In Clinical Trials of Nasonex, 3774 Adult Adolescent Allergy Patients (Patients 12 Years

1) - Nasonex

In clinical trials of Nasonex, 3774 adult adolescent allergy patients (patients 12 years and older) were randomly divided into two groups. The patients in group 1 (experimental group) received 200 mcg of Nasonex, while the patients in Group 2 (control group) received a placebo. Of the 2103 patients in the experimental group, 547 reported headaches as side effect. Of the 1671 patients in the control group, 368 reported headaches as a side effect.

Part 1 - Is there significant evidence to support the claim that the proportion of Nasonex users that experienced headaches as a side effect is greater than the proportion in the control group at the 0.05 significance level?

Part 2 – Use a feature of your calculator to construct a 90% confidence interval estimate for the difference between the two population proportions. What is the interval suggesting?

Population 1: Experimental group = allergy patients (12-years and older) who received 200 mcg of NasonexPopulation 2: Placebo group = allergy patients (12-years and older) who received a placebo

Success attribute: experience headache

p1 is the proportion of all Nasonex users who experience headaches)

p2 is the proportion of all placebo (Non-Nasonex) users who experience headaches)

First: Verify assumptions

Check that in each population np and nq are both 10 or more

a) Set both hypothesis

This is a right tailed test

b) Sketch graph, shade rejection region, label, and indicate possible locations of the point estimate in the graph.

You do this

The point estimate is

****You should be wondering: Is the proportion that experience headaches in the experimental group larger than the one in the control group by chance, or is it significantly higher? The p-value found below will help you in answering this.

c) Use a feature of the calculator to test the hypothesis. Indicate the feature used and the results:

Use 2-Prop-ZTest and get

Test statistic z = 2.84

P() = P(z > 2.84) = p-value = .0023 < .05 (significance level)

The p-value is very small. It is very unlikely (p = 0.023) to observe such a difference between sample proportions (p1 – p2 = 0.04) when the proportion experiencing headaches is the same in both populations. Such a difference between the sample proportions is significantly larger than zero and it is more likely to be observed when p1 is larger than p2.

At the 5% significance level we support the claim that proportion of Nasonex users that experienced headaches as a side effect is greater than the proportion in the control group

Part 2 – Use a feature of your calculator to construct a 90% confidence interval estimate for the difference between the two population proportions. What is the interval suggesting?

The point estimate is

Is by chance or significantly lower?

Note: In the experimental group, a higher percentage experience headache, could that be because of the drug?

Construct the interval by using 2-Prop-ZInterval and get .01695 < < .0628

We are 90% confident that the difference between the proportion experiencing headaches in the Nasonex and the placebo groups is between 0.01695 and 0.0628. Since the interval is completely above zero, it suggests that > 0 which means that . This is the same as the conclusion to the hypothesis testing part.

What is the margin of error?

0.0628 – 0.04 = 0.0228

(2) In view of your answers to part 1, could you reasonably conclude that Nasonex causes headaches as a side effect?

This was an experiment and in the case of an experimental study we could interpret statistical significance as a causal relationship.

In this case, the difference of 4% is statistically significant, but it may not have any practical significance. Most parents would be willing to accept the additional “risk” of a headache in order to relieve their child’s allergy symptoms.

2) – Vasectomies and Prostate Cancer

Approximately 450,000 vasectomies are performed each year in the U.S. In this surgical procedure for contraception, the tube carrying sperm from the testicles is cut and tied. Several studies have been conducted to analyze the relationship between vasectomies and prostate cancer. The results of one such study by E. Giovannucci et al. appeared in the paper “A Retrospective Cohort Study of Vasectomy and Prostate Cancer in U.S. Men”. Of 21,300 men who had not had a vasectomy, 69 were found to have prostate cancer; of 22,000 men who had had a vasectomy, 113 were found to have prostate cancer.

Part 1 - At the 1% significance level, do the data provide sufficient evidence to conclude that men who have had a vasectomy are at greater risk of having prostate cancer?

Part 2 – Use the calculator to determine a 98% confidence interval for the difference between the prostate cancer rates of men who have had a vasectomy and those who have not.

Population 1: men without vasectomy

Population 2: men with vasectomy

Success attribute: have prostate cancer

Let p1 be the proportion of men without a vasectomy who have prostate cancer

Let p2 be the proportion of men with a vasectomy who have prostate cancer

NO VASECTOMYVASECTOMY

p-hat(1) = 0.0032 is our first estimate for p1

p-hat (2) = 0.0051 is our first estimate for p2

p-hat(1) – p-hat(2) = 0.0032 – 0.0051= -0.0019 is our first estimate for p1 – p2

0.32% of men in the NO-vasectomy group and 0.51% in thevasectomy group had prostate cancer. Is the percent higher in the vasectomy group by chance or is it significantly higher? Is the proportion of men with prostate cancer lower in the group of men without a vasectomy?

We are going to assume that all assumptions are met and we can perform a test with the methods learned in class.

Part 1 - At the 1% significance level, do the data provide sufficient evidence to conclude that men who have had a vasectomy are at greater risk of having prostate cancer?

a) Set both hypothesis

This is a left tailed test

b) Sketch graph, shade rejection region, label, and indicate possible locations of the point estimate in the graph.

You do this.

The point estimate is

****You should be wondering: Is the proportion of men with prostate cancer in the group without vasectomy lower than in the group with vasectomy by chance, or is it significantly lower? The p-value found below will help you in answering this.

c) Use a feature of the calculator to test the hypothesis. Indicate the feature used and the results:

Use 2-Prop-ZTest and get

Test statistic z = - 3.05

P() = P(z < - 3.05) = p-value = .001 < .01 (significance level)

It is unlikely to observe such a difference (-0.0019) or a more extreme one between the sample proportions when you select samples from two populations that have the same proportions?

The proportion of men with prostate cancer in the group without vasectomy is significantly lower than the proportion in the group with vasectomy.

At the 1% significance level, the data provide sufficient evidence to conclude that men who have had a vasectomy are at greater risk of having prostate cancer.

Part 2 – Use the calculator to determine a 98% confidence interval for the difference between the prostate cancer rates of men who have had a vasectomy and those who have not. Are the results consistent with the results of the hypothesis test? Explain.

The point estimate is

Is by chance or significantly lower?

Construct the interval by using 2-Prop-ZInterval and get -.0033 < < -.0005

Since the interval is completely below zero, it suggests that < 0 which means

This is the same as. We get the same conclusion as in the hypothesis testing part.

With 98% confidence the data provide sufficient evidence to conclude that men who have had a vasectomy are at greater risk of having prostate cancer.

Some other related questions:

(1) Is this study a designed experiment or an observational study?

Observational

(2) In view of your answers to part 1, could you reasonably conclude that having a vasectomy causes an increased risk of prostate cancer?

No, for an observational study, it is not reasonable to interpret statistical significance as a causal relationship. In the case of an experimental study we could interpret statistical significance as a causal relationship.