Risk factors explained_v01

Risk Factors Explained

E. Kaldoudi, DUTH

Sep 2016

risk factors relate to the effect an exposure may have to a person’s health

exposure (good or bad)

healthy person outcome



exposure can be a drug or an intervention but it can also be any other factor affecting the person, either from the environment (e.g. air pollution) or from the person’s physical state or health (e.g. age, pregnancy, obesity, diabetes, etc.)

outcome




the outcome can be any effect on health, positive or negative

outcome




example:

what is the risk of having heart failure in those who are overweight ?

outcome

the outcome can be any effect on health, positive or negative

the outcome of the exposure sometimes happens, sometimes not

thus, risks are reported as a likelihood of an outcome to happen in the presence of an exposure


important: an increased likelihood that a certain exposure leads to a certain outcome does not necessarily imply causation!!!

outcomeoutcome

measures of likelihood of an event to appear in a group

– probability

– hazard

– odds

measures of relative likelihood between two different groups, usually one which is exposed (study group) vs a group of normal population (control group)

– relative risk or relative ratio (RR)

– hazard ratio (HR)

– odds ratio (OR)

Probability an event occurs is the number of events in a population divided by the total population

example: in a group of 100 people, 5 people experience an event (orange) and the remaining 95 do not (black)

=


0≤𝑝 ≤1Probability is always a number between 0 and 1

The bigger the number, the more probable is the event …

𝑝=5100=0.05

60


Probability can easily be expressed as a percentage

𝑝=5100=0.05𝑚𝑒𝑎𝑛𝑠5% 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑝=

60100=0.60𝑚𝑒𝑎𝑛𝑠60% 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦

Odds an event to occur is the ratio of the probability an event to occur to the probability an event does not occur

=

example: in a group of 100 people, 5 people experience an event (orange) and the remaining 95 do not (black)

odds are always higher than probability (unless probability is 100%)

probability odds

same numerator

denominator in the odds is always less than the denominator in the probability, (as it is the whole population minus the numerator)

whole population whole population minus the numerator

odds can be misleading ….

probability odds

Examples of risks (given as fractions or percentages) and their corresponding odds (given as fractions)

If the event is rare, then probability and odds are almost equal

For example, if the event occurs once every 100 persons, then

𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦=𝑝=𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑣𝑒𝑛𝑡𝑠𝑡𝑜𝑡𝑎𝑙𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 =0.01

𝑜𝑑𝑑𝑠= 𝑝1−𝑝=

0.010.99=0.010101≈0.01=𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 (𝑟𝑎𝑟𝑒𝑒𝑣𝑒𝑛𝑡)

If the event is common, then probability and odds are different

For example, if the event occurs 60 times for every 100 persons, then

60

𝑜𝑑𝑑𝑠= 𝑝1−𝑝=

0.600.40=1.5≠𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 (𝑐𝑜𝑚𝑚𝑜𝑛𝑒𝑣𝑒𝑛𝑡 )

comparing two groups

outcome


outcome

reference (or normal) group population without the exposure

exposure (or study) group population with the exposure

Relative Risk or Risk Ratio (RR) is the ratio of the probability the event occurs in a study population (exposed to a risk factor) to the probability the event occurs in the normal population:

Expresses how many times more (or less likely) an ‘exposed’ person will experience an event compared to an unexposed person.

RR = 1 means no difference in risks RR > 1 means increased risk in the study groupRR < 1 means decreased risk in the study group

when relative risk is of value RR, then we can say that

if in the normal population n persons experience an event,

in the exposed population nxRR persons will experience the event

example, RR=3.8

then in the exposed population the persons who experience the event are 3.8 times the persons who experience the event in the normal population

normal population

patient group

RR=3.8 means that:

if 1 person in the reference

group presents the outcome,

then in the exposed

population the persons who

experience the event are 3.8

times the persons who

experience the event in the

reference population

Hazard is an instantaneous event rate

Hazard is the probability of an event at a given moment in time

h𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑖𝑜=𝐻 𝑅=h𝑎𝑧𝑎𝑟𝑑𝑝𝑎𝑡𝑖𝑒𝑛𝑡

h𝑎𝑧𝑎𝑟𝑑𝑛𝑜𝑟𝑚𝑎𝑙=𝑝𝑝𝑎𝑡𝑖𝑒𝑛𝑡 (𝑎𝑡 𝑡𝑖𝑚𝑒𝑡)𝑝𝑛𝑜𝑟𝑚𝑎𝑙 (𝑎𝑡 𝑡𝑖𝑚𝑒𝑡)

Hazard ratio can be interpreted as relative risk ratio at any given time – but technically, it is not!


exposed group

Odds ratio compares the odds an event to occur amongst two different groups

𝑜𝑑𝑑𝑠𝑟𝑎𝑡𝑖𝑜=𝑂𝑅=𝑜𝑑𝑑𝑠𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑜𝑑𝑑𝑠𝑛𝑜𝑟𝑚𝑎𝑙

=

𝑝𝑝𝑎𝑡𝑖𝑒𝑛𝑡

1−𝑝𝑝𝑎𝑡𝑖𝑒𝑛𝑡

𝑝𝑛𝑜𝑟𝑚𝑎𝑙

1−𝑝𝑛𝑜𝑟𝑚𝑎𝑙

=𝑝𝑝𝑎𝑡𝑖𝑒𝑛𝑡 (1−𝑝𝑛𝑜𝑟𝑚𝑎𝑙)𝑝𝑛𝑜𝑟𝑚𝑎𝑙 (1−𝑝𝑝𝑎𝑡𝑖𝑒𝑛𝑡 )


exposed group


For example,

suppose 1 out of every 100 normal persons get hospitalized every year (

while

7 out of every 100 patients with a certain disease get hospitalized every year (


exposed group



exposed group

𝑜𝑑𝑑𝑠𝑟𝑎𝑡𝑖𝑜=𝑂𝑅=𝑝𝑒𝑥𝑝 (1−𝑝𝑛𝑜𝑟𝑚𝑎𝑙)𝑝𝑟𝑒𝑓 (1−𝑝𝑝𝑎𝑡𝑖𝑒𝑛𝑡)

= 0.07×0.990.01×0.93

=7.45𝑏𝑢𝑡 𝑅𝑅=𝑝𝑒𝑥𝑝

𝑝𝑟𝑒𝑓=0.070.01

=7

transforming odds ratio (OR) into relative risk (RR)

is the probability of the outcome in the reference group (without exposure)

is the probability of the outcome in the reference group (without exposure)

𝑅𝑅=𝑂𝑅1−𝑝𝑒𝑥𝑝

1−𝑝𝑟𝑒𝑓= 𝑂𝑅

(1−𝑝𝑟𝑒𝑓 )+𝑂𝑅×𝑝𝑟𝑒𝑓

when the outcome is rare, then RR OR

e.g. =1% and

when the outcome is common, then RR < OR, RR is only a fraction of OR

e.g. =25% and then

bigger differences between exposed & reference groups, more pronounced differences RR << OR

e.g. =10% and then

Suppose that there is a OR odds ratio that a particular patient group experiences an event as compared to normal population –

How to visualize this in terms of groups of 100 persons?

Suppose you have 100 persons in the reference group and n of them present the outcome

if you have 100 persons in the exposed group,

then of them will have the condition.

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97100

0

20

40

60

80

100

120

Series1 Series2

Series3 Series4

Series5 Series6

Series7

OR = 1OR = 1.1OR = 1.5OR = 2

OR = 5OR = 20

number of persons with the outcome in the reference group

number of persons with the outcome in the exposed group

odds ratio OR = 1.44 means that if you are in group 2 it is likely to be of orange color

group 1 – normal population, some people may present the outcome, in this example 5 out of 100 (n=5)

group 2 – patients of a certain condition, some people may present the outcome – the relative risk is 1.44 as compared to the normal population

outcome = 7.05

outcome = 5

rare outcome – visualizing OR

odds ratio OR = 1.44 means that if you are in group 2 it is likely to be of orange color

group 1 – group 1 – normal population, some people may become orange, in this example 60 out of 100 (n=60)

group 2 – patients of a certain condition, some people may get orange – the odds ratio is 1.44 as compared to the normal population

68.6 orange

60 orange

common outcome – visualizing OR



outcome = 5

outcome = 5 X 1.44 = 7.2 for RR=1.44

outcome = = 7.05 for OR=1.44

rare outcome – RR and OR are comparable



outcome = 60 X 1.44 = 86.4 for RR=1.44

outcome = = 68.6, for OR=1.44

outcome = 60

common outcome – RR and OR are NOT comparable

Presentations & Public Speaking

Risk factors explained_v01