Title: Two-part models with stochastic processes for modelling longitudinal semicontinuous data: computationally efficient inference and modelling the overall marginal mean,
Abstract: 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.