Abstract
Random effects or shared parameter models are commonly advocated for the analysis of combined repeated measurement and event history data, including dropout from longitudinal trials. Their use in practical applications has generally been limited by computational cost and complexity, meaning that only simple special cases can be fitted by using readily available software. We propose a new approach that exploits recent distributional results for the extended skew normal family to allow exact likelihood inference for a flexible class of random-effects models. The method uses a discretization of the timescale for the time-to-event outcome, which is often unavoidable in any case when events correspond to dropout. We place no restriction on the times at which repeated measurements are made. An analysis of repeated lung function measurements in a cystic fibrosis cohort is used to illustrate the method.
Highlights
There is a close relationship between modelling longitudinal data subject to dropout and modelling survival time data in the presence of imprecisely observed time varying covariates
Henderson et al (2000) argued that when follow-up is relatively long it is unreasonable to assume a sustained trend in the trajectory of Y and advocated inclusion of an unobserved stationary Gaussian process W.t/ in a linear predictor for Y to bring more flexibility. In principle this assumes the presence of an infinite dimensional random effect but, under either a discrete dropout or a semiparametric proportional hazards model for S, likelihood inference requires the value of W.t/ at only measurement times or event times
We shall make use of results concerning the properties of the skew normal distribution (Azzalini, 1985, 2005; Arnold and Beaver, 2000; Arnold, 2009) to obtain a closed form for the likelihood
Summary
There is a close relationship between modelling longitudinal data subject to dropout and modelling survival time data in the presence of imprecisely observed time varying covariates. Henderson et al (2000) argued that when follow-up is relatively long it is unreasonable to assume a sustained trend in the trajectory of Y and advocated inclusion of an unobserved stationary Gaussian process W.t/ in a linear predictor for Y to bring more flexibility In principle this assumes the presence of an infinite dimensional random effect but, under either a discrete dropout or a semiparametric proportional hazards model for S, likelihood inference requires the value of W.t/ at only measurement times or event times. For the most general model we define W.s/ = B.s/U to be a p-vector of linear combinations of the random effects U, where B.s/ is a p × p matrix which may depend on the time interval s.
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