Many diagnostic tests are based on statistical models that predict the probability that a given subject will be positive for that test. Although the ROC curve evaluates the overall performance of the test, the choice of the probability threshold to differentiate between positives and negatives will condition the performance of the test in a given clinical scenario.

The binomial distribution is used when we want to calculate the probability of obtaining a certain number of successes in a series of Bernoulli trials, assuming we already know the probability of success in each trial. In contrast, the beta distribution is used in the opposite situation: we have observed a given number of successes and failures, and we want to estimate how likely each possible value of the success probability is. In other words, it allows us to update our beliefs about that probability based on the data we have collected.

Binary logistic regression uses the sigmoid function to estimate the probability of the target variable when it is binary. However, this function does not allow direct probability estimates when dealing with nominal variables with more than two categories. In these cases, we will use multinomial logistic regression, which will use the softmax function to estimate the probabilities with respect to a reference category.

The tau-squared represents the variability of effects between the different populations from which the primary studies of a systematic review are derived, according to the assumption of the random effects model of meta-analysis. Its usefulness for weighting studies and for calculating prediction intervals is described, understanding how its significance goes beyond being a mere indicator of heterogeneity.