine 100 patients for dyspnea in a respiratory disease clinic and that doctor A diagnosed 15 patients as having dyspnea, doctor B diagnosed 10 patients as having dyspnea, and both doctor A and doctor B diagnosed 7 patients as having dyspnea.

10.16 Compute the Kappa statistic and its standard error regarding reproducibility of the diagnosis of dyspnea in this clinic.

Hepatic Disease
Refer to Data Set HORMONE. DAT, provided as an attachment.

10.37 What test procedure can be used to compare the percentage of hens whose pancreatic secretions increased (post- pre) among the five treatment regimens?
10.38 Implement the test procedure in Problem 10.37, and report a p-value.

Cancer
A topic of current interest is whether abortion is a risk factor for breast cancer. One issue is whether women who have had abortions are comparable to women who have not had abortions in terms of other breast cancer risk factors. One of the best- known breast cancer risk factors is parity (i. e., number of children), with parous women with many children having about a 30% lower risk of breast cancer than nulliparous women (i. e., women with no children). Hence it is important to assess whether the parity distribution of women with and without previous abortions is comparable. The data in Table 10.32 (see attachment) were obtained from the Nurses' Health Study on this issue.

10.61 What test can be performed to compare the parity distribution of women with and without induced abortions?
10.62 Implement the test in Problem 10.61, and report a two- tailed p- value.

Ophthalmology
A 5-year study among 601 participants with retinitis pigmentosa assessed the effects of high- dose vitamin A (15,000 IU per day) and vitamin E (400 IU per day) on the course of their disease. One issue is to what extent supplementation with vitamin A affected their serum- retinol levels. The serum- retinol data in Table 10.33 (see attachment) were obtained over 3 years of follow- up among 73 males taking 15,000 IU/ day of vitamin A (vitamin A group) and among 57 males taking 75 IU/ day of vitamin A (the trace group; this is a negligible amount compared with usual dietary intake of 3000 IU/ day).

10.64 What test can be used to assess whether mean serum retinol has increased over 3 years among subjects in the vitamin A group?

One interesting aspect of the study described in Problem 10.64 is to assess changes in other parameters as a result of supplementation with vitamin A. One quantity of interest is the level of serum triglycerides. Researchers found that among 133 participants in the vitamin A group (males and females combined) who were in the normal range at baseline (< 2.13 µmol/ L), 15 were above the upper limit of normal at each of their last 2 consecutive study visits. Similarly, among 138 participants in the trace group who were in the normal range at baseline (< 2.13 µmol/ L), 2 were above the upper limit of normal at each of their last two consecutive study visits.
10.68 What test can be performed to compare the percent-age of participants who developed abnormal triglyceride levels between the vitamin A group and the trace group?
10.69 Implement the test in Problem 10.68, and report a two- tailed p- value.

Obstetrics
The standard screening test for Down's syndrome is based on a combination of maternal age and the level of serum alpha- fetoprotein. Using this test, 80% of Down's syndrome cases can be identified, while 5% of normals are detected as positive.

10.121 What is the sensitivity and specificity of the test? Suppose that 1 out of 500 infants are born with Down's syndrome.