Question

A randomized, double-blind, clinical trial was conducted on patients who had coronary angioplasty to compare the drug lovastatin to a placebo. The percentage of stenosis (narrowing of the blood vessels) following angioplasty was measured on 160 patients given lovastatin and on 161 patients given the placebo. For the lovastatin group the average was \(46 \%,\) with an \(\mathrm{SD}\) of \(20 \%\). For the placebo group the average was \(44 \%,\) with an \(S D\) of \(21 \% .^{21}\) What type of analysis is appropriate for these data?

Short answer

The appropriate analysis for comparing the average percentage of stenosis between the lovastatin and placebo groups would be a two-sample t-test.

Step-by-step solution

Understanding the Data

Before analyzing the data, it is crucial to understand what kind of data we have and its significance. We are dealing with two groups of patients, one receiving lovastatin and the other receiving a placebo. The variables we are focusing on are the averages and standard deviations of the percentage of stenosis in both groups.

Identifying the Type of Data

The data for both groups include the average percentage of stenosis and the standard deviations from these averages. The data points are numeric and continuous, which is relevant when selecting the type of analysis to conduct.

Selecting the Appropriate Analysis

Given that we have two groups and continuous data, we would typically use a two-sample t-test to compare the means of these two independent groups to determine if there is a statistically significant difference between them.

Considering Study Design

The study is randomized and double-blind, which makes it more appropriate for hypothesis testing using parametric methods, such as the t-test, since these methods assume random sampling from a defined population and typically require the data to follow a normal distribution.

Key concepts

Clinical Trial Analysis

In clinical trial analysis, we assess the effectiveness and safety of medical interventions, like drugs or medical devices. Clinical trials are typically structured in phases, including a comparison between experimental treatments and a control group, which in this case, is the placebo group. Key factors like randomization and blind assessments are used to mitigate biases.

In the provided exercise, patients were split into two groups - one receiving lovastatin and one receiving a placebo. The primary measure of interest is the percentage of stenosis, indicative of the degree of vessel narrowing, post-angioplasty. This kind of comparative analysis is crucial, as it helps determine whether the drug has a statistically significant effect compared to non-treatment.

The clinical trial's outcome depends on adequate analysis methods, such as the two-sample t-test in this scenario, to handle the continuous data captured from both patient groups. Such analyses help determine the efficacy of the treatments, which is vital for regulatory approvals and future medical recommendations.

Statistical Hypothesis Testing

Statistical hypothesis testing is a method used to make decisions using data. It centers around the null hypothesis, which states that there is no effect or no difference, and the alternative hypothesis, which suggests the opposite.

In the context of the exercise, a two-sample t-test would be employed. This test compares the means of two independent groups (in this case, the lovastatin group vs. the placebo group) to see if they differ from one another in a statistically significant way. The null hypothesis would assert that there is no difference in stenosis percentage post-angioplasty between the two groups, while the alternative hypothesis would claim there is a difference.

To perform the t-test, assumptions need to be met, such as the data being approximately normally distributed and the variances between groups being equal. Once the test is executed, a p-value is calculated, which helps to determine whether the observed results are statistically significant. If the p-value is less than the chosen significance level (often set at 0.05), the null hypothesis is rejected, favoring the alternative hypothesis.

Standard Deviation

The standard deviation (SD) is a measure of the amount of variation or dispersion in a set of values. It quantifies how much the numbers in the data set tend to deviate from the mean (average) of the set.

In the study under discussion, the SD gives us insight into the variability in percentage of stenosis in the patient groups. Lower SD indicates that the data points are clustered closely around the mean, while a higher SD indicates more spread. In the exercise, the SD is given for both groups: 20% for those on lovastatin and 21% for the placebo group. This is important for the two-sample t-test, as the test uses the mean and standard deviation from both groups to compare the variability, alongside mean differences.

Understanding SD is crucial for interpreting clinical data. For instance, a small SD alongside a meaningful difference in means between treatment and control groups could suggest a potential therapeutic effect of the drug that is consistent across the patient population.