Prediction of the next hypercalcemia free period: application of random effect models with selection on first event

The length of repeated hypercalcemia free periods of patients with bone metastasis of breast cancer with at least one hypercalcemic event was modelled according to a generalized linear mixed model formulated in terms of transition probabilities and according to a latent variable model. In the former case the periods were assumed to be lognormally distributed with two variance components (patients and residue). In the latter case the conditional intensity given a patient was assumed to be the intensity of the Weibull distribution, while the random patient effect (frailty) was assumed to be drawn from a gamma distribution. In both cases the selection of only patients with at least one hypercalcemic event was taken into consideration. In both models the variance of the patient effect turned out to be negligible. For the second and later periods the Weibull appeared to fit better than the lognormal model. For the first period there was almost no information available.