Data in Table 2.1 was used to examine the association between smoking and cancer in a hypothetical cohort study in the general population. Assume no misclassification or confounding.

Table 2.1 - "True" association

Community Population

	Smoker
Cancer	Yes	No	Total
Yes	400	200	600
No	100,000	200,000	300,000
Total	100,400	200,200	300,600

a) Calculate the most appropriate effect estimate (and 95% CI) for the "Truth" and interpret.

Bias may be caused when patients with two disease conditions or high-risk behaviors are more likely to be hospitalized than those with a single condition. In hospital-based studies, these patients will tend to be over-represented in the study population compared to the community population.

Cigarette smoking is strongly associated with several cancers. In a hospital-based case control study we would expect a relationship between cigarette smoking and almost any cancer to demonstrate a stronger relationship (bias away from null) than would exist in a community.

Suppose of the 600 cases, 300 are selected for the case control study from several hospitals and 225 of the 300 selected cases are smokers. Assume there are 300 controls randomly selected as a 0.10% sample of all non-cases from the community. Assume no bias or random error in choosing these controls.

b) Complete Table 2.2.

Table 2.2 - Data for hospital-based case-control study

Study Sample

	Smoker
Cancer	Yes	No	Total
Cases			300
Controls			300
Total			600

c) Calculate the most appropriate effect estimate 95% CI for hospital study and interpret.

d) Calculate the bias parameters, selection probabilities, for the case-control study?

a = b =

d = g =

e) Is there selection bias? Why? - explain in terms of bias parameters

f) Calculate the magnitude and state the direction of the bias

In the previous study we sampled the cases from the hospital - controls from the community. We can also choose hospitalized controls. Data in Table 2.3 is similar to the study above for cases (Table 2.2), but now 300 hospitalized total controls were selected as controls equally by exposure status.

g) Complete Table 2.3

Table 2.3 - hospital controls

	Smoker
Cancer	Yes	No	Total
Yes			300
No			300
Total			600

h) Calculate the most appropriate effect estimate 95% CI for hospital study and interpret.

i) Are selected controls in Table 2.3 representative of the controls from the community? Why or why not?

j) What are the selection probabilities for the hospital-based case control study.

a = b =

d = g =

k) Given the bias parameters, briefly describe two recommendations to the investigator to minimize selection bias in a similar hospital-based case control study in the future.