Generalised linear models for correlated pseudo-observations, with applications to multi-state models

In multi-state models regression analysis typically involves the modelling of each transition intensity separately.Each probability of interest, namely the probability that a subject will be in a given state at some time, is a complex nonlinear function of the intensity regression coefficients. We present a technique which models the state probabilities directly. This method is based on the pseudo-values from a jackknife statistic constructed from simple summary statistic estimates of the state probabilities. These pseudo-values are then used in a generalised estimating equation to obtain estimates of the model parameters. We illustrate how this technique works by studying examples of common regression problems. We apply the technique to model acute graft-versus-host disease in bone marrow transplants.