Odd’s Ratio

(188)      6

REF: Park 20^th edition page 69

Odds ratio = (30 x 40)/ (20 x 10)

=6

Relative risk REF: Park 20^th edition page 69

ODDS RATIO (CROSS PRODUCT RATIO):

From a case control study, we can derive what is known as Odds ratio which is a measure of the strength of the association between risk factors and outcomes. Odds ratio is closely related to relative risk.

Risk B has the strongest association [Ref: http://www.thedoctorsdoctorcom/labtests/statistics.htm

• Odds ratio is a measure of the strength of the association between risk factor and the outcome.
• It is used to assess the risk of a particular outcome (or disease) if a certain factor (or exposure) is present. The odds ratio is a relative measure of risk, telling us how much more likely it is that someone who is exposed to the factor under study will develop the outcome as compared to someone who is not exposed.
• Odds ratio is the ratio of the odds that a case was exposed to the odds that a control was exposed.

Odds ratio = 

= 

• It can vary from 0 to infinity.
• For example: The data in the table below is information about infant birth weights and mortality among white infants in New York City in 1974.

The odds ratio for death in one year is

OR= 

This odds ratio illustrates that mortality is far more likely in the low birth weight group

Internreating Odd’s Ratios

• In order to interperate the odds ratio we need to calculate a confidence interval.
• We can say that a proposed risk factor acts as a significant risk to disease if the odds ratio is greater than one and the lower bound of the confidence interval does not include 1.
• Confidence interval

The 95% confidence interval (or 95% confidence limits) would include 95% of results from studies of the same size and design in the same population. This is close but not identical to saying that the true size of the effect (never exactly known) has a 95% chance of falling within the confidence interval. If the 95% confidence interval for a relative risk (RR) or an odds ratio (OR) includes 1, then this is taken as no evidence of an effect. The practical advantages of a confidence interval (rather than a P value) is that they present the range of likely effects.

• An odds ratio of 1 indicates that a person with the disease is no more likely to have been exposed to the risk factor than is a person without the disease, suggesting that the risk factor is not related to the disease. An odds ratio of 1 implies that the event is equally likely in both groups.
• An odds ratio of less than 1 indicates that a person with the disease is less likely to have been exposed to the risk factor than is a person without the disease, implying that the proposed risk factor may actually be a protective factor against the disease.
• An odds ratio of more than 1 indicates that the person with disease is more likely to have been exposed to the risk factor than a person without the disease, meaning there is association between the disease and the risk factor.

5

Relative risk

Using case control study only odds ratio can be calculated.

Incidence rates, relative risk and attributable risk can be calculated using cohort study. Case control study is inexpensive, easy to carry out, used to investigate rare diseases, used to identify risk factors, allows study of different etiological factors and is associated with minimal ethical problems.

Reference:
Parks Textbook of Preventive And Social Medicine 20th edition, page 70.

Odds ratio=  a×d/b×c  = 33×27/55×2= 8.1

Ans. is ‘a’ i.e., Odds ratio estimation 

o Final step in case control study is analysis to find out ‑

i)    Exposure rates among cases and controls to suspected factor.

ii)  Estimation of disease risk associated with exposure (odds ratio).

i)         Exposure rates

o A case control study provides a direct estimation of the exposure rates (frequency of exposure) to a suspected factor.

ii)         Odds – ratio (cross product ratio)

o From a case control study odds ratio can be derived which a measure of the strength of association between risk factor and outcome.

o Odds ratio is closely related to relative risk (which is analysed in cohort study) —> odds ratio represents only an estimate of relative risk.

o The odds ratio is cross product of entries in above table

o Odds ratio is a key parameter in analysis of case control studies.

Why is it not possible to estimate relative risk in case-control study ‑

o Relative risk is the ratio between the incidence of disease among exposed and incidence among non-exposed. o So, for relative risk estimation, incidence rate is required.

o But incidence rate can not be calculated by case control study as there is no denominator (poulation at risk).

o Because both disease and exposure have already occured, there is no risk for the subjects in the study —> There is no population at risk.

Ans. is ‘a’ i.e., 8

o Odds ratio is cross product of entries in the table.

o So, it is very important to make a correct table construct –

i)    History of exposure (risk factor) is arranged on left column (row).

ii)  Disease is arranged on the top ‑

a)       Cases in middle column (row)

b)      Controls in right column (row)

Ans. is ‘b’ i.e., Relative risk can be calculated 

Relative risk can not be calculated (Has been explained -4 see previous explanations).

o We can calculate “an estimate of relative risk”, known as “odds ratio (cross product ratio)”. Case control study

ADVANTAGES

1. Relatively easy to carry out.
2. Rapid and inexpensive (compared with cohort studies).
3. Require comparatively few subjects.
4. Particularly suitable to investigate rare diseases or diseases about which little is known.
5. No risk to subjects
6. Allows the study of several different aetiological factors (e.g., smoking, physical activity and personality characteristic in myocardial infarction).
7. Risk factors can he identified. Rational prevention and control programmes can be established.
8. No attrition problems, because case control studies do not require follow-up of individuals into the future.
9. Ethical problems minimal.

DISADVANTAGES

1. Problems of bias relies on memory or past records, the accuracy of which may be uncertain; validation of information obtained is difficult or sometimes impossible.
2. Selection of an appropriate control group may be difficult.
3. We cannot measure incidence, and can only estimate the relative risk (odds ratio).
4. Do not distinguish between causes and associated factors.
5. Not suited to the evaluation of therapy or prophylaxis of diseas,:.
6. Another major concern is the representativeness of cases and controls

Ans. is ‘a’ i.e., Relative risk 

o Both relative risk and odds ratio are measures of strength of association between risk factor and outcome.

           Relative risk is estimated in cohort study

           Odds ratio is measured in case-control study

“Case control study generally yields only estimate of relative risk, i.e. odds ratio”

Ans. is ‘b’ i.e., Odds ratio can be calculated 

Ans. is ‘a’ i.e., Only odd’s ratio 

Ans. is ‘d’ i.e., Odds ratio

Ans. is ‘b’ i.e., 1 : 3 

Odds

        It is another measure for the occurence of a outcome or event.

        It is the chance of frequency of occurrence of a characteristic relative to its non-occurrence, i.e., it is the ratio of occurrence.

Odds Vs probability

        The probability is a proportion, i.e., it is the number of times a given outcome occurs divided by all the occurrences. If we take a sample of blood from a patient five times, and the sample is positive one time, then the probability is 1 in 5 or 0.20.

        On the other hand, the odds is a ratio, i.e., it is the number of times a given outcome occurs divided by the number of times that specific outcome does not occur. With same blood sample example, the odds of a positive sample is = No. of positive slide/No of negative slide = 1/4.

Example

        If the probability of occurence of a cancer is 0.25 (25%).

In otherword the nonoccurence of cancer will be = 1 – 0.25 = 0.75 (75%).

Ans. is ‘c’ i.e., 7^.5

Odds ratio is cross product of entries in the table.

So, it is very important to make a correct table construct ‑

i) History of exposure (risk factor) is arranged on left column (row).

ii) Disease is arranged on the top ‑

a) Cases in middle column (row)

b) Controls in right column (row)

Ans. is ‘d’ i.e., ad/bc

Odds – ratio (cross product ratio)

• From a case control study odds ratio can be derived which a measure of the strength of association between risk factor and outcome.
• Odds ratio is closely related to relative risk (which is analysed in cohort study) → odds ratio represents only an estimate of relative risk.