To solve these questions, we need to calculate the odds ratio and relative risk from the given data. Let's start by summarizing the information:
- Total population: 22,364
- Percentage of individuals who suffered an AMI (acute myocardial infarction): 1.33%
- Among those with AMI, 35% were on aspirin, and the remainder (65%) were on a placebo.
- Number of people on aspirin who did not suffer an AMI: 11,037
First, let's calculate the number of people who suffered an AMI:
\[ \text{Total AMI cases} = 22,364 \times 1.33\% \]
From this, we can calculate the number of AMI cases in the aspirin group and the placebo group. Then, we'll calculate the number of people in each group (aspirin and placebo) and find out the number of people in the placebo group who did not suffer an AMI. Using these figures, we can calculate the odds and relative risk.
Let's start with these calculations.
Based on the calculations:
- Total AMI cases: Approximately 297
- AMI cases in the aspirin group: Approximately 104
- AMI cases in the placebo group: Approximately 193
- Total people in the aspirin group: Approximately 11,141
- Total people in the placebo group: Approximately 11,223
- People in the placebo group who did not suffer an AMI: Approximately 11,030
Now, let's calculate:
a) The odds that aspirin will reduce the incidence of an AMI. The odds are calculated as the ratio of the probability of an event happening to the probability of it not happening.
\[ \text{Odds of AMI with aspirin} = \frac{\text{AMI cases in aspirin group}}{\text{Total aspirin group} - \text{AMI cases in aspirin group}} \]
b) The odds that not being on aspirin will increase the incidence of an AMI.
\[ \text{Odds of AMI with placebo} = \frac{\text{AMI cases in placebo group}}{\text{Total placebo group} - \text{AMI cases in placebo group}} \]
c) The relative risk (RR) of an AMI occurring when on aspirin compared to not being on aspirin. The RR is calculated as the ratio of the probability of an event occurring in the exposed group to the probability of the event occurring in the non-exposed group.
\[ \text{Relative Risk (RR)} = \frac{\text{Probability of AMI with aspirin}}{\text{Probability of AMI with placebo}} \]
Let's calculate these values.
Here are the results:
a) The odds that aspirin will reduce the incidence of an AMI are approximately 0.0094. This means that for every individual who had an AMI while on aspirin, there are about 0.0094 individuals who did not have an AMI while on aspirin.
b) The odds that not being on aspirin will increase the incidence of an AMI are approximately 0.0175. This indicates that for every individual who had an AMI while not on aspirin, there are about 0.0175 individuals who did not have an AMI while not on aspirin.
c) The relative risk (RR) of an AMI occurring when on aspirin compared to not being on aspirin is approximately 0.54. This suggests that the risk of having an AMI while on aspirin is about 54% of the risk of having an AMI while not on aspirin.
These results indicate that being on aspirin is associated with a lower risk and lower odds of experiencing an AMI compared to not being on aspirin.
