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Chapter 23: Problem 18

Effects of an Appetite Suppressant. Subjects with preexisting cardiovascular symptoms who received sibutramine, an appetite suppressant, were found to be at increased risk of cardiovascular events while taking the drug. The study included 9804 overweight or obese subjects with preexisting cardiovascular disease and/or type 2 diabetes. The subjects were randomly assigned to sibutramine (4906 subjects) or a placebo (4898 subjects) in a double-blind fashion. The primary outcome measured was the occurrence of any of the following events: nonfatal myocardial infarction or stroke, resuscitation after cardiac arrest, or cardiovascular death. The primary outcome was observed in 561 subjects in the sibutramine group and 490 subjects in the placebo group. 18 a. Find the proportion of subjects experiencing the primary outcome for both the sibutramine and placebo groups. b. Can we safely use the large-sample confidence interval for comparing the proportions of sibutramine and placebo subjects who experienced the primary outcome? Explain. c. Give a \(95 \%\) confidence interval for the difference between the proportions of sibutramine and placebo subjects who experienced the primary outcome.

Short Answer

Expert verified
a) Sibutramine: 11.44%, Placebo: 10.01%. b) Yes; conditions are met. c) CI: [-0.0025, 0.0311].

Step by step solution

01

Calculate Proportion for Sibutramine Group

To find the proportion of subjects experiencing the primary outcome in the sibutramine group, divide the number of events by the total number of subjects in that group. The formula is \( p_1 = \frac{x_1}{n_1} \), where \( x_1 = 561 \) (number of events) and \( n_1 = 4906 \) (number of subjects). Thus, \( p_1 = \frac{561}{4906} \approx 0.1144 \).
02

Calculate Proportion for Placebo Group

Similarly, to find the proportion of subjects experiencing the primary outcome in the placebo group, divide the number of events by the total number of subjects in that group. The formula is \( p_2 = \frac{x_2}{n_2} \), where \( x_2 = 490 \) and \( n_2 = 4898 \). Thus, \( p_2 = \frac{490}{4898} \approx 0.1001 \).
03

Check Conditions for Using Large-Sample Confidence Interval

For the large-sample confidence interval to be valid, both groups need their number of events and non-events to be at least 5. The calculations are: \( 561, 4906-561, 490, \) and \( 4898-490 \) all exceed 5. Therefore, using the large-sample confidence interval is appropriate.
04

Calculate the 95% Confidence Interval

Compute the standard error \( SE \) for the difference between the proportions using the formula: \( SE = \sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}} \). Substituting the known values: \[ SE = \sqrt{\frac{0.1144(1-0.1144)}{4906} + \frac{0.1001(1-0.1001)}{4898}} \approx 0.0086 \]. The confidence interval \( CI \) is: \( p_1 - p_2 \pm z*SE \), where \( z \approx 1.96 \) for a 95% confidence level. Thus, the confidence interval becomes: \[ 0.1144 - 0.1001 \pm 1.96 \times 0.0086 = 0.0143 \pm 0.0168 \]Resulting in the interval \([-0.0025, 0.0311]\).

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Key Concepts

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

Confidence Interval
In statistics, a confidence interval is a range of values that is used to estimate the true value of a population parameter. This interval provides an upper and lower limit which, with a certain degree of confidence (often 95%), contains the true parameter. For example, if we have a confidence interval for the difference between proportions, it helps us understand how much the proportions differ in the entire population beyond just our sample.

Confidence intervals are based on sampling variability and are computed using the sample data. The interval is constructed around a sample estimate, such as a mean or a proportion, by adding and subtracting a margin of error from the estimate. This margin of error is influenced by the standard error, which accounts for variability, and a critical value (z-score), which reflects the confidence level chosen (often 1.96 for 95% confidence).

To compute a confidence interval for the proportion difference, we find the difference between the sample proportions first, then determine the standard error for this difference. This calculation can show, for instance, whether or not there is a statistically significant difference between treatment groups in a study, while also considering sampling variability.
Proportion Comparison
When comparing proportions, we are interested in determining if there is a statistically significant difference between the two independent groups. In the context of the given study, the proportion of subjects experiencing certain cardiovascular outcomes is compared between those taking sibutramine and those receiving a placebo.

This involves calculating the proportion of subjects who experience the event in both groups. The formula for a proportion is straightforward: divide the number of subjects experiencing the event by the total number of subjects in the group. In mathematical terms, for the sibutramine group, it is computed as \(p_1 = \frac{x_1}{n_1}\), and for the placebo group, as \(p_2 = \frac{x_2}{n_2}\).

Once we have these proportions, statistical inference can help decide if the observed difference between them is due to chance or indicates a real difference. This typically involves checking conditions that validate the methods used (e.g., ensuring a large enough sample size), computing the standard error for the difference, and ultimately applying statistical tests or constructing confidence intervals.
Double-Blind Study
A double-blind study is a crucial design in clinical research where neither the participants nor the researchers know which treatment the participants are receiving. This approach minimizes bias and ensures the results are more reliable and valid.

In the study mentioned, subjects were randomly assigned to receive either sibutramine or a placebo, with both the participants and the experimenters kept unaware of the assignment. This setup prevents expectations or preconceptions from influencing the results, as neither group knows who is taking the actual drug versus the placebo.
  • Bias Reduction: It helps in reducing both the experimenter bias and the participant bias.
  • Random Assignment: Subjects are randomly assigned to each group to ensure similarities across groups and eliminate bias from selection.
  • Objective Outcomes: Any differences in outcomes can more confidently be attributed to the treatment effect as opposed to external factors or biases.
By employing a double-blind approach, the study ensures that its findings regarding the effectiveness and safety of sibutramine compared to placebo are accurate and not distorted by expectations.

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Most popular questions from this chapter

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