Maternity length of stay modelling by gamma mixture regression with random effects

Maternity length of stay (LOS) is an important measure of hospital activity, but its empirical distribution is often positively skewed. A two-component gamma mixture regression model has been proposed to analyze the heterogeneous maternity LOS. The problem is that observations collected from the same hospital are often correlated, which can lead to spurious associations and misleading inferences. To account for the inherent correlation, random effects are incorporated within the linear predictors of the two-component gamma mixture regression model. An EM algorithm is developed for the residual maximum quasi-likelihood estimation of the regression coefficients and variance component parameters. The approach enables the correct identification and assessment of risk factors affecting the short-stay and long-stay patient subgroups. In addition, the predicted random effects can provide information on the inter-hospital variations after adjustment for patient characteristics and health provision factors. A simulation study shows that the estimators obtained via the EM algorithm perform well in all the settings considered. Application to a set of maternity LOS data for women having obstetrical delivery with multiple complicating diagnoses is illustrated.