Hypothetical Scenario, Case-Control, Odds Ratio Example Problem:
A medical facility’s oncology program reported an increased number of cases of liver cancer during a certain month. In an effort to research the problem, an epidemiologist searched tumor registry records to identify all cases of liver cancer during a ten-year period; cancer patients were matched with patients treated for other diseases during the same ten-year period. All subjects in the study were questioned about lifestyle factors including alcohol, tea, and soda consumption. The resulting data are displayed in the table below. Additional information: there were a total of 150 women cancer patients and a total of 300 women patients with disease other than cancer.
DATA
Cancer Patients Other Patients
Men Women Men Women
LIFESTYLE
VARIABLE
Alcohol 180 119 265 259
Tea Drinking 135 109 225 224
Soda Drinking 185 139 265 239
NOTES:
Total number of women cancer patients = 150
Total number of women patients (other diseases) = 300
The above data may be “simplified,” by ignoring data for “men,” since the specific question refers only to women patients. Then combine “tea” and “soda” into non-exposed group. Then create 2x2 table and calculate Odds Ratio (OR).
Considering the 2X2 table: A=number of exposed w/ disease; B=number of exposed w/out disease; C=number not exposed but w/ disease; D=number w/out disease or exposure.).
Disease
Yes No
Exposure Yes A B
No C D
In this example “exposed” will refer to exposure to (usage of) alcohol
Here’s how you work it out using the “simplified” data set using a 2x2 table (for women patients only):
Cancer
Yes No
Alcohol Yes 119 259
No C D
Total 150 300
You can calculate “C” (cancer patients without alcohol usage)
C=Total cancer patients – Cancer patients with alcohol usage
C=150-119=31 cancer patients without alcohol usage
You can calculate “D” (non-cancer patients without alcohol usage)
D=Total non-cancer patients – non-cancer patients with alcohol usage
D=300 – 259 = 41 non-cancer patients without alcohol usage
Plug “C” and “D” into the 2x2 table and solve for the Odds Ratio (OR).
The final version of the 2x2 table is therefore:
Cancer
Yes No
Alcohol Yes 119 259
No 31 41
Total 150 300
OR = AD/BC = [119 x 41] / [31 x 259] = 4,879/8,029 = 0.61
