Holst, Kromhout, and Brand conducted a case-control study to determine if keeping birds increased the chances of getting lung cancer.20 It is believed that people who keep birds may inhale more allergens and dust particles and thus may be more likely to get lung cancer. They collected data on 49 people with lung cancer and 98 people with similar demographics who did not have lung cancer.
Gender: 1 represents females
Status: 1 represents high economic status
Age: owner’s age
Smoked: number of years the person has been smoking
Cigarettes: number of cigarettes smoked per day
Bird: 1 represents owning a bird
LungCancer: 1 represents having lung cancer
The first five variables (Gender, Status, Age, Smoked, and Cigarettes) are known to impact the likelihood of having lung cancer and are assumed to be important in modeling the likelihood of having lung cancer. We are primarily interested in determining if the odds of lung cancer change based on whether an individual is a bird keeper.
a. Create a logistic regression model using all six explanatory variables to estimate the probability of having lung cancer. Based on Wald’s test, which variables appear to be significant? Based on the likelihood ratio test, can we conclude that at least one of these terms is significant?
b. Create a logistic regression model using the first five variables (Gender, Status, Age, Smoked, and Cigarettes) to estimate the probability of having lung cancer.
c. Use the drop-in-deviance test to compare the models in Parts A and B. Can you conclude that birdkeeping is related to the probability of having lung cancer?
d. Construct a model using only the variable Bird to estimate the probability of having lung cancer. What do Wald’s test and the likelihood ratio test reveal?
e. Explain why the drop-in-deviance test in Part C is better than the approach in Part D for determining if birdkeeping is related to the probability of having lung cancer.