Calculate The Odds Ratio Of Disease And Exposure From Study

Calculate the odds ratio of the disease and exposure from survey data

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.

Paper For Above instruction

Introduction

Understanding the association between smoking and respiratory symptoms is essential for public health interventions aimed at reducing respiratory illness. Case-control studies often utilize odds ratios to quantify the strength of the association between an exposure—in this case, smoking—and a health outcome, such as respiratory symptoms. This study analyzes survey data collected from randomly selected individuals to evaluate whether smoking increases the likelihood of experiencing respiratory symptoms. Using a 2x2 contingency table, the odds ratio provides a measure of this association, which we interpret to understand potential causal links and inform health policies.

Methodology and Data Preparation

The data originates from 4,000 respondents, with key variables being smoking status and respiratory symptoms. The information provided allows one to construct a 2x2 table of exposure (smoking) versus disease (respiratory symptoms). The parameters from the question include:

- Total respondents: 4,000

- Smokers: 1,100

- Respiratory symptoms: 1,000

- Both smokers and respiratory symptoms: 700

- Neither smokers nor respiratory symptoms: 2,600

- Smokers but no respiratory symptoms: 400

From this data, we can organize the counts into a contingency table:

| | Respiratory Symptoms (Disease) | No Respiratory Symptoms | Total |

|--------------------------|------------------------------|------------------------|--------|

| Smoker (Exposed) | 700 | 400 | 1,100 |

| Non-Smoker (Unexposed) | 300 | 2,600 | 2,900 |

| Total | 1,000 | 3,000 | 4,000 |

Calculation of the cells is based on the provided data:

- Smoker and respiratory symptoms: 700

- Smoker and no respiratory symptoms: 400

- Total smokers: 1,100

- Respiratory symptoms: 1,000 respondents in total

- Non-smokers with symptoms: 1,000 - 700 = 300

- Non-smokers without symptoms: 2,600 (given as neither smoked nor had symptoms)

The odds ratio (OR) helps estimate the strength of the association between smoking and respiratory symptoms.

Calculating the Odds Ratio

The odds ratio is calculated as:

OR = (a/c) / (b/d) = (ad) / (bc)

Where:

- a = number of exposed cases (smokers with symptoms) = 700

- b = number of exposed non-cases (smokers without symptoms) = 400

- c = number of unexposed cases (non-smokers with symptoms) = 300

- d = number of unexposed non-cases (non-smokers without symptoms) = 2,600

Plugging in the numbers:

OR = (700 2,600) / (300 400)

OR = (1,820,000) / (120,000)

OR ≈ 15.17

Interpretation:

The odds ratio of approximately 15.17 indicates that individuals who smoke are about 15 times more likely to experience respiratory symptoms than those who do not smoke. This substantial association suggests that smoking is a significant risk factor for respiratory symptoms in this population. While the high OR indicates a strong positive association, causality cannot be definitively established from observational data alone. Nonetheless, these findings support public health efforts to reduce smoking prevalence as a means of lowering respiratory disease incidence.

Conclusion

The calculated odds ratio demonstrates a strong correlation between smoking and respiratory symptoms within this sample. Public health strategies should prioritize smoking cessation initiatives to mitigate respiratory health risks. Further research, ideally through longitudinal studies, could provide more definitive evidence regarding causality and help refine intervention programs.

References

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