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Questionnaires were mailed to 5,000 people who were selected randomly. Each person was asked to list age, sex, smoking habits, and respiratory symptoms during the preceding seven days. About 80% of the questionnaires were completed and returned, making the final completed sample of 4,000. There were 1,100 total smokers in the sample. There were 1,000 respondents who had respiratory symptoms.
About 700 of the respondents reported having upper respiratory symptoms and also smoked. There were 2,600 respondents who neither smoked nor had any respiratory symptoms. There were 400 respondents who smoked but had no respiratory symptoms. Calculate the odds ratio of the disease and exposure. Be sure to provide the correct interpretation of your results.
Paper For Above instruction
To analyze the relationship between smoking and respiratory symptoms in the sampled population, we construct a 2x2 contingency table (or grid) based on the provided data. This facilitates the calculation of the odds ratio (OR), a measure commonly used in epidemiology to assess the strength of association between an exposure (smoking) and an outcome (respiratory symptoms).
First, let's organize the data into the contingency table. The key categories are:
- Smokers with respiratory symptoms (a)
- Smokers without respiratory symptoms (b)
- Non-smokers with respiratory symptoms (c)
- Non-smokers without respiratory symptoms (d)
From the data:
- Total respondents: 4,000
- Smokers: 1,100
- Respiratory symptoms: 1,000
- Respondents with respiratory symptoms who smoked: 700
- Respondents who neither smoked nor had respiratory symptoms: 2,600
- Smokers without respiratory symptoms: 400
Since 700 smokers have respiratory symptoms, and total respondents with respiratory symptoms are 1,000, the remaining 300 respondents with respiratory symptoms must be non-smokers. Likewise, of 1,100 smokers, 400 have no respiratory symptoms, implying 700 smokers have respiratory symptoms (already noted), and the remaining 700 respondents with respiratory symptoms are non-smokers.
To find the number of non-smokers without respiratory symptoms:
Total respondents: 4,000
Smokers: 1,100
Respiratory symptoms: 1,000
Smokers with respiratory symptoms: 700
Smokers without respiratory symptoms: 400
Respondents with respiratory symptoms who are non-smokers: 300 (since total with symptoms = 1,000, and 700 are smokers)
Number of non-smokers: 4,000 - 1,100 = 2,900
Non-smokers with respiratory symptoms: 300
Non-smokers without respiratory symptoms: 2,900 - 300 = 2,600
Now, the contingency table is:
| | Respiratory Symptoms | No Respiratory Symptoms | Total |
|--------------------------|------------------------|-------------------------|--------|
| Smoked | 700 | 400 | 1,100 |
| Did Not Smoke | 300 | 2,600 | 2,900 |
| Total | 1,000 | 3,000 | 4,000 |
Next, we calculate the odds ratio (OR):
OR = (a/c) / (b/d) = (700/300) / (400/2600) = (700 2600) / (300 400)
Calculating:
- Numerator: 700 * 2600 = 1,820,000
- Denominator: 300 * 400 = 120,000
Therefore:
OR = 1,820,000 / 120,000 = 15.17
Interpretation:
An odds ratio of approximately 15.17 indicates a strong association between smoking and respiratory symptoms in this sample. Specifically, smokers are about 15 times more likely to report respiratory symptoms during the past week compared to non-smokers. This suggests that smoking significantly increases the risk of experiencing respiratory symptoms, underscoring the importance of smoking cessation interventions as a public health strategy.
While the odds ratio is high, it is also important to interpret these results within the context of potential confounders not accounted for in this simple analysis. Factors such as age, occupational exposures, environmental pollutants, and pre-existing health conditions could influence respiratory symptoms. Nonetheless, the data reflect a strong likely causal link between smoking and respiratory symptoms, aligning with extensive epidemiological literature indicating smoking as a primary risk factor for respiratory diseases.
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