Epidemiologists use data from a sample to draw conclusions about the population from which it is drawn. Probability enables epidemiologists to link samples to populations and to draw conclusions about populations from samples.
Sample Risk factors
Population IHD Cancer Osteomalacia DM
Probability of an event will happen under given circumstances may be defined as the proportion of repetition of these circumstances.
Examples The outcome of a tossed coin will be either a head or a tail A thrown die can show one of sic faces
Coin
Head or Tail
die
1 2 3 4 5 6
Random variables
Definition of Frequency definition of probability also applies to continuous measurement e.g. height Example: suppose a median of height of population of women is 168 cm. If we choose at random then in the long run half of the women chosen will have the height of > 168 cm. Then the probability of woman having a height more than 168 cm is 0.5
If 1/10 of women have height greater than 180 cm. What is the probability of choosing at random a woman has a height of > 180 cm?
Properties of probability: 1- Probability lies between 0 to 1. 2- Addition rule. Suppose two event are mutually exclusive i.e. when one happen the other even can not happen. The probability that one or another happen is the sum of their probabilities. Example A thrown die may show 1 or 2 but not both. The probability it shows 1 or 2 is 1/6 + 1/6 = 2/6
Probability distribution and random variables: In tossed coin
X = 0 if the coin shows a tail X = 1 if the coin shows a head X is the number of heads shown in a single toss, which must be 0 or 10
1
Probability
0.5
If we toss two coins at once then there are four possible events: A head and a head = 2 A head and a tail A tail and a head A tail and a tail = 0
= 1
X = 0 When we get two tails X = 1 When we get either a head and a tail or a tail and a head X = 2 when we get two heads
0
1
Probability
0.5
2
0.25
If we toss 15 coins, then
Probability0.3
0.2
5
10
15
Number of heads
The fig. above called Binomial distribution
Binomial distribution is the distribution followed by the number of successes in n independent trials when the probability of any single trial being success is p. The binomial distribution is in fact a family of distributions, the members of which are defined by values of n and p.
Coins and dice have no relevance to medicine but for explaining purposes. Suppose we are carrying out a random sample survey to estimate the unknown prevalence p of a disease. Since members of sample are chosen at random and independently from population. Then the probability of any chosen subject having the disease is p, and number of success i.e. member of sample with disease will follow binomial distribution.
If we measure Blood pressure, then the number classified as hypertensive form binomial distribution If we treat a group of patients, then the number who recovered forms a binomial distribution.
What is the probability that an individual chosen will survive to age 10?
959 / 1000 = 0.959What is the probability that this individual die before age 10? PROB(survive)+ PROB(death) = 1 1- 0.959 = 0.041
What are the probabilities that the individual will survive to ages 10, 20, 30, 40, 50, 60, 70, 80, 90, 100?