Professor Malcolm Faddy, Queensland University of Technology, Australia
Analysing hospital length of stay data: models that fit, models that don’t and does it matter?

Hospital length of stay data typically show a distribution with a mode near zero and a long right tail, and can be hard to model adequately. Traditional models include the gamma and log-normal distributions, both with a quadratic variance-mean relationship. Phase-type distributions which describe the length of time to absorption of a Markov chain with a single absorbing state also have a quadratic variance-mean relationship. Covariates of interest include an estimate of the length of stay for an uncomplicated admission, with excess length of stay modelled relative to this quantity either multiplicatively or additively. A number of different models can therefore be constructed, and the results of fitting these models will be discussed in terms of goodness of fit, significance of covariate effects and estimation of quantities of interest to health economists.