Estimating and interpolating a Markov chain from aggregate data

Given aggregated longitudinal data generated by a Markov chain, which may be non-homogeneous, the problem considered is that of modelling, estimating and interpolating the logarithms of partial odds and hence the transition probabilities. By partial odds is meant the probability of a transition to another state divided by the probability of no transition. A result establishing asymptotic normality leads to vector weighted least squares estimation of parameterised partial odds using standard regression methods. It is shown how to obtain estimates of one-step transition probabilities from widely or irregularly spaced data. The methods are illustrated on an example concerning competing causes of death.