Transcript ******* 1 - muhadharaty.com

ThiQar college of Medicine
Family & Community medicine dept.
Biostatistics L- propability
Third stage
by: Dr. Muslim N. Saeed
December 29th,2016
‫كل عام وأنتم بخير‬
‫أطيب األماني بمناسبة‬
‫السنة الجديدة‬
Objectives
1- Define the probability.
2- Explain the applications of probability in
medical sciences.
3- Describe types of probability.
Introduction
Why should we understand probability?
Is probability essential for physician?
-Example 1: Genetic Counseling: A couple has a baby
with a genetic defect. They are considering having
another baby. What is the likelihood that the second child
will have a genetic defect also?
-Example 2: Prognosis; A physician is considering several
therapies for the treatment of a patient. Which therapy
should be used? Each therapy produces a result that is
somewhere between success and failure. The final choice
is “weighed the probability” against the others.
Example 3: Is a food additive carcinogenic? An
investigator explores this in an experiment that compares
two groups. Some of the treated individuals develop
cancer and only few of the controls develop cancer.. Is the
excess number of cancers meaningful (higher probability
than control)?
Example 4: Smoking and Cancer: Lung cancer occurs
commonly in smoker but only sometimes in non smokers.
Probability of other factors related to a variable outcome.
Probabilities are a tool in decision making, and the key
to understand inferential statistics
-Example 5: The data below shows the finding of a
survey. Is living near electricity transmission
equipment associated with occurrence of cancer?
Cancer
Not
Near
200
1646
11%
Not
50
7289
1%
Among those living near electricity equipment, 11%
have cancer. Among those living elsewhere, only
1% have cancer. Is this a meaningful difference?
- The difference (if significant) in this example is
reflected for population and called inference
-Probability is the bridge between Descriptive
Statistics and Inferential Statistics.
Probability Definition:
It is the likelihood of occurrence of a certain
event compared to the total events.
no. of times E occur
P(E)= ----------------------------------------no. of times E can occur
*P(E) probability of occurrence of event E
The concept of probability is frequently
encountered in every day communication of
health workers, we may here the physician say
that a patient has 50-50 chance of surviving,
or a patient 95% has the disease.
-The value of probability = 0 – 1
-No negative value in probability.
-Probability (E) = 0 means event is impossible
-Probability (E) = 1 means event is sure
sometimes proportion and probability are used
interchangeably.
Example: the probability of serum cholesterol
level between 180 and 210(mg/100 ml) is the
proportion of people in a certain target
population having their cholesterol levels
falling between 180 and 210 (mg/100 ml).
Element of probability
1) Total probability value must be between 1 &
zero (0 ≤ P≤1), no negative value.
P = 0 → Not occur. P = 1→ should occur.
P = 0.5→ 50% will occur & 50% will not occur.
2) The sum of the probabilities of mutually
exclusive (can't occur simultaneously)
outcome is equal to one.(black or white, male
or female, blood group A or B or AB or O)
In other word :
The sum of the probabilities (or relative
frequencies) of all event that can occur in the
sample must be 1 (or 100%).
Ex. In a sample of 50 people, 21 had blood group O, 22
had blood group A, 5 had type B, and 2 had blood
group AB
p(O)= 0.42
p(A)= 0.44
p(B)= 0.1
p(AB)= 0.04
p(neither A nor O)= 0.14
p(not AB)= 1 - 0.04= 0.96
There are 3 types of probability:
1) Classical Probability:
Assume that all outcomes in the sample space are equally
likely to occur. One does not actually have to perform the
experiment to determine the probability.
Ex: When a single die is rolled, each outcome has the
same probability of occurring Since there are 6 outcomes,
each outcome has a probability of 1/6.
2) Empirical Probability (Relative frequency):
Depend on actual experience to determine the
likelihood of outcomes
Ex: In a study, we have the following table for
serum cholesterol of 1047 male patients aged
40-59 year.
-The probability to get
individuals with serum
cholesterol of 820-319 is
145 / 1047 = 13.7%
Probability to get those
below 200 is (31 +134)/
1047 = 15.8 %
So we can express
probability in terms of
relative frequency or
cumulative relative
frequency.
3) Subjective (personalistic) Probability:
Based on person’s experience and evaluation of the
situation But does not rely on the repeatability of any
process.
A physician might say that on the basis of his diagnosis,
there is a 30% chance that the patient will need an
operation.
If a doctor says “you have a 50% chance of recovery,”
the doctor believes that half of similar cases will recover
in the long run.
Presumably, this is based on knowledge, and not on a
whim. The benefit of stating subjective probabilities is
that they can be tested and modified according to
experience.
Joint probability:
It is the probability that the events (2 or more, E1,
E2 ..etc) can occur simultaneously. We have the
following 2 rules:
1) Multiplication rule (And, ∩, both).
a) Independent events (E1 not affected by E2).
-Two events are statistically independent if the
chances, or likelihood, of one event is in no way
related to the likelihood of the other event.
Individual is male with red hair.
EX: Event A = “a woman is hypertensive”
Event B = “her husband (not relative) is hypertensive”.
The assumption of independence seems reasonable since
the two persons are not genetically related. If the
probability of being hypertensive is 0.07 for woman and
0.09 for man, then the probability that BOTH the woman
and her husband are hypertensive is:
P(A and B) = P(A) x P(B) = 0.07 x 0.09 = 0.0063
Ex: The probability that an individual belonging
to blood group A is 0.42, and the individual
being a football player is 0.50. What is the
probability of the individual both belonging to
blood group A & being football player?
Since the events are independent → P (E1∩E2) =
P (E1) x P (E2) = 0.42 x 0.50 = 0.21
b) Dependent events (E1 affected by E2).
EX: Probability of being male 1s 0.5, and that
that male being bold is 0,05. What is the
probability of both being male and bold?
Since the events are dependent→ P (E1∩E2) =
P(E2) x P(E1 / E2) =0.5 x 0.05/0.5= 0.005
EX: the chance that person has Huntington ’s chorea is
0.0002 (if the parent does not have Huntington’s Chorea).
An offspring of a person with Huntington’s Chorea has a
50% chance of contracting Huntington’s Chorea
(offspring with chorea giving that his father had chorea).
Probability 2 persons have Huntington’s Chorea =
P(A and B) = 0.0002 X 0.0002= 0.00000008
Probability both parent and child have Huntington’s
Chorea = P(A) P(B|A) = 0.0002 x 0.5 = 0.0001
Conditional probability: Probability of an event
occurring (E1) giving that the other event (E2)
has already occur.
Ex: Using the information of table
below:
Calculate:
1- The probability of selection
person dis. +ve & test +ve.
2- The probability of selection
person dis. -ve & test -ve.
As the variables are dependent, so
P (E1∩E2) = P (E2)x P(E1 / E2)
1- P (dis. +ve & test +ve.) = 11/100
x 7/11 = 7/100
2- P (dis. -ve & test -ve.) = 90/100 x
86/90 = 86/100
2) Additional rule. (Or, U, either)
a) Mutually exclusive events (can't occur
together).
Two events are mutually exclusive if they cannot
occur at the same time.
EX: if a baby has a 0·04% chance of being
homozygous for the sickle cell gene and a 3·92%
chance of being a heterozygote, then the
probability that it carries the gene either as a
homozygote or as a heterozygote is 0·04 + 3·92 =
3·96%.
Ex: The probability that an individual belonging
to blood group A is 0.4 and the individual
belonging to blood group B is 0.3. What is the
probability of the individual belonging to
blood group A or B?
As the variables are mutually exclusive events
(can't occur together), so:
P (E1UE2) = P (E1) +P (E2) = 0.4 +0.3 = 0.7
b) Not mutually exclusive events (can occur together).
Ex: Using the information of table above, calculate the
probability of selection person dis. -ve or test -ve.
As the variables are not mutually exclusive events (can
occur together), so:
P (E1UE2) = P (E1) +P (E2)-P (E1 and E2) =
{90\100+89\100 } – 86\100 = 0.93
EX: From table, what is
the probability to have
a person that is CT scan
–ve or CXR negative?
= 0.90+0.89-0.86
=0.93=93%
Mutually & non-mutually exclusive