Formulas, Algorithms and Examples for Binomial Distributed Data Confidence Interval Calculation: Excess Risk, Relative Risk and Odds Ratio

Odds Ratio, Hazard Ratio and Relative Risk

Odds ratio (OR) is a statistic commonly encountered in professional or scientific medical literature. Most readers perceive it as relative risk (RR), although most of them do not know why that would be true. But since such perception is mostly correct, there is nothing (or almost nothing) wrong with that. It is nevertheless useful to be reminded now and then what is the relation between the rel...

Relative Risk and Odds Ratios Examples

Understanding the odds ratio and the relative risk.

Both the odds ratio and the relative risk compare the relative likelihood of an event occurring between two groups. The relative risk is easier to interpret and is consistent with general intuition. Some designs, however, allow only for the calculation of the odds ration. Covariate adjustment is easier for an odds ratio. Finally, the odds ratio avoids ambiguity by being invariant to lthe labeli...

Confidence Intervals for the Risk Ratio Using Double Sampling with Misclassified Binomial Data

We derive three likelihood-based confidence intervals for the risk ratio of two proportion parameters using a double sampling scheme for misclassified binomial data. The risk ratio is also known as the relative risk. We obtain closed-form maximum likelihood estimators of the model parameters by maximizing the full-likelihood function. Moreover, we develop three confidence intervals: a naive Wal...

Relative Risk, Odds Ratio, Attributable Risk and Number Needed to Treat

The research may or may not be epidemiological but there is a high likelihood that it would use the epidemiological indices discussed in this note. Rate, risk, hazard, incidence, and prevalence are everyday indices of disease occurrence that are used in a large number of research endeavours. Although these indices apparently look simple but many researchers are not fully comfortable in their us...