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1.  Dirichlet negative multinomial regression for overdispersed correlated count data 
Biostatistics (Oxford, England)  2012;14(2):395-404.
A generic random effects formulation for the Dirichlet negative multinomial distribution is developed together with a convenient regression parameterization. A simulation study indicates that, even when somewhat misspecified, regression models based on the Dirichlet negative multinomial distribution have smaller median absolute error than generalized estimating equations, with a particularly pronounced improvement when correlation between observations in a cluster is high. Estimation of explanatory variable effects and sources of variation is illustrated for a study of clinical trial recruitment.
PMCID: PMC3590929  PMID: 23221819
Dirichlet negative multinomial; Longitudinal count data; Regression; Sources of variation
2.  A multistate model for events defined by prolonged observation 
Biostatistics (Oxford, England)  2010;12(1):102-111.
Time-to-event and similar analyses can be problematic if the event of interest is operationally defined by some condition being true for a prolonged period of time. A particular example of this, remission in psoriatic arthritis, is considered in detail for illustration. A 3-state model is proposed for characterizing the transition rates into and out of remission. Remission is linked to an initial and subsequent state for the purpose of introducing the condition that remission must be of some duration to be clinically meaningful. The model is compared with alternative approaches that have been used in such situations. These involve 2-state models where the duration of remission is allowed for through different definitions for the time of entry into remission. Both definitions are linked to prolonged observation of a particular clinical state.
PMCID: PMC3006122  PMID: 20581216
Misclassification; Multistate models; Time to remission
3.  Bias in 2-part mixed models for longitudinal semicontinuous data 
Biostatistics (Oxford, England)  2009;10(2):374-389.
Semicontinuous data in the form of a mixture of zeros and continuously distributed positive values frequently arise in biomedical research. Two-part mixed models with correlated random effects are an attractive approach to characterize the complex structure of longitudinal semicontinuous data. In practice, however, an independence assumption about random effects in these models may often be made for convenience and computational feasibility. In this article, we show that bias can be induced for regression coefficients when random effects are truly correlated but misspecified as independent in a 2-part mixed model. Paralleling work on bias under nonignorable missingness within a shared parameter model, we derive and investigate the asymptotic bias in selected settings for misspecified 2-part mixed models. The performance of these models in practice is further evaluated using Monte Carlo simulations. Additionally, the potential bias is investigated when artificial zeros, due to left censoring from some detection or measuring limit, are incorporated. To illustrate, we fit different 2-part mixed models to the data from the University of Toronto Psoriatic Arthritis Clinic, the aim being to examine whether there are differential effects of disease activity and damage on physical functioning as measured by the health assessment questionnaire scores over the course of psoriatic arthritis. Some practical issues on variance component estimation revealed through this data analysis are considered.
PMCID: PMC2648907  PMID: 19136448
Correlated random effects; Excess zeros; Outcome-dependent sampling; Repeated measures

Results 1-3 (3)