Introduction

The odds ratio is a fundamental statistical method, extensively used in health sciences and particularly in epidemiology. Through it, we express the likelihood that an event will or will not occur, making it a key tool for capturing the relationship between two variables. Unlike simple probability, which measures the proportion of favorable outcomes to total possible outcomes, the odds ratio measures the proportion of probability to its complementary probability. This characteristic makes the index especially useful in analyzing associations and interpreting risk.

Definition and Theoretical Background

Odds are defined as the ratio of the probability of an event occurring (p) to the probability of it not occurring (1-p). The odds ratio compares two such indicators, usually between groups of a population or different levels of an independent variable. Its interpretation is crucial, as it does not directly express probabilities, but relative risk in the form of a ratio.
Odds are considered a “natural” measure in stochastic risk modeling, since they are consistent with Bayes’ theorem and remain time-invariant in statistical models. Their use in logit models, which are based on the logarithmic function of odds, allows for the linear estimation of the relationship between explanatory variables and a binary outcome.

Advantages and Limitations

One of the main advantages of the odds ratio is that it provides a clear measure of relative association, even when the actual probability is difficult to calculate directly. Nevertheless, its use is not free of limitations. The odds ratio is not an absolute number, like probability p, but depends on the given sample and the specification of the statistical model.
Furthermore, its interpretation can be misleading if not applied correctly. For instance, equating the odds ratio directly with the relative risk can lead to errors, especially when the event under study has a high probability of occurrence. Thus, care is required in its reporting and use in scientific studies.

Effect of Complementary Variables

In many epidemiological and social studies, researchers examine how the odds ratio changes when additional explanatory variables are included in the model. These may be potential confounding factors that influence both the dependent and independent variable.
If the additional variables explain part of the variance of the dependent variable, then the odds ratio is modified, providing a more accurate estimate of the relationship. On the other hand, if they offer no explanatory power, then the coefficient r decreases and the odds ratio may increase artificially. This demonstrates that odds ratio estimates are not absolutely stable but sensitive to the selection of variables included in the model.

Comparisons with Alternative Models

Beyond classical logit models, studies have compared the odds ratio with more complex models that progressively incorporate more variables. The purpose of such comparisons is to test the stability and reliability of the estimates. It is often found that even in robust models, the estimated value of the odds ratio differs, confirming the need for careful interpretation and the use of complementary validation methods.

Conclusions

The relative ratio of complementary probabilities is a powerful yet complex statistical tool. Its use in epidemiology and other research fields provides valuable insights into understanding relationships between variables and assessing risks. However, its proper interpretation requires awareness of its limitations, as well as recognition of the influence exerted by confounding factors and modeling choices.
In summary, while the odds ratio offers a more detailed picture of the relative relationship between events, it cannot be considered independent of the statistical context within which it is calculated. The scientific community is thus called upon to use it with a critical approach, in order to derive safe and valid conclusions.