A transition model for ordinal response data with random dropout: an application to the fluvoxamine data

A Markov random field model with cumulative logistic functions for spatially dependent ordinal data

This paper presents a class of regression models with cumulative logistic functions that are chiefly designed to analyse spatially dependent ordinal data. In contrast to previous works, the proposed model requires neither the sites to be regularly spaced nor the assumption of an underlying continuous variable. It belongs to a more general class of Markov random field models, and can be considered an extension of the ordinal regression model with the proportional odds link function. Our proposed model allows practitioners to interpret the model parameters using odds ratios. Apart from the theoretical developments, this work also highlights the practical aspects of model fitting, including parameterisation, selection of neighbourhood, and calculation of standard errors. Simulation studies with regularly and irregularly spaced sites were conducted. Modelling strategies including pseudo-likelihood methods were found to be useful in both settings. The proposed model and the non-spatial counterpart were applied to the daily air quality index measured in the United Kingdom. The results indicate the presence of spatial effects and the incorporation of spatial effects led to better model performance in terms of various goodness-of-fit measures.

Bayesian sample size determination for longitudinal studies with continuous response based on different scientific questions of interest

Longitudinal study designs are commonly applied in much scientific research, especially in the medical, social, and economic sciences. Longitudinal studies allow researchers to measure changes in each individual's responses over time and often have higher statistical power than cross-sectional studies. Choosing an appropriate sample size is a crucial step in a successful study. In longitudinal studies, because of the complexity of their design, including the selection of the number of individuals and the number of repeated measurements, sample size determination is less studied. This paper uses a simulation-based method to determine the sample size from a Bayesian perspective. For this purpose, several Bayesian criteria for sample size determination are used, of which the most important one is the Bayesian power criterion. We determine the sample size of a longitudinal study based on the scientific question of interest, by the choice of an appropriate model. Most of the methods of determining sample size are based on the definition of a single hypothesis. In this paper, in addition to using this method, we determine the sample size using multiple hypotheses. Using several examples, the proposed Bayesian methods are illustrated and discussed.

Assessing type I error and power of multistate Markov models for panel data-A simulation study

Ordinal outcomes collected at multiple follow-up visits are common in clinical trials. Sometimes, one visit is chosen for the primary analysis and the scale is dichotomized amounting to loss of information. Multistate Markov models describe how a process moves between states over time. Here, simulation studies are performed to investigate the type I error and power characteristics of multistate Markov models for panel data with limited non-adjacent state transitions. The results suggest that the multistate Markov models preserve the type I error and adequate power is achieved with modest sample sizes for panel data with limited non-adjacent state transitions.