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Chantix is different from most other quitsmoking products in that it targets nicotine receptors in the brain, attaches to them, and blocks nicotine from reaching them. A randomized, double-blind, placebo-controlled clinical trial on Chantix was conducted with a 24-week treatment period. Participants in the study were cigarette smokers who were either unwilling or unable to quit smoking in the next month but were willing to reduce their smoking and make an attempt to quit within the next three months. Subjects received either Chantix or a placebo for 24 weeks, with a target of reducing the number of cigarettes smoked by \(50 \%\) or more by week \(4,75 \%\) or more by week 8, and a quit attempt by 12 weeks. The primary outcome measured was continuous abstinence from smoking during weeks 15 through 24. Of the 760 subjects taking Chantix, 244 abstained from smoking during weeks 15 through 24 , whereas 52 of the 750 subjects taking the placebo abstained during this same time period. \({ }^{24}\) Give a \(99 \%\) confidence interval for the difference (treatment minus placebo) in the proportions of smokers who would abstain from smoking during weeks 15 through \(24 .\)

Step by step solution

01

Identify the Known Values

First, extract all the necessary data from the problem. We have: - Number of subjects on Chantix = 760 - Number of subjects on placebo = 750 - Number of Chantix abstainers = 244 - Number of placebo abstainers = 52.

02

Calculate Sample Proportions

Calculate the proportions of subjects who abstained in each group. For Chantix: \[ \hat{p}_1 = \frac{244}{760} \approx 0.321 \] For Placebo: \[ \hat{p}_2 = \frac{52}{750} \approx 0.069 \]

03

Find the Difference in Proportions

Find the difference between the two sample proportions:\[ \hat{p}_1 - \hat{p}_2 = 0.321 - 0.069 = 0.252 \]

04

Calculate Standard Error of the Difference

Use the formula for the standard error of the difference in two independent proportions:\[ SE = \sqrt{ \frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2} } \]where \( n_1 = 760 \) and \( n_2 = 750 \).Putting the values:\[ SE = \sqrt{ \frac{0.321 \times 0.679}{760} + \frac{0.069 \times 0.931}{750} } \approx 0.021 \]

05

Determine Z-score for 99% Confidence

For a 99% confidence interval, the Z-score is approximately 2.576 (since 99% confidence corresponds to a critical region with 1% in both tails).

06

Compute Confidence Interval

Using the formula for the confidence interval of the difference in proportions, we have:\[(\hat{p}_1 - \hat{p}_2) \pm Z \times SE\]Plug in the values:\[0.252 \pm 2.576 \times 0.021\]The confidence interval is:\[(0.252 - 0.0541, 0.252 + 0.0541) = (0.1979, 0.3061)\]

07

Interpret the Results

The 99% confidence interval for the difference in abstinence rates between the Chantix and placebo groups is (0.198, 0.306). This suggests that Chantix is associated with a higher rate of abstinence compared to placebo, and we are 99% confident that the true difference in proportions is between these values.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Randomized Controlled Trial

Randomized Controlled Trials (RCTs) are often considered the gold standard in clinical research trials. They are designed to objectively evaluate the effectiveness of a new intervention or treatment by randomly allocating subjects into either the treatment group or a control group. This random assignment reduces the risk of bias and ensures that the results are due to the intervention itself rather than other external factors.

In the context of the Chantix study, participants were randomly assigned to receive either Chantix or a placebo. This ensures that any differences in smoking abstinence between the two groups can be attributed directly to Chantix and not influenced by prior habits, personal motivation, or other variables that were not controlled for.

Moreover, the study was double-blind, meaning neither the participants nor the researchers knew which subjects were receiving the treatment and which were receiving the placebo. This further eliminates bias, as it prevents expectations from influencing the results.

Sample Proportions

Sample proportions are used to summarize binary outcome data from study groups. In research, they help to show the ratio or percentage of subjects experiencing a particular outcome out of the total subjects in a group.

In the given exercise, two sample proportions were calculated: one for the Chantix group and one for the placebo group. The formula used was \[ \hat{p} = \frac{x}{n} \] where \( x \) is the number of subjects achieving the outcome (abstinence), and \( n \) is the total number of subjects in the group.

• For the Chantix group: 244 out of 760 subjects abstained, giving a proportion \( \hat{p}_1 \approx 0.321 \).
• For the placebo group: 52 out of 750 subjects abstained, resulting in a proportion \( \hat{p}_2 \approx 0.069 \).

Understanding these proportions helps in assessing the effectiveness of the treatment being studied. A higher proportion in the Chantix group compared to the placebo group implies that Chantix may be more effective in aiding smoking cessation.

Standard Error

The standard error (SE) is a measure of the variability or spread of a sample statistic. In hypothesis testing, it provides an estimate of how much the sample mean or proportion is expected to vary from the true population value.

When comparing two proportions, the standard error helps to determine how reliable the observed difference is between them. It is calculated using the formula: \[ SE = \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}} \] Here, \( \hat{p}_1 \) and \( \hat{p}_2 \) are the sample proportions, and \( n_1 \) and \( n_2 \) are the sample sizes.

For the Chantix example, SE was calculated to be approximately 0.021. This value allows researchers to construct confidence intervals to draw conclusions about the population from the sample studied. A smaller standard error suggests a more precise estimate of the true population parameter.

Abstinence Rate

The abstinence rate is a critical measure used in smoking cessation studies to evaluate the effectiveness of interventions intended to reduce or stop smoking. It refers to the proportion of individuals who successfully refrain from smoking for a specified period.

In the Chantix study, the abstinence rate during weeks 15 through 24 was the primary outcome of interest. For the Chantix group, 244 out of 760 participants abstained from smoking, while for the placebo group, it was 52 out of 750. These figures were translated into proportions to make comparisons easier.

The calculation of the abstinence rate is crucial as it directly impacts the interpretation and conclusion of the study: whether Chantix is effective in increasing the likelihood of quitting smoking compared to a placebo. Understanding the abstinence rate enables a clearer communicative insight into how a drug like Chantix may influence behavioral change in individuals attempting to quit smoking.