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Refer to a study on hormone replacement therapy. Until \(2002,\) hormone replacement therapy (HRT), taking hormones to replace those the body no longer makes after menopause, was commonly prescribed to post-menopausal women. However, in 2002 the results of a large clinical trial \({ }^{48}\) were published, causing most doctors to stop prescribing it and most women to stop using it, impacting the health of millions of women around the world. In the experiment, 8506 women were randomized to take HRT and 8102 were randomized to take a placebo. Table 6.8 shows the observed counts for several conditions over the five years of the study. (Note: The planned duration was 8.5 years. If Exercises 6.181 through 6.184 are done correctly, you will notice that several of the intervals just barely exclude zero. The study was terminated as soon as some of the intervals included only positive values, because at that point it was unethical to continue forcing women to take HRT.) $$ \begin{array}{lcc} \hline \text { Condition } & \text { HRT Group } & \text { Placebo Group } \\ \hline \text { Cardiovascular Disease } & 164 & 122 \\ \text { Invasive Breast Cancer } & 166 & 124 \\ \text { Cancer (all) } & 502 & 458 \\ \text { Fractures } & 650 & 788 \\ \hline \end{array} $$ Find a \(95 \%\) confidence interval for the difference in proportions of women who get cardiovascular disease taking HRT vs taking a placebo.

Step by step solution

01

Calculate the Proportions

Calculate the proportion of women who developed cardiovascular disease for each group. For the HRT group, it's \( p1 = 164/8506 \approx 0.0193 \), and for the placebo group, it's \( p2 = 122/8102 \approx 0.0150 \).

02

Calculate the Difference in Proportions

Find the difference in proportions. This can be done by subtracting the proportion of the placebo group from the HRT group, giving us \( p1 - p2 \approx 0.0193 - 0.0150 = 0.0043 \).

03

Calculate the Standard Error

Calculate the standard error using the formula \[ SE = \sqrt{ \frac{p1 * (1 - p1)} {n1} + \frac{p2 * (1 - p2)} {n2} } \], where \(n1\) and \(n2\) are sizes of the HRT and placebo groups respectively. Substituting the values, we get \( SE \approx \sqrt{ \frac{0.0193 * 0.9807}{8506} + \frac{0.0150 * 0.9850}{8102} } \approx 0.0014 \).

04

Calculate the Confidence Interval

Calculate the 95% confidence interval using the formula \[ CI = (p1 - p2) \pm Z * SE \], where Z represents the Z score for a 95% confidence level, which is approximately 1.96. Substituting our values, we get \[ CI \approx 0.0043 \pm 1.96 * 0.0014 = (0.0015, 0.0071) \].

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Key Concepts

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

HRT (Hormone Replacement Therapy)

Hormone Replacement Therapy (HRT) involves taking hormones to replace those the body no longer produces after menopause. For many years, HRT was widely used to manage menopausal symptoms such as hot flashes and to prevent long-term health issues such as osteoporosis. The use of HRT changed dramatically after a landmark study in 2002 showed potential risks, including an increased incidence of cardiovascular disease and certain cancers.

Understanding the implications of HRT on women's health requires rigorous clinical trials and statistical analysis to determine its benefits and risks. Healthcare decisions often hinge on such evidence, which can impact the lives of millions of women around the world.

Cardiovascular Disease in Clinical Trials

Clinical trials are essential for establishing the relationship between medical interventions, like HRT, and health outcomes, such as cardiovascular disease (CVD). In the study referenced, the occurrence of CVD in both the HRT group and placebo group was meticulously recorded. Cardiovascular disease remains a leading cause of mortality in women, and understanding how HRT could influence its incidence is crucial.

In clinical trials, researchers often look for differences in disease occurrence between groups to assess the efficacy or risks associated with a treatment. A confidence interval for the difference in proportions, which was calculated based on the study data, helps quantify the uncertainty around the observed effect of HRT on CVD rates.

Statistics in Medical Research

Statistics play a pivotal role in medical research, allowing for the rigorous evaluation of clinical trial data. In the context of the HRT study, calculating the confidence interval for the difference in proportions of women developing CVD while on HRT versus a placebo is an essential statistical process.

A confidence interval provides a range of values that are believed, with a certain level of confidence, to contain the true difference in proportions. In this case, the 95% confidence interval suggests that we can be 95% confident that the true difference in the proportion of CVD cases between the HRT and placebo groups lies within the calculated interval. The process involves several steps: calculating the proportions in each group, finding the difference, determining standard error, and finally constructing the confidence interval using a Z score for the desired confidence level. By providing clarity on the magnitude and precision of the effect, statistics support informed decision-making in healthcare.