Question

Researchers recruited 200 70 year-old former factory workers who had been diagnosed with lung cancer, and an additional 200 70 yr. old former factory workers who were screened and found to be free of lung cancer. The study participants were asked about their smoking history during the past 50 years. Among those with lung cancer, 127 were smokers. Among those without lung cancer, 35 were smokers.

What is the study design?

What is the timing?

Using the data above, construct a 2 x 2 table. Identify and calculate the approapriate measures of frequency and association. Interpret your findings.

Answer 1

Study Design:

Answer:

Case-control study

Explanation:

Since we are observing the data over a period of time and not intervening or changing the individuals who participated in the study, this is a type of observational study. There are types of observational studies;

1) cohort studies, 2) case-control studies, and 3) cross-sectional studies.

In a case-control study, we select the cases with and without the disease outcome and study the past exposure and then draw a conclusion based on exposure. In this context the researcher receruited the former factory workers based on on their health status and studied their past exposure to the smoking.

Timing

Answer:

Retrospective study.

Explanation:

In this scenario, the researcher studies the past events (smoking habits) based on present exposure status (lung cancer), this is a retrospective study.

Measures of frequency and association

The Chi-square test of independence is performed to test whether the exposure status and smoking habits are associated.

Hypothesis:

Null hypothesis: The variables exposure status and smoking habits are independent

Alternative hypothesis: The variables exposure status and smoking habits are dependent

Critical value

The critical value for the chi-square statistic is obtained from the chi-square distribution table for the degree of freedom = (r-1)(c-1) = (2-1)(1-1)= for significance level = 0.05. The critical value is,

Test statistic

The observed values are,

.	Smoker	Non-smoker	Total
Cancer	127	73	200
Without cancer	35	165	200
Total	162	238	400

The expected values are obtained using the formula,

.	Smoker	Non-smoker	Total
Cancer	200*162/400=81	200*238/400=119	200
Without cancer	200*162/400=81	200*238/400=119	200
Total	162	238	400

The Chi-Square value is obtained using the formula

Conclusion:

Since the chi-square value is greater than the critical value, the null hypothesis is rejected at a 5% significance level.

Hence there is sufficient evidence to conclude that the variables exposure status and the smoking habits are dependent.