Repository logo

Two-part models with stochastic processes for modelling longitudinal semicontinuous data: Computationally efficient inference and modelling the overall marginal mean

Published version



Change log


Yiu, S 
Tom, BD 


Several researchers have described two-part models with patient-specific stochastic processes for analysing longitudinal semicontinuous data. In theory, such models can offer greater flexibility than the standard two-part model with patient-specific random effects. However, in practice, the high dimensional integrations involved in the marginal likelihood (i.e. integrated over the stochastic processes) significantly complicates model fitting. Thus, non-standard computationally intensive procedures based on simulating the marginal likelihood have so far only been proposed. In this paper, we describe an efficient method of implementation by demonstrating how the high dimensional integrations involved in the marginal likelihood can be computed efficiently. Specifically, by using a property of the multivariate normal distribution and the standard marginal cumulative distribution function identity, we transform the marginal likelihood so that the high dimensional integrations are contained in the cumulative distribution function of a multivariate normal distribution, which can then be efficiently evaluated. Hence, maximum likelihood estimation can be used to obtain parameter estimates and asymptotic standard errors (from the observed information matrix) of model parameters. We describe our proposed efficient implementation procedure for the standard two-part model parameterisation and when it is of interest to directly model the overall marginal mean. The methodology is applied on a psoriatic arthritis data set concerning functional disability.



semicontinuous data, two-part models, overall marginal mean, patient-specific inference, serial correlation, psoriatic arthritis

Journal Title

Statistical Methods in Medical Research

Conference Name

Journal ISSN


Volume Title


SAGE Publications
MRC (unknown)
This work was financially supported by the UK Medical Research Council [Unit program numbers U105261167 and MC_UP_1302/3].