Grid Attached: Questionnaires Mailed To 5,000 People
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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. But there were 400 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. Create a grid to calculate the rates, proportion, and odds ratio of the disease and exposure. Use the grid below as a guide. In 1 or 2 paragraphs provide an interpretation of your results. Paper should: be 1-2 pages in length. Show how you calculated your answers. Be free of spelling and grammar errors.
Paper For Above instruction
The investigation into the association between smoking and respiratory symptoms was conducted through a well-structured survey, yielding valuable insights into potential correlations between exposure and disease. The objective was to determine whether smoking is associated with an increased risk of respiratory symptoms by calculating the odds ratio, a measure frequently used in epidemiology to assess the strength of association between an exposure and an outcome.
Data Summary and Construction of the Contingency Table
Based on the provided data, the sample includes 4,000 respondents with known smoking status and respiratory symptoms. The data points are as follows:
- Total respondents: 4,000
- Smokers: 1,100
- Respiratory symptoms: 1,000
- Smokers with respiratory symptoms: 700
- Non-smokers with respiratory symptoms: 300 (since 1,000 total with symptoms minus 700 who smoke)
- Smokers without respiratory symptoms: 400
- Non-smokers without respiratory symptoms: 2,600 (total non-smokers: 4,000 – 1,100 = 2,900; minus 300 with symptoms leaves 2,600)
Using these figures, the data can be arranged in a 2x2 contingency table:
| | Respiratory Symptoms | No Respiratory Symptoms | Total |
|------------------------|---------------------|-------------------------|-----------|
| Smoker | 700 | 400 | 1,100 |
| Non-Smoker | 300 | 2,600 | 2,900 |
| Total | 1,000 | 3,000 | 4,000 |
Calculations of Odds and Odds Ratio
The odds of respiratory symptoms among smokers:
\[ \text{Odds}_{\text{smoker}} = \frac{\text{Number of smokers with symptoms}}{\text{Number of smokers without symptoms}} = \frac{700}{400} = 1.75 \]
The odds of respiratory symptoms among non-smokers:
\[ \text{Odds}_{\text{non-smoker}} = \frac{300}{2600} \approx 0.115 \]
The odds ratio (OR), which measures the strength of the association between smoking and respiratory symptoms, is calculated as:
\[ OR = \frac{\text{Odds}_{\text{smoker}}}{\text{Odds}_{\text{non-smoker}}} = \frac{1.75}{0.115} \approx 15.22 \]
Interpretation of Results
An odds ratio of approximately 15.22 indicates a strong association between smoking and respiratory symptoms. Specifically, smokers in this sample are about 15 times more likely to report respiratory symptoms compared to non-smokers. This substantial increase in odds suggests that smoking is a significant risk factor for respiratory issues within this population. It is important to note that while the odds ratio demonstrates association, it does not necessarily imply causation. Confounding variables such as age, environmental exposure, or pre-existing health conditions could also influence the likelihood of respiratory symptoms.
The results underscore the importance of smoking cessation programs and public health interventions aimed at reducing smoking prevalence to mitigate respiratory illnesses. Additionally, further studies could explore the causal mechanisms and control for potential confounders to strengthen the evidence linking smoking with respiratory health outcomes.
References
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