?Suppose the incidence rate of myocardial infarction (MI) was 5 per 1000 among 45- to

Fundamentals of Biostatistics | 8th Edition | ISBN: 9781305268920 | Authors: Bernard Rosner

Chapter 7: Problem 1 Fundamentals of Biostatistics 8

The mean serum-creatinine level measured in 12 patients 24 hours after they received a newly proposed antibiotic was 1.2 mg/dL. If the mean and standard deviation of serum creatinine in the general population are 1.0 and 0.4 mg/dL, respectively, then, using a significance level of .05, test whether the mean serum-creatinine level in this group is different from that of the general population.

Chapter 7: Problem 2 Fundamentals of Biostatistics 8

The mean serum-creatinine level measured in 12 patients 24 hours after they received a newly proposed antibiotic was 1.2 mg/dL. What is the p-value for the test?

Chapter 7: Problem 3 Fundamentals of Biostatistics 8

The mean serum-creatinine level measured in 12 patients 24 hours after they received a newly proposed antibiotic was 1.2 mg/dL. Suppose the sample standard deviation of serum creatinine in Problem 7.1 is 0.6 mg/dL. Assume that the standard deviation of serum creatinine is not known, and perform the hypothesis test in Problem 7.1. Report a p-value.

Chapter 7: Problem 4 Fundamentals of Biostatistics 8

The mean serum-creatinine level measured in 12 patients 24 hours after they received a newly proposed antibiotic was 1.2 mg/dL. Compute a two-sided 95% CI for the true mean serum-creatinine level in Problem 7.3.

Chapter 7: Problem 5 Fundamentals of Biostatistics 8

The mean serum-creatinine level measured in 12 patients 24 hours after they received a newly proposed antibiotic was 1.2 mg/dL. How does your answer to Problem 7.4 relate to your answer to Problem 7.3.

Chapter 7: Problem 6 Fundamentals of Biostatistics 8

The mean serum-creatinine level measured in 12 patients 24 hours after they received a newly proposed antibiotic was 1.2 mg/dL. Suppose and a one-sample t test is performed based on seven subjects. What is the two-tailed p-value?

Chapter 7: Problem 7 Fundamentals of Biostatistics 8

The mean serum-creatinine level measured in 12 patients 24 hours after they received a newly proposed antibiotic was 1.2 mg/dL. Use a computer program to compute the probability that a t distribution with 36 df exceeds 2.5.

Chapter 7: Problem 8 Fundamentals of Biostatistics 8

The mean serum-creatinine level measured in 12 patients 24 hours after they received a newly proposed antibiotic was 1.2 mg/dL. Use a computer program to compute the lower 10th percentile of a t distribution with 54 df.

Chapter 7: Problem 9 Fundamentals of Biostatistics 8

Plasma-glucose levels are used to determine the presence of diabetes. Suppose the mean ln (plasma-glucose) concentration (mg/dL) in 35- to 44-year-olds is 4.86 with standard deviation = 0.54. A study of 100 sedentary people in this age group is planned to test whether they have a higher or lower level of plasma glucose than the general population. If the expected difference is 0.10 ln units, then what is the power of such a study if a two-sided test is to be used with = .05?

Chapter 7: Problem 10 Fundamentals of Biostatistics 8

Plasma-glucose levels are used to determine the presence of diabetes. Suppose the mean ln (plasma-glucose) concentration (mg/dL) in 35- to 44-year-olds is 4.86 with standard deviation = 0.54. A study of 100 sedentary people in this age group is planned to test whether they have a higher or lower level of plasma glucose than the general population. Answer Problem 7.9 if the expected difference is 0.20 ln units.

Chapter 7: Problem 11 Fundamentals of Biostatistics 8

Plasma-glucose levels are used to determine the presence of diabetes. Suppose the mean ln (plasma-glucose) concentration (mg/dL) in 35- to 44-year-olds is 4.86 with standard deviation = 0.54. A study of 100 sedentary people in this age group is planned to test whether they have a higher or lower level of plasma glucose than the general population. How many people would need to be studied to have 80% power under the assumptions in Problem 7.9?

Chapter 7: Problem 12 Fundamentals of Biostatistics 8

Suppose the incidence rate of myocardial infarction (MI) was 5 per 1000 among 45- to 54-year-old men in 2000. To look at changes in incidence over time, 5000 men in this age group were followed for 1 year starting in 2010. Fifteen new cases of MI were found. Using the critical-value method with = .05, test the hypothesis that incidence rates of MI changed from 2000 to 2010.

Chapter 7: Problem 13 Fundamentals of Biostatistics 8

Suppose the incidence rate of myocardial infarction (MI) was 5 per 1000 among 45- to 54-year-old men in 2000. To look at changes in incidence over time, 5000 men in this age group were followed for 1 year starting in 2010. Fifteen new cases of MI were found. Report a p-value to correspond to your answer to Problem 7.12.

Chapter 7: Problem 14 Fundamentals of Biostatistics 8

Suppose the incidence rate of myocardial infarction (MI) was 5 per 1000 among 45- to 54-year-old men in 2000. To look at changes in incidence over time, 5000 men in this age group were followed for 1 year starting in 2010. Fifteen new cases of MI were found. Suppose that 25% of patients with MI in 2000 died within 24 hours. This proportion is called the 24-hour case-fatality rate. Of the 15 new MI cases in the preceding study, 5 died within 24 hours. Test whether the 24-hour case fatality rate changed from 2000 to 2010.

Chapter 7: Problem 15 Fundamentals of Biostatistics 8

Suppose the incidence rate of myocardial infarction (MI) was 5 per 1000 among 45- to 54-year-old men in 2000. To look at changes in incidence over time, 5000 men in this age group were followed for 1 year starting in 2010. Fifteen new cases of MI were found. Suppose that 25% of patients with MI in 2000 died within 24 hours. This proportion is called the 24-hour case-fatality rate. Suppose we eventually plan to accumulate 50 MI cases during the period 2010–2015. Assume that the 24-hour case-fatality rate is truly 20% during this period. How much power would such a study have in distinguishing between case-fatality rates in 2000 and 2010–2015 if a two-sided test with significance level .05 is planned?

Chapter 7: Problem 16 Fundamentals of Biostatistics 8

Suppose the incidence rate of myocardial infarction (MI) was 5 per 1000 among 45- to 54-year-old men in 2000. To look at changes in incidence over time, 5000 men in this age group were followed for 1 year starting in 2010. Fifteen new cases of MI were found. Suppose that 25% of patients with MI in 2000 died within 24 hours. This proportion is called the 24-hour case-fatality rate. How large a sample is needed in Problem 7.15 to achieve 90% power?

Chapter 7: Problem 17 Fundamentals of Biostatistics 8

Suppose the annual incidence of asthma in the general population among children 0–4 years of age is 1.4% for boys and 1% for girls. If 10 cases are observed over 1 year among 500 boys 0–4 years of age with smoking mothers, then test whether there is a significant difference in asthma incidence between this group and the general population using the critical-value method with a two-sided test.

Chapter 7: Problem 18 Fundamentals of Biostatistics 8

Suppose the annual incidence of asthma in the general population among children 0–4 years of age is 1.4% for boys and 1% for girls. Report a p-value corresponding to your answer to Problem 7.17.

Chapter 7: Problem 19 Fundamentals of Biostatistics 8

Suppose the annual incidence of asthma in the general population among children 0–4 years of age is 1.4% for boys and 1% for girls. Suppose that four cases are observed over 1 year among 300 girls 0–4 years of age with smoking mothers. Answer Problem 7.17 based on these data.

Chapter 7: Problem 20 Fundamentals of Biostatistics 8

Suppose the annual incidence of asthma in the general population among children 0–4 years of age is 1.4% for boys and 1% for girls. Report a p-value corresponding to your answer to Problem 7.19.

Chapter 7: Problem 21 Fundamentals of Biostatistics 8

Ribosomal 5S RNA can be represented as a sequence of 120 nucleotides. Each nucleotide can be represented by one of four characters: A (adenine), G (guanine), C (cytosine), or U (uracil). The characters occur with different probabilities for each position. We wish to test whether a new sequence is the same as ribosomal 5S RNA. For this purpose, we replicate the new sequence 100 times and find there are 60 A’s in the 20th position. If the probability of an A in the 20th position in ribosomal 5S RNA is .79, then test the hypothesis that the new sequence is the same as ribosomal 5S RNA using the critical-value method.

Chapter 7: Problem 22 Fundamentals of Biostatistics 8

Ribosomal 5S RNA can be represented as a sequence of 120 nucleotides. Each nucleotide can be represented by one of four characters: A (adenine), G (guanine), C (cytosine), or U (uracil). The characters occur with different probabilities for each position. We wish to test whether a new sequence is the same as ribosomal 5S RNA. For this purpose, we replicate the new sequence 100 times and find there are 60 A’s in the 20th position. Report a p-value corresponding to your results in Problem 7.21. Suppose we wish to test the hypothesis : µ = 45 vs. : µ > 45.

Chapter 7: Problem 23 Fundamentals of Biostatistics 8

Ribosomal 5S RNA can be represented as a sequence of 120 nucleotides. Each nucleotide can be represented by one of four characters: A (adenine), G (guanine), C (cytosine), or U (uracil). The characters occur with different probabilities for each position. We wish to test whether a new sequence is the same as ribosomal 5S RNA. For this purpose, we replicate the new sequence 100 times and find there are 60 A’s in the 20th position. What will be the result if we conclude that the mean is greater than 45 when the actual mean is 45? (i) We have made a type I error. (ii) We have made a type II error. (iii) We have made the correct decision.

Chapter 7: Problem 24 Fundamentals of Biostatistics 8

Ribosomal 5S RNA can be represented as a sequence of 120 nucleotides. Each nucleotide can be represented by one of four characters: A (adenine), G (guanine), C (cytosine), or U (uracil). The characters occur with different probabilities for each position. We wish to test whether a new sequence is the same as ribosomal 5S RNA. For this purpose, we replicate the new sequence 100 times and find there are 60 A’s in the 20th position. What will be the result if we conclude that the mean is 45 when the actual mean is 50? (i) We have made a type I error. (ii) We have made a type II error. (iii) We have made the correct decision. Suppose we wish to test : µ = 30 vs. : µ ? 30 based on a sample of size 31.

Chapter 7: Problem 25 Fundamentals of Biostatistics 8

Ribosomal 5S RNA can be represented as a sequence of 120 nucleotides. Each nucleotide can be represented by one of four characters: A (adenine), G (guanine), C (cytosine), or U (uracil). The characters occur with different probabilities for each position. We wish to test whether a new sequence is the same as ribosomal 5S RNA. For this purpose, we replicate the new sequence 100 times and find there are 60 A’s in the 20th position. Which of the following sample results yields the smallest p-value and why? (i) = 28, s = 6 (ii) = 27, s = 4 (iii) = 32, s = 2 (iv) = 26, s = 9

Chapter 7: Problem 27 Fundamentals of Biostatistics 8

The drug erythromycin has been proposed to possibly lower the risk of premature delivery. A related area of interest is its association with the incidence of side effects during pregnancy. Assume 30% of all pregnant women complain of nausea between weeks 24 and 28 of pregnancy. Furthermore, suppose that of 200 women who are taking erythromycin regularly during the period, 110 complain of nausea. Test the hypothesis that the incidence rate of nausea for the erythromycin group is the same for a typical pregnant woman.

Chapter 7: Problem 28 Fundamentals of Biostatistics 8

A pilot study of a new antihypertensive agent is performed for the purpose of planning a larger study. Five patients who have a mean DBP of at least 95 mm Hg are recruited for the study and are kept on the agent for 1 month. After 1 month the observed mean decline in DBP in these five patients is 4.8 mm Hg with a standard deviation of 9 mm Hg. If = true mean difference in DBP between baseline and 1 month, then how many patients would be needed to have a 90% chance of detecting a significant change in DBP over 1 month using a one-tailed test with a significance level of 5%? Assume that the true mean and standard deviation of the DBP difference were the same as observed in the pilot study.

Chapter 7: Problem 29 Fundamentals of Biostatistics 8

A pilot study of a new antihypertensive agent is performed for the purpose of planning a larger study. Five patients who have a mean DBP of at least 95 mm Hg are recruited for the study and are kept on the agent for 1 month. After 1 month the observed mean decline in DBP in these five patients is 4.8 mm Hg with a standard deviation of 9 mm Hg. Suppose we conduct a study of the preceding hypothesis based on 20 participants. What is the probability we will be able to reject using a one-sided test at the 5% level if the true mean and standard deviation of the DBP difference are the same as in the pilot study?

Chapter 7: Problem 30 Fundamentals of Biostatistics 8

The proportion of deaths due to lung cancer in males ages 15–64 in England and Wales during the period 1970– 1972 was 12%. Suppose that of 20 deaths that occur among male workers in this age group who have worked for at least 1 year in a chemical plant, 5 are due to lung cancer. We wish to determine whether there is a difference between the proportion of deaths from lung cancer in this plant and the proportion in the general population. State the hypotheses to use in answering this question.

Chapter 7: Problem 31 Fundamentals of Biostatistics 8

The proportion of deaths due to lung cancer in males ages 15–64 in England and Wales during the period 1970– 1972 was 12%. Suppose that of 20 deaths that occur among male workers in this age group who have worked for at least 1 year in a chemical plant, 5 are due to lung cancer. We wish to determine whether there is a difference between the proportion of deaths from lung cancer in this plant and the proportion in the general population. Is a one-sided or two-sided test appropriate here?

Chapter 7: Problem 32 Fundamentals of Biostatistics 8

The proportion of deaths due to lung cancer in males ages 15–64 in England and Wales during the period 1970– 1972 was 12%. Suppose that of 20 deaths that occur among male workers in this age group who have worked for at least 1 year in a chemical plant, 5 are due to lung cancer. We wish to determine whether there is a difference between the proportion of deaths from lung cancer in this plant and the proportion in the general population. Perform the hypothesis test, and report a p-value.

Chapter 7: Problem 33 Fundamentals of Biostatistics 8

The proportion of deaths due to lung cancer in males ages 15–64 in England and Wales during the period 1970– 1972 was 12%. Suppose that of 20 deaths that occur among male workers in this age group who have worked for at least 1 year in a chemical plant, 5 are due to lung cancer. We wish to determine whether there is a difference between the proportion of deaths from lung cancer in this plant and the proportion in the general population. After reviewing the results from one plant, the company decides to expand its study to include results from three additional plants. It finds that of 90 deaths occurring among 15- to 64-year-old male workers who have worked for a least 1 year in these four plants, 19 are due to lung cancer. Answer Problem 7.32 using the data from four plants, and report a p-value.

Chapter 7: Problem 34 Fundamentals of Biostatistics 8

The proportion of deaths due to lung cancer in males ages 15–64 in England and Wales during the period 1970– 1972 was 12%. Suppose that of 20 deaths that occur among male workers in this age group who have worked for at least 1 year in a chemical plant, 5 are due to lung cancer. We wish to determine whether there is a difference between the proportion of deaths from lung cancer in this plant and the proportion in the general population. One criticism of studies of this type is that they are biased by the “healthy worker” effect. That is, workers in general are healthier than the general population, particularly regarding cardiovascular endpoints, which makes the proportion of deaths from noncardiovascular causes seem abnormally high. If the proportion of deaths from ischemic heart disease (IHD) is 40% for all 15- to 64-year-old men in England and Wales, whereas 18 of the preceding 90 deaths are attributed to IHD, then answer Problem 7.33 if deaths caused by IHD are excluded from the total.

Chapter 7: Problem 35 Fundamentals of Biostatistics 8

Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 51 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.50 mg with standard deviation 4.75 mg. Suppose the mean daily iron intake among a large population of 9- to 11-year-old boys from all income strata is 14.44 mg. We want to test whether the mean iron intake among the low-income group is different from that of the general population. State the hypotheses that we can use to consider this question.

Chapter 7: Problem 36 Fundamentals of Biostatistics 8

Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 51 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.50 mg with standard deviation 4.75 mg. Suppose the mean daily iron intake among a large population of 9- to 11-year-old boys from all income strata is 14.44 mg. We want to test whether the mean iron intake among the low-income group is different from that of the general population. Carry out the hypothesis test in Problem 7.35 using the critical-value method with an ? level of .05, and summarize your findings.

Chapter 7: Problem 37 Fundamentals of Biostatistics 8

Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 51 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.50 mg with standard deviation 4.75 mg. Suppose the mean daily iron intake among a large population of 9- to 11-year-old boys from all income strata is 14.44 mg. We want to test whether the mean iron intake among the low-income group is different from that of the general population. What is the p-value for the test conducted in Problem 7.36?

Chapter 7: Problem 38 Fundamentals of Biostatistics 8

Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 51 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.50 mg with standard deviation 4.75 mg. Suppose the mean daily iron intake among a large population of 9- to 11-year-old boys from all income strata is 14.44 mg. We want to test whether the mean iron intake among the low-income group is different from that of the general population. The standard deviation of daily iron intake in the larger population of 9- to 11-year-old boys was 5.56 mg. We want to test whether the standard deviation from the low-income group is comparable to that of the general population. State the hypotheses that we can use to answer this question.

Chapter 7: Problem 39 Fundamentals of Biostatistics 8

Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 51 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.50 mg with standard deviation 4.75 mg. Suppose the mean daily iron intake among a large population of 9- to 11-year-old boys from all income strata is 14.44 mg. We want to test whether the mean iron intake among the low-income group is different from that of the general population. The standard deviation of daily iron intake in the larger population of 9- to 11-year-old boys was 5.56 mg. We want to test whether the standard deviation from the low-income group is comparable to that of the general population. Carry out the test in Problem 7.38 using the critical value method with an level of .05, and summarize your findings.

Chapter 7: Problem 40 Fundamentals of Biostatistics 8

Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 51 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.50 mg with standard deviation 4.75 mg. Suppose the mean daily iron intake among a large population of 9- to 11-year-old boys from all income strata is 14.44 mg. We want to test whether the mean iron intake among the low-income group is different from that of the general population. The standard deviation of daily iron intake in the larger population of 9- to 11-year-old boys was 5.56 mg. We want to test whether the standard deviation from the low-income group is comparable to that of the general population. What is the p-value for the test conducted in Problem 7.39?

Chapter 7: Problem 41 Fundamentals of Biostatistics 8

Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 51 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.50 mg with standard deviation 4.75 mg. Suppose the mean daily iron intake among a large population of 9- to 11-year-old boys from all income strata is 14.44 mg. We want to test whether the mean iron intake among the low-income group is different from that of the general population. The standard deviation of daily iron intake in the larger population of 9- to 11-year-old boys was 5.56 mg. We want to test whether the standard deviation from the low-income group is comparable to that of the general population. Compute a 95% CI for the underlying variance of daily iron intake in the low-income group. What can you infer from this CI?

Chapter 7: Problem 42 Fundamentals of Biostatistics 8

Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 51 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.50 mg with standard deviation 4.75 mg. Suppose the mean daily iron intake among a large population of 9- to 11-year-old boys from all income strata is 14.44 mg. We want to test whether the mean iron intake among the low-income group is different from that of the general population. The standard deviation of daily iron intake in the larger population of 9- to 11-year-old boys was 5.56 mg. We want to test whether the standard deviation from the low-income group is comparable to that of the general population. Compare the inferences you made from the procedures in Problems 7.39, 7.40, and 7.41.

Chapter 7: Problem 43 Fundamentals of Biostatistics 8

Suppose a new test is proposed to identify patients with a specific condition. One specimen is obtained from each of 220 subjects in the population to whom the test will be applied. Fifty-one (51) subjects have the condition and 169 do not, according to a gold standard used to assess the presence of the condition (referred to as a reference standard below). The following results are obtained: What is the estimated sensitivity of the test?

Chapter 7: Problem 44 Fundamentals of Biostatistics 8

Suppose a new test is proposed to identify patients with a specific condition. One specimen is obtained from each of 220 subjects in the population to whom the test will be applied. Fifty-one (51) subjects have the condition and 169 do not, according to a gold standard used to assess the presence of the condition (referred to as a reference standard below). The following results are obtained: Provide a 95% CI for the sensitivity.

Chapter 7: Problem 45 Fundamentals of Biostatistics 8

Suppose a new test is proposed to identify patients with a specific condition. One specimen is obtained from each of 220 subjects in the population to whom the test will be applied. Fifty-one (51) subjects have the condition and 169 do not, according to a gold standard used to assess the presence of the condition (referred to as a reference standard below). The following results are obtained: What is the estimated specificity of the test?

Chapter 7: Problem 46 Fundamentals of Biostatistics 8

Suppose a new test is proposed to identify patients with a specific condition. One specimen is obtained from each of 220 subjects in the population to whom the test will be applied. Fifty-one (51) subjects have the condition and 169 do not, according to a gold standard used to assess the presence of the condition (referred to as a reference standard below). The following results are obtained: Provide a 95% CI for the specificity (Hint: Use a computer program.)

Chapter 7: Problem 47 Fundamentals of Biostatistics 8

Suppose a new test is proposed to identify patients with a specific condition. One specimen is obtained from each of 220 subjects in the population to whom the test will be applied. Fifty-one (51) subjects have the condition and 169 do not, according to a gold standard used to assess the presence of the condition (referred to as a reference standard below). The following results are obtained: Suppose a quality score is constructed for the test. A true positive identified by the test is given a score of +20. A true negative identified by the test is given a score of +10. A false positive identified by the test is given a score of -5. A false negative identified by the test is given a score of -20. The FDA will approve the new test if the lower bound of a 90% CI for the mean score is ?+5. Should the FDA approve the test? A yes/no answer is not sufficient.

Chapter 7: Problem 48 Fundamentals of Biostatistics 8

The mortality experience of 8146 male employees of a research, engineering, and metal-fabrication plant in Tonawanda, New York, was studied from 1946 to 1981 [2]. Potential workplace exposures included welding fumes, cutting oils, asbestos, organic solvents, and environmental ionizing radiation, as a result of waste disposal during the Manhattan Project of World War II. Comparisons were made for specific causes of death between mortality rates in workers and U.S. white-male mortality rates from 1950 to 1978. Suppose that 17 deaths from cirrhosis of the liver were observed among workers who were hired prior to 1946 and who had worked in the plant for 10 or more years, whereas 6.3 were expected based on U.S. white-male mortality rates. What is the SMR for this group?

Chapter 7: Problem 49 Fundamentals of Biostatistics 8

The mortality experience of 8146 male employees of a research, engineering, and metal-fabrication plant in Tonawanda, New York, was studied from 1946 to 1981 [2]. Potential workplace exposures included welding fumes, cutting oils, asbestos, organic solvents, and environmental ionizing radiation, as a result of waste disposal during the Manhattan Project of World War II. Comparisons were made for specific causes of death between mortality rates in workers and U.S. white-male mortality rates from 1950 to 1978. Suppose that 17 deaths from cirrhosis of the liver were observed among workers who were hired prior to 1946 and who had worked in the plant for 10 or more years, whereas 6.3 were expected based on U.S. white-male mortality rates. Perform a significance test to assess whether there is an association between long duration of employment and mortality from cirrhosis of the liver in the group hired prior to 1946. Report a p-value.

Chapter 7: Problem 50 Fundamentals of Biostatistics 8

The mortality experience of 8146 male employees of a research, engineering, and metal-fabrication plant in Tonawanda, New York, was studied from 1946 to 1981 [2]. Potential workplace exposures included welding fumes, cutting oils, asbestos, organic solvents, and environmental ionizing radiation, as a result of waste disposal during the Manhattan Project of World War II. Comparisons were made for specific causes of death between mortality rates in workers and U.S. white-male mortality rates from 1950 to 1978. Suppose that 17 deaths from cirrhosis of the liver were observed among workers who were hired prior to 1946 and who had worked in the plant for 10 or more years, whereas 6.3 were expected based on U.S. white-male mortality rates. A similar analysis was performed among workers who were hired after 1945 and who were employed for 10 or more years. It found 4 deaths from cirrhosis of the liver, whereas only 3.4 were expected. What is the SMR for this group?

Chapter 7: Problem 51 Fundamentals of Biostatistics 8

The mortality experience of 8146 male employees of a research, engineering, and metal-fabrication plant in Tonawanda, New York, was studied from 1946 to 1981 [2]. Potential workplace exposures included welding fumes, cutting oils, asbestos, organic solvents, and environmental ionizing radiation, as a result of waste disposal during the Manhattan Project of World War II. Comparisons were made for specific causes of death between mortality rates in workers and U.S. white-male mortality rates from 1950 to 1978. Suppose that 17 deaths from cirrhosis of the liver were observed among workers who were hired prior to 1946 and who had worked in the plant for 10 or more years, whereas 6.3 were expected based on U.S. white-male mortality rates. Perform a significance test to assess whether there is an association between mortality from cirrhosis of the liver and duration of employment in the group hired after 1945. Report a p-value.

Chapter 7: Problem 52 Fundamentals of Biostatistics 8

Researchers have reported that the incidence rate of cataracts may be elevated among people with excessive exposure to sunlight. To confirm this, a pilot study is conducted among 200 people ages 65–69 who report an excessive tendency to burn on exposure to sunlight. Of the 200 people, 4 develop cataracts over a 1-year period. Suppose the expected incidence rate of cataracts among 65- to 69-year-olds is 1% over a 1-year period. What test procedure can be used to compare the 1-year rate of cataracts in this population with that in the general population?

Chapter 7: Problem 53 Fundamentals of Biostatistics 8

Researchers have reported that the incidence rate of cataracts may be elevated among people with excessive exposure to sunlight. To confirm this, a pilot study is conducted among 200 people ages 65–69 who report an excessive tendency to burn on exposure to sunlight. Of the 200 people, 4 develop cataracts over a 1-year period. Suppose the expected incidence rate of cataracts among 65- to 69-year-olds is 1% over a 1-year period. Implement the test procedure in Problem 7.52, and report a p-value (two-sided).

Chapter 7: Problem 54 Fundamentals of Biostatistics 8

Researchers have reported that the incidence rate of cataracts may be elevated among people with excessive exposure to sunlight. To confirm this, a pilot study is conducted among 200 people ages 65–69 who report an excessive tendency to burn on exposure to sunlight. Of the 200 people, 4 develop cataracts over a 1-year period. Suppose the expected incidence rate of cataracts among 65- to 69-year-olds is 1% over a 1-year period. IThe researchers decide to extend the study to a 5-year period and find that 20 of the 200 people develop a cataract over a 5-year period. Suppose the expected incidence of cataracts among 65- to 69-year-olds in the general population is 5% over a 5-year period. Test the hypothesis that the 5-year incidence rate of cataracts is different in the excessive-sunlight-exposure group compared with the general population, and report a p-value (two-sided).

Chapter 7: Problem 55 Fundamentals of Biostatistics 8

Researchers have reported that the incidence rate of cataracts may be elevated among people with excessive exposure to sunlight. To confirm this, a pilot study is conducted among 200 people ages 65–69 who report an excessive tendency to burn on exposure to sunlight. Of the 200 people, 4 develop cataracts over a 1-year period. Suppose the expected incidence rate of cataracts among 65- to 69-year olds is 1% over a 1-year period. IThe researchers decide to extend the study to a 5-year period and find that 20 of the 200 people develop a cataract over a 5-year period. Suppose the expected incidence of cataracts among 65- to 69-year-olds in the general population is 5% over a 5-year period. Construct a 95% CI for the 5-year true rate of cataracts among the excessive-sunlight-exposure group.

Chapter 7: Problem 56 Fundamentals of Biostatistics 8

Left ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 80th percentile for their age, gender, and height) and an elevated bp group (? 90th percentile for their age, gender, and height) and compare change in LVM between the 2 groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period. To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The data are given in Table 7.6. What test can be used to assess if there is a change in mean LVM over 4 years?

Chapter 7: Problem 57 Fundamentals of Biostatistics 8

Left ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 80th percentile for their age, gender, and height) and an elevated bp group (? 90th percentile for their age, gender, and height) and compare change in LVM between the 2 groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period. To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The data are given in Table 7.6. Implement the test in Problem 7.56 and provide a two-tailed p-value.

Chapter 7: Problem 58 Fundamentals of Biostatistics 8

Left ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 80th percentile for their age, gender, and height) and an elevated bp group (? 90th percentile for their age, gender, and height) and compare change in LVM between the 2 groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period. To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The data are given in Table 7.6. Provide a 95% CI for the change in LVM over 4 years based on the data in Table 7.6.

Chapter 7: Problem 59 Fundamentals of Biostatistics 8

Left ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 80th percentile for their age, gender, and height) and an elevated bp group (? 90th percentile for their age, gender, and height) and compare change in LVM between the 2 groups. Before this can be done, one needs to demonstrate that LVM actually changes in children over a 4-year period. To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The data are given in Table 7.6. Since this was a pilot study, the main question of interest is how many subjects would be needed to detect an increase of 10 g in mean LVM over 4 years using a two sided test with = 0.05 and power = 80%? Hint: Assume that the estimated variance of change in LVM in the pilot study is the true variance of change in LVM.

Chapter 7: Problem 60 Fundamentals of Biostatistics 8

Previous studies have shown that supplementing the diet with oat bran may lower serum-cholesterol levels. However, it is not known whether the cholesterol is reduced by a direct effect of oat bran or by replacing fatty foods in the diet. To address this question, a study was performed to compare the effect of dietary supplementation with high-fiber oat bran (87 g/day) to dietary supplementation with a low-fiber refined wheat product on the serum cholesterol of 20 healthy participants ages 23–49 years [3]. Each subject had a cholesterol level measured at baseline and then was randomly assigned to receive either a high-fiber or a low-fiber diet for 6 weeks. A 2-week period followed during which no supplements were taken. Participants then took the alternate supplement for a 6-week period. The results are shown in Table 7.7. Test the hypothesis that the high-fiber diet has an effect on cholesterol levels as compared with baseline (report your results as p < .05 or p > .05).

Chapter 7: Problem 61 Fundamentals of Biostatistics 8

Previous studies have shown that supplementing the diet with oat bran may lower serum-cholesterol levels. However, it is not known whether the cholesterol is reduced by a direct effect of oat bran or by replacing fatty foods in the diet. To address this question, a study was performed to compare the effect of dietary supplementation with high-fiber oat bran (87 g/day) to dietary supplementation with a low-fiber refined wheat product on the serum cholesterol of 20 healthy participants ages 23–49 years [3]. Each subject had a cholesterol level measured at baseline and then was randomly assigned to receive either a high-fiber or a low-fiber diet for 6 weeks. A 2-week period followed during which no supplements were taken. Participants then took the alternate supplement for a 6-week period. The results are shown in Table 7.7. Test the hypothesis that the low-fiber diet has an effect on cholesterol levels as compared with baseline (report your results as p < .05 or p > .05).

Chapter 7: Problem 62 Fundamentals of Biostatistics 8

Previous studies have shown that supplementing the diet with oat bran may lower serum-cholesterol levels. However, it is not known whether the cholesterol is reduced by a direct effect of oat bran or by replacing fatty foods in the diet. To address this question, a study was performed to compare the effect of dietary supplementation with high-fiber oat bran (87 g/day) to dietary supplementation with a low-fiber refined wheat product on the serum cholesterol of 20 healthy participants ages 23–49 years [3]. Each subject had a cholesterol level measured at baseline and then was randomly assigned to receive either a high-fiber or a low-fiber diet for 6 weeks. A 2-week period followed during which no supplements were taken. Participants then took the alternate supplement for a 6-week period. The results are shown in Table 7.7. Test the hypothesis that the high-fiber diet has a differential effect on cholesterol levels compared with a low fiber diet (report your results as p < .05 or p > .05).

Chapter 7: Problem 63 Fundamentals of Biostatistics 8

Previous studies have shown that supplementing the diet with oat bran may lower serum-cholesterol levels. However, it is not known whether the cholesterol is reduced by a direct effect of oat bran or by replacing fatty foods in the diet. To address this question, a study was performed to compare the effect of dietary supplementation with high-fiber oat bran (87 g/day) to dietary supplementation with a low-fiber refined wheat product on the serum cholesterol of 20 healthy participants ages 23–49 years [3]. Each subject had a cholesterol level measured at baseline and then was randomly assigned to receive either a high-fiber or a low-fiber diet for 6 weeks. A 2-week period followed during which no supplements were taken. Participants then took the alternate supplement for a 6-week period. The results are shown in Table 7.7. What is the approximate standard error of the mean for the high-fiber compared with the low-fiber diet (that is, the mean difference in cholesterol level between high- and low-fiber diets)?

Chapter 7: Problem 64 Fundamentals of Biostatistics 8

Previous studies have shown that supplementing the diet with oat bran may lower serum-cholesterol levels. However, it is not known whether the cholesterol is reduced by a direct effect of oat bran or by replacing fatty foods in the diet. To address this question, a study was performed to compare the effect of dietary supplementation with high-fiber oat bran (87 g/day) to dietary supplementation with a low-fiber refined wheat product on the serum cholesterol of 20 healthy participants ages 23–49 years [3]. Each subject had a cholesterol level measured at baseline and then was randomly assigned to receive either a high-fiber or a low-fiber diet for 6 weeks. A 2-week period followed during which no supplements were taken. Participants then took the alternate supplement for a 6-week period. The results are shown in Table 7.7. How many participants would be needed to have a 90% chance of finding a significant difference in mean cholesterol lowering between the high- and low-fiber diets if the high-fiber diet lowers mean cholesterol by 5 mg/dL more than the low-fiber diet and a two-sided test is used with significance level = .05?

Chapter 7: Problem 65 Fundamentals of Biostatistics 8

Refer to Data Set VALID.DAT, at www.cengagebrain.com. Assess whether reported nutrient consumption (saturated fat, total fat, alcohol consumption, total caloric intake) is comparable for the diet record and the food-frequency questionnaire. Use either hypothesis-testing and/or CI methodology.

Chapter 7: Problem 66 Fundamentals of Biostatistics 8

Refer to Data Set VALID.DAT, at www.cengagebrain.com. Answer Problem 7.65 for the percentage of calories from fat (separately for total fat and saturated fat) as reported on the diet record and the food-frequency questionnaire. Assume there are 9 calories from fat for every gram of fat consumed.

Chapter 7: Problem 67 Fundamentals of Biostatistics 8

Refer to Data Set SEXRAT.DAT at www.cengagebrain.com. Apply hypothesis-testing methods to answer the questions posed in Problem 4.53.

Chapter 7: Problem 68 Fundamentals of Biostatistics 8

Refer to Data Set NIFED.DAT at www.cengagebrain.com. Use hypothesis-testing methods to assess whether either treatment affects blood pressure or heart rate in patients with severe angina.

Chapter 7: Problem 69 Fundamentals of Biostatistics 8

The combination of photochemotherapy with oral methoxsalen (psoralen) and ultraviolet A radiation (called PUVA treatment) is an effective treatment for psoriasis. However, PUVA is mutagenic, increases the risk of squamous-cell skin cancer, and can cause irregular, pigmented skin lesions. Stern et al. [4] performed a study to assess the incidence of melanoma among patients treated with PUVA. The study identified 1380 patients with psoriasis who were first treated with PUVA in 1975 or 1976. Patients were subdivided according to the total number of treatments received (<250 or ?250 from 1975 to 1996). Within each group, the observed number of melanomas was determined from 1975 to 1996 and compared with the expected number of melanomas as determined by published U.S. age- and gender-specific melanoma incidence rates. The results were as in Table 7.8 Suppose we want to compare the observed and expected number of events among the group with <250 treatments. Perform an appropriate significance test, and report a two-tailed p-value.

Chapter 7: Problem 70 Fundamentals of Biostatistics 8

The combination of photochemotherapy with oral methoxsalen (psoralen) and ultraviolet A radiation (called PUVA treatment) is an effective treatment for psoriasis. However, PUVA is mutagenic, increases the risk of squamous-cell skin cancer, and can cause irregular, pigmented skin lesions. Stern et al. [4] performed a study to assess the incidence of melanoma among patients treated with PUVA. The study identified 1380 patients with psoriasis who were first treated with PUVA in 1975 or 1976. Patients were subdivided according to the total number of treatments received (<250 or ?250 from 1975 to 1996). Within each group, the observed number of melanomas was determined from 1975 to 1996 and compared with the expected number of melanomas as determined by published U.S. age- and gender-specific melanoma incidence rates. The results were as in Table 7.8 Provide a 95% CI for the expected number of events in the group with ? 250 treatments.

Chapter 7: Problem 71 Fundamentals of Biostatistics 8

The combination of photochemotherapy with oral methoxsalen (psoralen) and ultraviolet A radiation (called PUVA treatment) is an effective treatment for psoriasis. However, PUVA is mutagenic, increases the risk of squamous-cell skin cancer, and can cause irregular, pigmented skin lesions. Stern et al. [4] performed a study to assess the incidence of melanoma among patients treated with PUVA. The study identified 1380 patients with psoriasis who were first treated with PUVA in 1975 or 1976. Patients were subdivided according to the total number of treatments received (<250 or ?250 from 1975 to 1996). Within each group, the observed number of melanomas was determined from 1975 to 1996 and compared with the expected number of melanomas as determined by published U.S. age- and gender-specific melanoma incidence rates. The results were as in Table 7.8 Interpret the results for Problems 7.69 and 7.70.

Chapter 7: Problem 72 Fundamentals of Biostatistics 8

Breast cancer is strongly influenced by a woman’s reproductive history. In particular, the longer the length of time from the age at menarche (the age when menstruation begins) to the age at first childbirth, the greater the risk is for breast cancer. A projection was made based on a mathematical model that the 30-year risk of a woman in the general U.S. population developing breast cancer from age 40 to age 70 is 7%. Suppose a special subgroup of five hundred 40-year-old women without breast cancer was studied whose age at menarche was 17 (compared with an average age at menarche of 13 in the general population) and age at first birth was 20 (compared with an average age at first birth of 25 in the general population). These women were followed for development of breast cancer between ages 40 and 70. The study found that 18 of the women developed breast cancer between age 40 and age 70. Test the hypothesis that the underlying rate of breast cancer is the same or different in this group as in the general population.

Chapter 7: Problem 73 Fundamentals of Biostatistics 8

Breast cancer is strongly influenced by a woman’s reproductive history. In particular, the longer the length of time from the age at menarche (the age when menstruation begins) to the age at first childbirth, the greater the risk is for breast cancer. A projection was made based on a mathematical model that the 30-year risk of a woman in the general U.S. population developing breast cancer from age 40 to age 70 is 7%. Suppose a special subgroup of five hundred 40-year-old women without breast cancer was studied whose age at menarche was 17 (compared with an average age at menarche of 13 in the general population) and age at first birth was 20 (compared with an average age at first birth of 25 in the general population). These women were followed for development of breast cancer between ages 40 and 70. The study found that 18 of the women developed breast cancer between age 40 and age 70. Provide a 95% CI for the true incidence rate of breast cancer over the period from age 40 to 70 in this special subgroup.

Chapter 7: Problem 74 Fundamentals of Biostatistics 8

Breast cancer is strongly influenced by a woman’s reproductive history. In particular, the longer the length of time from the age at menarche (the age when menstruation begins) to the age at first childbirth, the greater the risk is for breast cancer. A projection was made based on a mathematical model that the 30-year risk of a woman in the general U.S. population developing breast cancer from age 40 to age 70 is 7%. Suppose a special subgroup of five hundred 40-year-old women without breast cancer was studied whose age at menarche was 17 (compared with an average age at menarche of 13 in the general population) and age at first birth was 20 (compared with an average age at first birth of 25 in the general population). These women were followed for development of breast cancer between ages 40 and 70. The study found that 18 of the women developed breast cancer between age 40 and age 70. Suppose 100 million women in the U.S. populaData set available tion have not developed breast cancer by the age of 40. What is your best estimate of the number of breast-cancer cases that would be prevented from age 40 to 70 if all women in the U.S. population reached menarche at age 17 and gave birth to their first child at age 20? Provide a 95% CI for the number of breast-cancer cases prevented.

Chapter 7: Problem 75 Fundamentals of Biostatistics 8

An investigator wants to test a new eye drop that is supposed to prevent ocular itching during allergy season. To study the drug, she uses a contralateral design whereby for each participant one eye is randomized (using a random-number table) to get active drug (A) while the other eye gets placebo (P). The participants use the eye drops three times a day for a 1-week period and then report their degree of itching in each eye on a 4-point scale (1 = none, 2 = mild, 3 = moderate, 4 = severe) without knowing which eye drop is used in which eye. Ten participants are randomized into the study. What is the principal advantage of the contralateral design? Suppose the randomization assignment is as given in Table 7.9.

Chapter 7: Problem 76 Fundamentals of Biostatistics 8

An investigator wants to test a new eye drop that is supposed to prevent ocular itching during allergy season. To study the drug, she uses a contralateral design whereby for each participant one eye is randomized (using a random-number table) to get active drug (A) while the other eye gets placebo (P). The participants use the eye drops three times a day for a 1-week period and then report their degree of itching in each eye on a 4-point scale (1 = none, 2 = mild, 3 = moderate, 4 = severe) without knowing which eye drop is used in which eye. Ten participants are randomized into the study. More left eyes seem to be assigned to A than to P, and the investigator wonders whether the assignments are really random. Perform a significance test to assess how well the randomization is working. (Hint: Use the binomial tables.)

Chapter 7: Problem 77 Fundamentals of Biostatistics 8

An investigator wants to test a new eye drop that is supposed to prevent ocular itching during allergy season. To study the drug, she uses a contralateral design whereby for each participant one eye is randomized (using a random-number table) to get active drug (A) while the other eye gets placebo (P). The participants use the eye drops three times a day for a 1-week period and then report their degree of itching in each eye on a 4-point scale (1 = none, 2 = mild, 3 = moderate, 4 = severe) without knowing which eye drop is used in which eye. Ten participants are randomized into the study. What test can be used to test the hypothesis that the mean degree of itching is the same for active vs. placebo eyes?

Chapter 7: Problem 78 Fundamentals of Biostatistics 8

An investigator wants to test a new eye drop that is supposed to prevent ocular itching during allergy season. To study the drug, she uses a contralateral design whereby for each participant one eye is randomized (using a random-number table) to get active drug (A) while the other eye gets placebo (P). The participants use the eye drops three times a day for a 1-week period and then report their degree of itching in each eye on a 4-point scale (1 = none, 2 = mild, 3 = moderate, 4 = severe) without knowing which eye drop is used in which eye. Ten participants are randomized into the study. Implement the test in Problem 7.77 using a two-sided test (report a p-value).

Chapter 7: Problem 79 Fundamentals of Biostatistics 8

Refer to Data Set BONEDEN.DAT at www.cengagebrain .com. Perform a hypothesis test to assess whether there are significant differences in mean BMD for the femoral neck between the heavier- and lighter-smoking twins.

Chapter 7: Problem 80 Fundamentals of Biostatistics 8

Refer to Data Set BONEDEN.DAT at www.cengagebrain .com. Answer Problem 7.79 for mean BMD at the femoral shaft.

Chapter 7: Problem 81 Fundamentals of Biostatistics 8

Concurrent sexual partnerships are widely believed to be one of the main drivers of the HIV epidemic in sub-Saharan Africa. F. Tanser and colleagues followed 7284 initially HIV-negative women (?15 years of age) residing in KwaZulu-Natal, South Africa, for an average of 5 years to evaluate relationships of the patterns of sexual activity with incidence of HIV [5]. Investigators surveyed men residing in the neighborhoods of the female study participants to determine patterns of sexual activity within each neighborhood. The table below shows the incidence of HIV acquisition according to whether a study participant resided in a neighborhood that was above vs. below the median in terms of the typical number of lifetime sexual partners among men in her neighborhood. Give an estimate for the incidence of HIV per 100 person-years among women who reside in neighborhoods with above-median numbers of sexual partners among men, and an estimate for the 5-year probability that a woman in this region will develop HIV.

Chapter 7: Problem 82 Fundamentals of Biostatistics 8

Concurrent sexual partnerships are widely believed to be one of the main drivers of the HIV epidemic in sub-Saharan Africa. F. Tanser and colleagues followed 7284 initially HIV-negative women (?15 years of age) residing in KwaZulu-Natal, South Africa, for an average of 5 years to evaluate relationships of the patterns of sexual activity with incidence of HIV [5]. Investigators surveyed men residing in the neighborhoods of the female study participants to determine patterns of sexual activity within each neighborhood. The table below shows the incidence of HIV acquisition according to whether a study participant resided in a neighborhood that was above vs. below the median in terms of the typical number of lifetime sexual partners among men in her neighborhood. Provide a 95% CI for the estimate in Problem 7.81.

Chapter 7: Problem 83 Fundamentals of Biostatistics 8

Concurrent sexual partnerships are widely believed to be one of the main drivers of the HIV epidemic in sub-Saharan Africa. F. Tanser and colleagues followed 7284 initially HIV-negative women (?15 years of age) residing in KwaZulu-Natal, South Africa, for an average of 5 years to evaluate relationships of the patterns of sexual activity with incidence of HIV [5]. Investigators surveyed men residing in the neighborhoods of the female study participants to determine patterns of sexual activity within each neighborhood. The table below shows the incidence of HIV acquisition according to whether a study participant resided in a neighborhood that was above vs. below the median in terms of the typical number of lifetime sexual partners among men in her neighborhood. Suppose 100 women who reside in a neighborhood with above-median numbers of sexual partners among men are followed for an average of 5 years. What is the probability that exactly 20 of the women will develop HIV?

Chapter 7: Problem 84 Fundamentals of Biostatistics 8

Concurrent sexual partnerships are widely believed to be one of the main drivers of the HIV epidemic in sub-Saharan Africa. F. Tanser and colleagues followed 7284 initially HIV-negative women (?15 years of age) residing in KwaZulu-Natal, South Africa, for an average of 5 years to evaluate relationships of the patterns of sexual activity with incidence of HIV [5]. Investigators surveyed men residing in the neighborhoods of the female study participants to determine patterns of sexual activity within each neighborhood. The table below shows the incidence of HIV acquisition according to whether a study participant resided in a neighborhood that was above vs. below the median in terms of the typical number of lifetime sexual partners among men in her neighborhood. What is the probability that 20 or more of these women will develop HIV?

Chapter 7: Problem 85 Fundamentals of Biostatistics 8

Concurrent sexual partnerships are widely believed to be one of the main drivers of the HIV epidemic in sub-Saharan Africa. F. Tanser and colleagues followed 7284 initially HIV-negative women (?15 years of age) residing in KwaZulu-Natal, South Africa, for an average of 5 years to evaluate relationships of the patterns of sexual activity with incidence of HIV [5]. Investigators surveyed men residing in the neighborhoods of the female study participants to determine patterns of sexual activity within each neighborhood. The table below shows the incidence of HIV acquisition according to whether a study participant resided in a neighborhood that was above vs. below the median in terms of the typical number of lifetime sexual partners among men in her neighborhood. Assume the rate of HIV in neighborhoods with below the median number of sexual partners is known (without error) to be 3.15 cases per 100 person years. Test whether the rate in women from neighborhoods above the median in lifetime sexual partners (?6.2 partners) is significantly different than the rate in neighborhoods below the median number of sexual partners.

Chapter 7: Problem 86 Fundamentals of Biostatistics 8

Consider the birthweight data in Example 7.2. Suppose that the true mean birthweight for the lowSES babies is 120 oz, the true standard deviation is 24 oz, and the distribution of birthweights is normal. Generate 100 random samples of size 100 each from this distribution. Perform the appropriate t test for each sample to test the hypothesis stated in Example 7.2, and compute the proportion of samples for which we declare a significant difference using a 5% level of significance with a one-tailed test.

Chapter 7: Problem 87 Fundamentals of Biostatistics 8

Consider the birthweight data in Example 7.2. What should this proportion be for a large number of simulated samples? How do the results in Problem 7.86 compare with this?

Chapter 7: Problem 88 Fundamentals of Biostatistics 8

Consider the birthweight data in Example 7.2. Now assume that the true mean birthweight is 115 oz and repeat the exercise in Problem 7.86, assuming that the other conditions stated in Problem 7.86 are still correct.

Chapter 7: Problem 89 Fundamentals of Biostatistics 8

Consider the birthweight data in Example 7.2. For what proportion of samples do you declare a significant difference? What should this proportion be for a large number of simulated samples?

Chapter 7: Problem 90 Fundamentals of Biostatistics 8

A screening program for neuroblastoma (a type of cancer) was undertaken in Germany among children born between November 1, 1993, and June 30, 2000, who were 9 to 18 months of age between May 1995 and April 2000 [6]. A total of 1,475,773 children participated in the screening program, of whom 204 were diagnosed between 12 and 60 months of age. The researchers expected the incidence rate of neuroblastoma to be 7.3 per 100,000 children during this period in the absence of screening. Test whether the number of cases detected by the screening program is significantly greater than expected.Provide a one-tailed p-value. (Hint: Use the normal approximation to the binomial distribution.)

Chapter 7: Problem 91 Fundamentals of Biostatistics 8

A screening program for neuroblastoma (a type of cancer) was undertaken in Germany among children born between November 1, 1993, and June 30, 2000, who were 9 to 18 months of age between May 1995 and April 2000 [6]. A total of 1,475,773 children participated in the screening program, of whom 204 were diagnosed between 12 and 60 months of age. The researchers expected the incidence rate of neuroblastoma to be 7.3 per 100,000 children during this period in the absence of screening. Provide a 95% CI for the incidence rate of neuroblastoma in the screened population. Express the 95% CI as (), where and are in the units of number of cases per 100,000 children. Is (7.3 cases per 100,000 children) in this interval? Another issue investigated in this study was the case-fatality rate (number of patients who died from neuroblastoma / number of cases identified by the screening program).

Chapter 7: Problem 92 Fundamentals of Biostatistics 8

A screening program for neuroblastoma (a type of cancer) was undertaken in Germany among children born between November 1, 1993, and June 30, 2000, who were 9 to 18 months of age between May 1995 and April 2000 [6]. A total of 1,475,773 children participated in the screening program, of whom 204 were diagnosed between 12 and 60 months of age. The researchers expected the incidence rate of neuroblastoma to be 7.3 per 100,000 children during this period in the absence of screening. Suppose the case-fatality rate from neuroblastoma is usually 1/6. Furthermore, 17 fatal cases occurred among the 204 cases identified in the screening program. Test whether the case-fatality rate under the screening program is different from the usual case-fatality rate. Provide a two-tailed p-value..

Chapter 7: Problem 93 Fundamentals of Biostatistics 8

A clinical epidemiologic study was conducted to determine the long-term health effects of workplace exposure to the process of manufacturing the herbicide (2,4,5 trichlorophenoxy) acetic acid (2,4,5-T), which contains the contaminant dioxin [7]. This study was conducted among active and retired workers of a Nitro, West Virginia, plant who were exposed to the 2,4,5-T process between 1948 and 1969. It is well known that workers exposed to 2,4,5-T have high rates of chloracne (a generalized acneiform eruption). Less well known are other potential effects of 2,4,5-T exposure. One of the variables studied was pulmonary function. Suppose the researchers expect from general population estimates that 5% of workers have an abnormal forced expiratory volume (FEV); defined as less than 80% of predicted, based on their age and height. They found that 32 of 203 men who were exposed to 2,4,5-T while working at the plant had an abnormal FEV. What hypothesis test can be used to test the hypothesis that the percentage of abnormal FEV values among exposed men differs from the general-population estimates?

Chapter 7: Problem 94 Fundamentals of Biostatistics 8

A clinical epidemiologic study was conducted to determine the long-term health effects of workplace exposure to the process of manufacturing the herbicide (2,4,5 trichlorophenoxy) acetic acid (2,4,5-T), which contains the contaminant dioxin [7]. This study was conducted among active and retired workers of a Nitro, West Virginia, plant who were exposed to the 2,4,5-T process between 1948 and 1969. It is well known that workers exposed to 2,4,5-T have high rates of chloracne (a generalized acneiform eruption). Less well known are other potential effects of 2,4,5-T exposure. One of the variables studied was pulmonary function. Suppose the researchers expect from general population estimates that 5% of workers have an abnormal forced expiratory volume (FEV); defined as less than 80% of predicted, based on their age and height. They found that 32 of 203 men who were exposed to 2,4,5-T while working at the plant had an abnormal FEV. Implement the test in Problem 7.93, and report a p-value (two-tailed).

Chapter 7: Problem 95 Fundamentals of Biostatistics 8

A clinical epidemiologic study was conducted to determine the long-term health effects of workplace exposure to the process of manufacturing the herbicide (2,4,5 trichlorophenoxy) acetic acid (2,4,5-T), which contains the contaminant dioxin [7]. This study was conducted among active and retired workers of a Nitro, West Virginia, plant who were exposed to the 2,4,5-T process between 1948 and 1969. It is well known that workers exposed to 2,4,5-T have high rates of chloracne (a generalized acneiform eruption). Less well known are other potential effects of 2,4,5-T exposure. One of the variables studied was pulmonary function. Suppose the researchers expect from general population estimates that 5% of workers have an abnormal forced expiratory volume (FEV); defined as less than 80% of predicted, based on their age and height. They found that 32 of 203 men who were exposed to 2,4,5-T while working at the plant had an abnormal FEV. Another type of outcome reported was fetal deaths. Suppose the investigators expect, given general population pregnancy statistics at the time of the survey, that 1.5% of pregnancies will result in a fetal death. They found that among 586 pregnancies where an exposed worker was the father, 11 resulted in a fetal death. Provide a 95% CI for the underlying fetal death rate among offspring of exposed men. Given the CI, how do you interpret the results of the study?

Chapter 7: Problem 96 Fundamentals of Biostatistics 8

An experiment was performed to assess the efficacy of an eye drop in preventing “dry eye.” A principal objective measure used to assess efficacy is the tear breakup time (TBUT),which is reduced in people with dry eye and which the researchers hope will be increased after use of the eye drop. n the actual study, participants will be randomized to either active drug or placebo, based on a fairly large sample size. However, a pilot study was first performed based on 14 participants. Under protocol A, the participants had their TBUT measured at baseline and were then instructed to not blink their eyes for 3 seconds, after which time the placebo eye drop was instilled. The TBUT was measured again immediately after instillation as well as at 5, 10, and 15 minutes postinstillation, during which time the study participants were in a controlled-chamber environment with low humidity to exacerbate symptoms of dry eye. On 2 other days participants received protocols B and C. Protocol B was identical to protocol A except that participants were told not to blink for 6 seconds prior to drop instillation. Protocol C was identical to protocol A except that participants were told not to blink their eyes for 10 seconds prior to drop instillation. Note that the same participants were used for each protocol and that for each protocol data are available for each of two eyes. Also, for each eye, two replicate measurements were provided. The data are available in TEAR.DAT with documentation in TEAR.DOC at www.cengagebrain.com. For each protocol, TBUT (in seconds) was measured (1) at baseline (before drop instillation), (2) immediately after drop instillation, (3) 5 minutes after instillation, (4) 10 minutes after instillation, and (5) 15 minutes after instillation. The standard protocol used in previous clinical studies of TBUT is a 6-second nonblink interval (protocol B). All the following questions concern protocol B data. For this purpose, average TBUT over two replicates and over both eyes to find a summary value for each time period for each participant. Is there an immediate effect of the eye drop on TBUT? (Hint: Compare mean TBUT immediately postinstillation vs. mean TBUT preinstillation.)

Chapter 7: Problem 97 Fundamentals of Biostatistics 8

An experiment was performed to assess the efficacy of an eye drop in preventing “dry eye.” A principal objective measure used to assess efficacy is the tear breakup time (TBUT),which is reduced in people with dry eye and which the researchers hope will be increased after use of the eye drop. n the actual study, participants will be randomized to either active drug or placebo, based on a fairly large sample size. However, a pilot study was first performed based on 14 participants. Under protocol A, the participants had their TBUT measured at baseline and were then instructed to not blink their eyes for 3 seconds, after which time the placebo eye drop was instilled. The TBUT was measured again immediately after instillation as well as at 5, 10, and 15 minutes postinstillation, during which time the study participants were in a controlled-chamber environment with low humidity to exacerbate symptoms of dry eye. On 2 other days participants received protocols B and C. Protocol B was identical to protocol A except that participants were told not to blink for 6 seconds prior to drop instillation. Protocol C was identical to protocol A except that participants were told not to blink their eyes for 10 seconds prior to drop instillation. Note that the same participants were used for each protocol and that for each protocol data are available for each of two eyes. Also, for each eye, two replicate measurements were provided. The data are available in TEAR.DAT with documentation in TEAR.DOC at www.cengagebrain.com. For each protocol, TBUT (in seconds) was measured (1) at baseline (before drop instillation), (2) immediately after drop instillation, (3) 5 minutes after instillation, (4) 10 minutes after instillation, and (5) 15 minutes after instillation. The standard protocol used in previous clinical studies of TBUT is a 6-second nonblink interval (protocol B). All the following questions concern protocol B data. For this purpose, average TBUT over two replicates and over both eyes to find a summary value for each time period for each participant. Does the effect of the placebo eye drop change over time after drop instillation? (Hint: Compare mean TBUT at 5, 10, and 15 minutes postinstillation vs. mean TBUT immediately after drop instillation.)

Chapter 7: Problem 98 Fundamentals of Biostatistics 8

Medical errors are common in hospitals throughout the world. One possible causal factor is the long work hours of hospital personnel. In a pilot study investigating this issue, medical residents were encouraged to sleep 6–8 hours per night for a 3-week period instead of their usual irregular sleep schedule. The researchers expected, given previous data, that there would be one medical error per resident per day on their usual irregular sleep schedule.Suppose two residents participate in the program (each for 3 weeks), and chart review finds a total of 20 medical errors made by the two residents combined. What test can be used to test the hypothesis that an increase in amount of sleep will change the number of medical errors per day?

Chapter 7: Problem 99 Fundamentals of Biostatistics 8

Medical errors are common in hospitals throughout the world. One possible causal factor is the long work hours of hospital personnel. In a pilot study investigating this issue, medical residents were encouraged to sleep 6–8 hours per night for a 3-week period instead of their usual irregular sleep schedule. The researchers expected, given previous data, that there would be one medical error per resident per day on their usual irregular sleep schedule.Suppose two residents participate in the program (each for 3 weeks), and chart review finds a total of 20 medical errors made by the two residents combined. Implement the test in Problem 7.98, and report a two tailed p-value.

Chapter 7: Problem 100 Fundamentals of Biostatistics 8

Medical errors are common in hospitals throughout the world. One possible causal factor is the long work hours of hospital personnel. In a pilot study investigating this issue, medical residents were encouraged to sleep 6–8 hours per night for a 3-week period instead of their usual irregular sleep schedule. The researchers expected, given previous data, that there would be one medical error per resident per day on their usual irregular sleep schedule.Suppose two residents participate in the program (each for 3 weeks), and chart review finds a total of 20 medical errors made by the two residents combined. Suppose the true effect of the intervention is to reduce the number of medical errors per day by 20% (to 0.8 medical errors per day). Suppose that in the actual study 10 residents participate in the program, each for a 3-week period. What would be the power of the type of test used in Problem 7.99 under these assumptions? (Hint: Use the normal approximation to the Poisson distribution.)

Chapter 7: Problem 101 Fundamentals of Biostatistics 8

A study was performed among patients with glaucoma, an important eye disease usually manifested by high intraocular pressure (IOP); left untreated, glaucoma can lead to blindness. The patients were currently on two medications (A and B) to be taken together for this condition. The purpose of this study was to determine whether the patients could drop medications A and B and be switched to a third medication (medication C) without much change in their IOP. Ten patients were enrolled in the study. They received medications A + B for 60 days and had their IOP measured at the end of the 60-day period (referred to as ). They were then taken off medications A and B and switched to medication C, which they took for an additional 60 days. IOP was measured a second time at the end of the 60-day period while the patient was on medication C (referred to as ). The results were as shown in Table 7.12 What procedure can be used to test the hypothesis that there has been no mean difference in IOP after 60 days Data set available between the two drug regimens?

Chapter 7: Problem 102 Fundamentals of Biostatistics 8

A study was performed among patients with glaucoma, an important eye disease usually manifested by high intraocular pressure (IOP); left untreated, glaucoma can lead to blindness. The patients were currently on two medications (A and B) to be taken together for this condition. The purpose of this study was to determine whether the patients could drop medications A and B and be switched to a third medication (medication C) without much change in their IOP. Ten patients were enrolled in the study. They received medications A + B for 60 days and had their IOP measured at the end of the 60-day period (referred to as ). They were then taken off medications A and B and switched to medication C, which they took for an additional 60 days. IOP was measured a second time at the end of the 60-day period while the patient was on medication C (referred to as ). The results were as shown in Table 7.12 Perform the procedure mentioned in Problem 7.101, and report a two-tailed p-value.

Chapter 7: Problem 103 Fundamentals of Biostatistics 8

A study was performed among patients with glaucoma, an important eye disease usually manifested by high intraocular pressure (IOP); left untreated, glaucoma can lead to blindness. The patients were currently on two medications (A and B) to be taken together for this condition. The purpose of this study was to determine whether the patients could drop medications A and B and be switched to a third medication (medication C) without much change in their IOP. Ten patients were enrolled in the study. They received medications A + B for 60 days and had their IOP measured at the end of the 60-day period (referred to as ). They were then taken off medications A and B and switched to medication C, which they took for an additional 60 days. IOP was measured a second time at the end of the 60-day period while the patient was on medication C (referred to as ). The results were as shown in Table 7.12 A goal of the study was to establish whether switching to medication C is “equivalent” to the original regimen of medication A and B. “Equivalence” here means that the underlying mean IOP after switching to medication C has not changed by more than 2 mm Hg in either direction. What procedure can be used to establish equivalence? Is equivalence the same as accepting the null hypothesis in Problem 7.101? Why or why not?

Chapter 7: Problem 104 Fundamentals of Biostatistics 8

A study was performed among patients with glaucoma, an important eye disease usually manifested by high intraocular pressure (IOP); left untreated, glaucoma can lead to blindness. The patients were currently on two medications (A and B) to be taken together for this condition. The purpose of this study was to determine whether the patients could drop medications A and B and be switched to a third medication (medication C) without much change in their IOP. Ten patients were enrolled in the study. They received medications A + B for 60 days and had their IOP measured at the end of the 60-day period (referred to as ). They were then taken off medications A and B and switched to medication C, which they took for an additional 60 days. IOP was measured a second time at the end of the 60-day period while the patient was on medication C (referred to as ). The results were as shown in Table 7.12 A goal of the study was to establish whether switching to medication C is “equivalent” to the original regimen of medication A and B. “Equivalence” here means that the underlying mean IOP after switching to medication C has not changed by more than 2 mm Hg in either direction. Implement the procedure in Problem 7.103 to address the question of whether the regimens are equivalent.

Chapter 7: Problem 105 Fundamentals of Biostatistics 8

Osteoporosis is an important cause of morbidity in middle aged and elderly women. Several drugs are currently used to prevent fractures in postmenopausal women. Suppose the incidence rate of fractures over a 4-year period is known to be 5% among untreated postmenopausal women with no previous fractures. A pilot study conducted among 100 women without previous fractures aims to determine whether a new drug can prevent fractures. It is found that two of the women have developed fractures over a 4-year period. Is there a significant difference between the fracture rate in individual treated women and the fracture rate in the untreated women? (Report a two-tailed p-value.)

Chapter 7: Problem 106 Fundamentals of Biostatistics 8

Osteoporosis is an important cause of morbidity in middle aged and elderly women. Several drugs are currently used to prevent fractures in postmenopausal women. Suppose the incidence rate of fractures over a 4-year period is known to be 5% among untreated postmenopausal women with no previous fractures. A pilot study conducted among 100 women without previous fractures aims to determine whether a new drug can prevent fractures. It is found that two of the women have developed fractures over a 4-year period. Suppose that 8 of the previous 100 women have developed abdominal pain during the trial, while only 1.5% would be expected to develop abdominal pain based on previous natural history studies. Provide a 95% CI for the rate of abdominal pain among the active treated women. Interpret the results compared with previous natural history studies.

Chapter 7: Problem 107 Fundamentals of Biostatistics 8

Osteoporosis is an important cause of morbidity in middle aged and elderly women. Several drugs are currently used to prevent fractures in postmenopausal women. Suppose the incidence rate of fractures over a 4-year period is known to be 5% among untreated postmenopausal women with no previous fractures. A pilot study conducted among 100 women without previous fractures aims to determine whether a new drug can prevent fractures. It is found that two of the women have developed fractures over a 4-year period. Suppose that 8 of the previous 100 women have developed abdominal pain during the trial, while only 1.5% would be expected to develop abdominal pain based on previous natural history studies. Suppose the new drug is hypothesized to yield a fracture rate of 2.5% over a 4-year period. How many subjects need to be studied to have an 80% chance of detecting a significant difference between the incidence rate of fractures in treated women and the incidence rate of fractures in untreated women (assumed to be 5% from Problem 7.105)?

Chapter 7: Problem 108 Fundamentals of Biostatistics 8

What is the 25th percentile of a ?2 distribution with 20 degrees of freedom? What symbol is used to denote this value?

Chapter 7: Problem 109 Fundamentals of Biostatistics 8

Suppose we wish to test the hypothesis : µ = 2 vs. : µ ? 2. We find a two-sided p-value of .03 and a 95% CI for µ of (1.5, 4.0). Are these two results possibly compatible? Why or why not?

Chapter 7: Problem 110 Fundamentals of Biostatistics 8

Treatment with statins can reduce the risk of a major cardiovascular event in people with specified risk factors. During about 2 years of follow-up in the JUPITER trial (P. M. Ridker et al. [8]) , 142 of 8901 subjects treated with a statin had a major cardiovascular event. Estimate the 2-year risk, and give a 95% confidence interval for this estimate.

Chapter 7: Problem 111 Fundamentals of Biostatistics 8

Treatment with statins can reduce the risk of a major cardiovascular event in people with specified risk factors. During about 2 years of follow-up in the JUPITER trial (P. M. Ridker et al. [8]) , 142 of 8901 subjects treated with a statin had a major cardiovascular event. Assuming that risk remains constant over time, give an estimate of the 10-year risk of a major cardiovascular event on statin therapy.

Chapter 7: Problem 112 Fundamentals of Biostatistics 8

Treatment with statins can reduce the risk of a major cardiovascular event in people with specified risk factors. During about 2 years of follow-up in the JUPITER trial (P. M. Ridker et al. [8]) , 142 of 8901 subjects treated with a statin had a major cardiovascular event. Suppose the expected 2-year risk of a major cardiovascular event in similar but untreated people is 0.028. Test whether the 2-year risk in those treated with a statin is significantly different from this expected risk at the 5% level. Make sure to state your null and alternative hypotheses and specify your conclusion.

Chapter 7: Problem 113 Fundamentals of Biostatistics 8

Treatment with statins can reduce the risk of a major cardiovascular event in people with specified risk factors. During about 2 years of follow-up in the JUPITER trial (P. M. Ridker et al. [8]) , 142 of 8901 subjects treated with a statin had a major cardiovascular event. Controversy persists about whether statins reduce risk of cardiovascular events entirely through their effects on cholesterol levels or whether other pathways, such as reductions in inflammation, are also relevant. In JUPITER, statin therapy was associated with an average reduction of 1.2 mmol per liter in concentration of LDL (low-density lipoprotein) cholesterol. Based on average effects over multiple clinical trials (C. Baigent et al. [9]), it is estimated that each 1 mmol per liter reduction in LDL cholesterol is associated with a 20% reduction in risk of major cardiovascular events. Hence, the expected event rate due to LDL reduction would be Assess whether the observed 2-year risk in the Jupiter study is consistent with this event rate at the 5% level. Hint: Use a confidence interval approach.

Chapter 7: Problem 114 Fundamentals of Biostatistics 8

A study was conducted in Sweden to relate the age at surgery for undescended testis to the subsequent risk of testicular cancer [10]. Twelve events were reported in 22,884 person-years of follow-up among men who were 13–15 years at age of surgery. What is the estimated incidence rate of testicular cancer among this group of men? Express the rate per 100,000 person-years.

Chapter 7: Problem 115 Fundamentals of Biostatistics 8

A study was conducted in Sweden to relate the age at surgery for undescended testis to the subsequent risk of testicular cancer [10]. Twelve events were reported in 22,884 person-years of follow-up among men who were 13–15 years at age of surgery. It was reported that the standardized incidence rate in this group compared with men in the general Swedish population was 5.06. What is the expected number of events in the general population over 22,884 person-years of follow-up?

Chapter 7: Problem 116 Fundamentals of Biostatistics 8

A study was conducted in Sweden to relate the age at surgery for undescended testis to the subsequent risk of testicular cancer [10]. Twelve events were reported in 22,884 person-years of follow-up among men who were 13–15 years at age of surgery. It was reported that the standardized incidence rate in this group compared with men in the general Swedish population was 5.06. Provide a 95% CI for the number of events among men who were 13–15 years at age of surgery.

Chapter 7: Problem 117 Fundamentals of Biostatistics 8

A study was conducted in Sweden to relate the age at surgery for undescended testis to the subsequent risk of testicular cancer [10]. Twelve events were reported in 22,884 person-years of follow-up among men who were 13–15 years at age of surgery. It was reported that the standardized incidence rate in this group compared with men in the general Swedish population was 5.06. Is there a significant difference (p < .05) between the incidence of testicular cancer in men treated surgically for undescended testis at age 13–15 vs. the general population?

Chapter 7: Problem 118 Fundamentals of Biostatistics 8

A study was conducted in Sweden to relate the age at surgery for undescended testis to the subsequent risk of testicular cancer [10]. Twelve events were reported in 22,884 person-years of follow-up among men who were 13–15 years at age of surgery. It was reported that the standardized incidence rate in this group compared with men in the general Swedish population was 5.06. What is the lifetime risk (from age 15 to age 70) of testicular cancer for men with age at surgery = 15,assuming that the incidence rate remains constant over time? Assume that all men do not die of any other disease up to age 70.

Chapter 7: Problem 119 Fundamentals of Biostatistics 8

Data from the Surveillance Epidemiology and End Results (SEER) registry provides incidence data for different cancers according to age and sex for various tumor registries throughout the world. The data in Table 7.13 were obtained for colon cancer in women from the Connecticut Tumor Registry from 1988?1992. What is the probability that a 40-year-old woman will develop colon cancer over the next 5 years?

Chapter 7: Problem 120 Fundamentals of Biostatistics 8

Data from the Surveillance Epidemiology and End Results (SEER) registry provides incidence data for different cancers according to age and sex for various tumor registries throughout the world. The data in Table 7.13 were obtained for colon cancer in women from the Connecticut Tumor Registry from 1988?1992. What is the probability that a 40-year-old woman will develop colon cancer over the next 20 years (i.e., from age 40.0 to age 59.9)?

Chapter 7: Problem 121 Fundamentals of Biostatistics 8

The data in Table 7.14 were obtained from the Nurses’ Health Study on colon cancer incidence over the time period 1980?2004. Do the SEER rates provide a good fit with the Nurses’ Health Study incidence data? Perform a separate test for each age group and simply report p > .05 or p < .05. (Hint: Use the Poisson distribution.)

Chapter 7: Problem 26 Fundamentals of Biostatistics 8

Suppose we identify 50 women 50 to 54 years of age who have both a mother and a sister with a history of breast cancer. Five of these women themselves have developed breast cancer at some time in their lives. If we assume that the expected prevalence rate of breast cancer in women whose mothers have had breast cancer is 4%, does having a sister with the disease add to the risk? Explain.

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