Which combination of distribution and link function best models hospitalization probability?

The combination of a binomial distribution and a logit link function is highly appropriate for modeling hospitalization probability, primarily due to the nature of the data involved. Hospitalization probability can be seen as a binary outcome, where the event of interest (hospitalization) can either occur or not occur for a given individual.

Using the binomial distribution allows for modeling this binary outcome effectively since it accounts for the number of successes (hospitalizations) in a series of trials (e.g., patients). The logit link function is particularly suitable because it transforms probabilities (which range from 0 to 1) into the entire real number line, thus allowing for linear relationships between the predictors and the outcome. Specifically, the logit function calculates the logarithm of odds, which is helpful in fitting the model and provides interpretable coefficients associated with risk factors for hospitalization.

This combination also helps in interpreting the effects of covariates in terms of odds ratios, making it valuable for healthcare-related applications such as determining risk factors. Overall, this approach aligns well with statistical practices in epidemiology and risk modeling, where binary outcomes are common.