DEFINITION OF THE RATE RATIO AND THE ODDS RATIO

Excess disease risk is measured as an absolute effect (Rate Difference or Risk 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.

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 very popular. Its simple computational forms are OR=ad/bc for independent proportions and OR= b/c for paired proportions. For paired proportions b and c refer to the numbers of discordant pairs since the concordant pairs contribute nothing to the contrast.

PROPERTIES OF THE ODDS RATIO:

Definition: The odds ratio is the backbone of analytic epidemiology. The odds ratio is also called the cross products ratio; OR=ad/bc= {åad/ni} / {åbd/ni}. OR values range from 0 to infinity.

Differences between the odds ratio and the risk ratio: 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: (a) 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. (b) The odds ratio has an advantage that it can be computed directly from the regression coefficients of logistic regression. (c) 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: (a) The odds ratio has the disadvantage that it ignores the level ie ratio 1:10 is the same as 10:100. (b) 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. The following show 2 ways of interpreting the magnitude of the odds ratio: According to Richard Monson: OR = 0.9 - 1.0    to   1.0 - 1.2 indicates no association. OR = 0.7 - 0.9    to   1.2 - 1.5 indicates weak association. OR = 0.4 - 0.7    to   1.5 - 3.0 indicates moderate association. OR = 0.1 - 0.4   to    3.0 - 10.0 indicates strong association. OR <0.1 and >10.0 indicates infinite association. According to Greenberg and Ibrahim, OR= 0- 0.3 indicates strong benefit, OR = 0.4-0.5 indicates moderate benefit, OR = 0.6-0.8 indicates weak benefit, OR= 0.9-1.1 indicates no effect, OR = 1.2-1.6 indicates weak hazard, OR = 1.7-2.5 indicates moderate hazard, and OR >2.6 indicates strong hazard

VALIDITY and PRECISION

Measurement in epidemiology: An epidemiological study should be considered as a sort of measurement with parameters for validity, precision, and reliability. Validity is a measure of accuracy. Precision measures variation in the estimate. Reliability is reproducibility.

Internal validity is impaired by study bias. Bias is defined technically as the situation in which the expectation(average) of the parameter is not zero. Bias may move the effect parameter away from the null value or toward the null value. In negative bias the parameter estimate is below the true parameter. In positive bias the parameter estimate is above the true parameter. A study is not valid if it is biased. Systematic errors lead to bias and therefore invalid parameter estimates. Random errors lead to imprecise parameter estimates. Internal validity is concerned with the results of each individual study..

External validity is generalizability of results. Traditionally results are generalized if the sample is representative of the population. In practice generalizability is achieved by looking at results of several studies each of which is individually internally valid. It is therefore not the objective of each individual study to be generalizable because that would require assembling a representative sample. Precision is a measure for lack of random error. An effect measure with a narrow confidence interval is said to be precise. An effect measure with a wide confidence interval in imprecise. Precision is increased in three ways: increasing the study size, increasing study efficiency, and care taken in measurement of variables to decrease mistakes.