Composite likelihood for aggregate data from clustered multistate processes under intermittent observation

Markov processes offer a useful basis for modeling the progression of organisms through successive stages of their life cycle. When organisms are examined intermittently in developmental studies, likelihoods can be constructed based on the resulting panel data in terms of transition probability functions. In some settings however, organisms cannot be tracked individually due to a difficulty in identifying distinct individuals, and in such cases aggregate counts of the number of organisms in different stages of development are recorded at successive time points. We consider the setting in which such aggregate counts are available for each of a number of tanks in a developmental study. We develop methods which accommodate clustering of the transition rates within tanks using a marginal modeling approach followed by robust variance estimation, and through use of a random effects model. Composite likelihood is proposed as a basis of inference in both settings. An extension which incorporates mortality is also discussed. The proposed methods are shown to perform well in empirical studies and are applied in an illustrative example on the growth of the Arabidopsis thaliana plant.