MEASURE OF EXCESS DISEASE RISK: THE ODDS RATIO AND THE RATE RATIO

Lecture for Year 2 Semester 1 medical student PPSD session on 12^th September 2007 by Professor Omar Hasan Kasule Sr.

Excess disease risk is measured as an absolute effect (Rate Difference) or a relative effect (Odds Ratio and Rate Ratio). Other terms with meaning similar to rate ratio are relative risk and risk ratio  

The following 2x2 contingency table shows the lay-out of data that can be used to define OR and RR.

	Disease +	Disease -		Time
Exposure +	a	B	a + b	T+
Exposure -	c	D	c + d	T-
	a + c	b + d	N	T

The Odds ratio is as OR = ad/bc by reference to the 2 x 2 contingency table above.

The Rate Ratio is defined as RR = (a/T+) / (a/T-)

A ratio of 1.0 is called the null value and is interpreted to mean that there is no relation between the disease and the exposure.

A ratio above 1.0 means that the exposure increases the risk of disease

A ratio below 1.0 means that the exposure protects from the disease.

The OR and RR are often not very different numerically. The OR is used for case control studies and the RR is used for follow-up studies. The odds ratio is unlike RR in 3 ways: OR can be combined over several strata, OR can be inverted for example if OR for death is 2 the OR for survival is 0.5, and OR is amenable to further mathematical manipulations.

Advantages of the odds ratio

The Odds has a great advantage that it is invariable across case control, follow-up, and cross-sectional studies and thus it can be used to directly compare findings of different study designs.

The odds ratio has an advantage that it can be computed directly from the regression coefficients of logistic regression.

The odds ratio is a good estimator of risk ratio if the disease is rare and the cases and controls are randomly selected from the population.

Disadvantages of the odds ratio

The odds ratio has the disadvantage that it ignores the level ie ratio 1:10 is the same as 10:100.

OR is good for establishing causal relations but is not that useful to the public health practitioner who is interested in knowing how much decrease in disease burden will be achieved by specific interventions. RD is a better measure than OR for such public health purposes.

Interpretation of the odds ratio

A high OR indicates that there is no confounding or minimal confounding.