Penalized estimation in latent Markov models, with application to monitoring serum calcium levels in end-stage kidney insufficiency

We introduce a penalized likelihood form for latent Markov models. We motivate its use for biomedical applications where the sample size is in the order of the tens, or at most hundreds, and there are only few repeated measures. The resulting estimates never break down, while spurious solutions are often obtained by maximizing the likelihood itself. We discuss model choice based on the Takeuchi Information Criterion. Simulations and a real-data application to monitoring serum Calcium levels in end-stage kidney disease are used for illustration.