What is Probability?
With regard to health outcomes probability is the proportion or percentage of events that occur in a group of people, i.e., the number of health outcomes or "events" divided by the total number of possible events.
Probabilities can be expressed as:
- A proportion from 0 to 1, e.g., 0.32 or
- A percentage, e.g., 0.32=32%
Example:
In the Physicians' Health Study on aspirin, male physicians were randomly assigned to take an aspirin or a placebo every other day.
| MI |
No MI |
Total |
Probability |
|
|
Aspirin |
126 |
10,911 |
11,037 |
126/11,037 = 0.0114= 1.14% |
|
Placebo |
213 |
10,821 |
11,034 |
213/11,034 = 0.0193= 1.93% |
Test Yourself
Consider the data in the table below from the New York City Cancer Registry
(Selected data from http://www.health.state.ny.us/statistics/cancer/registry/about.htm)
|
Cancer Type |
White Male |
White Female |
Black Male |
Black Female |
Total |
|
Colorectal |
1,236 |
1,251 |
449 |
584 |
3,520 |
|
Liver |
330 |
134 |
149 |
57 |
670 |
|
Lung |
1,449 |
1,332 |
537 |
497 |
3,815 |
|
Thyroid |
175 |
537 |
29 |
135 |
876 |
|
Non-Hodgkins |
582 |
523 |
170 |
159 |
1,434 |
|
Leukemia |
348 |
285 |
87 |
85 |
805 |
|
TOTALS |
4,120 |
4,062 |
1,421 |
1,517 |
11,120 |
What is the:
- Probability that a cancer patient is a black male? [P(Black male)]
- Probability that a cancer patient has thyroid cancer? [P(thyroid cancer)]
- Probability that a cancer patient is a white female with liver cancer? [P(White female with liver cancer)]
- Probability that a cancer patient is a black with lung cancer? [P(Black patient with lung cancer)]
Work these out yourself before looking at the answers.
Conditional Probability
Conditional probability is the probability of an event occurring, given that another condition is true or another event has occurred.
Example: What proportion of patients with colorectal cancer are white?
Another way of stating this question is "Given that a patient has colorectal cancer, what is the probability that the patient is white?
The notation for this is P(white | colorectal cancer), where the "|" signals the condition. In this case, P(white | colorectal cancer) = (1236 + 1251)/3520 = 0.7065 = 71%.
Test Yourself
Using the data in the table above:
- What proportion of patients with leukemia are white?
- What proportion of women have lung cancer?
Work these out yourself before looking at the answers.
