Given a study of 9804 overweight or obese subjects with preexisting cardiovascular disease and/or type 2 diabetes.
Subjects randomly assigned to subitramine (4906 subjects) or a placebo (4898 subjects) in a double-blind fashion.
Primary outcome was observed in 561 subjects in the subitramine group and 490 subjects in the placebo group.
Find the proportion of subjects experiencing the primary outcome for both the subitramine and placebo groups
I found subritramine proportion = 0.11 and placebo proportion = 0.10.
***Can we safely use the large sample confidence interval for comparing the proportions of subitramine and placebo subjects who experienced the primary outcome? explain.
this is where I need help. Thank you.
Yes, you should be able to use the large sample confidence interval due to the size of the samples in the study. The larger the sample size, the more you can safely approximate the normal distribution.
To determine whether we can safely use the large sample confidence interval for comparing the proportions of subitramine and placebo subjects who experienced the primary outcome, we need to consider the conditions required for the large sample confidence interval.
The large sample confidence interval assumes that the sample sizes are sufficiently large. One common guideline is that we need at least 10 successes and 10 failures in both groups (subitramine and placebo). In this case, we have 561 successes and 4345 failures in the subitramine group, and 490 successes and 4408 failures in the placebo group. Therefore, we meet the minimum requirement in both groups, and the condition for sample size is satisfied.
Another assumption of the large sample confidence interval is that the observations are independent. In this study, subjects were randomly assigned to either the subitramine or placebo group in a double-blind fashion. This randomization process helps to ensure independence, as it minimizes the potential for confounding factors that could influence the primary outcome. Therefore, the condition for independence is satisfied.
Based on these conditions, we can conclude that we can safely use the large sample confidence interval for comparing the proportions of subitramine and placebo subjects who experienced the primary outcome.
To calculate the confidence interval for proportions, you can use the following formula:
proportion ± Z * √(proportion * (1 - proportion) / n)
where proportion is the observed proportion, Z is the critical value from the standard normal distribution corresponding to the desired confidence level, and n is the sample size.
In this case, you have already calculated the proportions as 0.11 for the subitramine group, and 0.10 for the placebo group. To calculate the confidence interval, you also need to know the desired confidence level, such as 95%. The critical value for a 95% confidence level is approximately 1.96.
Let's calculate the confidence intervals for both groups:
For the subitramine group:
Proportion: 0.11
Sample Size: 4906
Critical Value (Z): 1.96
Using the formula, the confidence interval will be:
0.11 ± 1.96 * √(0.11 * (1 - 0.11) / 4906)
Similarly, for the placebo group, the confidence interval formula will be:
0.10 ± 1.96 * √(0.10 * (1 - 0.10) / 4898)
By calculating these intervals, you can compare the ranges to determine if they overlap, which would indicate no significant difference in proportions between the two groups.