Bayesian inference on the number of recurrent events: A joint model of recurrence and survival.

The number of recurrent events before a terminating event is often of interest. For instance, death terminates an individual's process of rehospitalizations and the number of rehospitalizations is an important indicator of economic cost. We propose a model in which the number of recurrences before termination is a random variable of interest, enabling inference and prediction on it. Then, conditionally on this number, we specify a joint distribution for recurrence and survival. This novel conditional approach induces dependence between recurrence and survival, which is often present, for instance, due to frailty that affects both. Additional dependence between recurrence and survival is introduced by the specification of a joint distribution on their respective frailty terms. Moreover, through the introduction of an autoregressive model, our approach is able to capture the temporal dependence in the recurrent events trajectory. A non-parametric random effects distribution for the frailty terms accommodates population heterogeneity and allows for data-driven clustering of the subjects. A tailored Gibbs sampler involving reversible jump and slice sampling steps implements posterior inference. We illustrate our model on colorectal cancer data, compare its performance with existing approaches and provide appropriate inference on the number of recurrent events.

Bayesian splines versus fractional polynomials in network meta-analysis.

BACKGROUND: Network meta-analysis (NMA) provides a powerful tool for the simultaneous evaluation of multiple treatments by combining evidence from different studies, allowing for direct and indirect comparisons between treatments. In recent years, NMA is becoming increasingly popular in the medical literature and underlying statistical methodologies are evolving both in the frequentist and Bayesian framework. Traditional NMA models are often based on the comparison of two treatment arms per study. These individual studies may measure outcomes at multiple time points that are not necessarily homogeneous across studies. METHODS: In this article we present a Bayesian model based on B-splines for the simultaneous analysis of outcomes across time points, that allows for indirect comparison of treatments across different longitudinal studies. RESULTS: We illustrate the proposed approach in simulations as well as on real data examples available in the literature and compare it with a model based on P-splines and one based on fractional polynomials, showing that our approach is flexible and overcomes the limitations of the latter. CONCLUSIONS: The proposed approach is computationally efficient and able to accommodate a large class of temporal treatment effect patterns, allowing for direct and indirect comparisons of widely varying shapes of longitudinal profiles.

Bayesian Autoregressive Frailty Models for Inference in Recurrent Events.

We propose autoregressive Bayesian semi-parametric models for gap times between recurrent events. The aim is two-fold: inference on the effect of possibly time-varying covariates on the gap times and clustering of individuals based on the time trajectory of the recurrent event. Time-dependency between gap times is taken into account through the specification of an autoregressive component for the frailty parameters influencing the response at different times. The order of the autoregression may be assumed unknown and is an object of inference. We consider two alternative approaches to perform model selection under this scenario. Covariates may be easily included in the regression framework and censoring and missing data are easily accounted for. As the proposed methodologies lie within the class of Dirichlet process mixtures, posterior inference can be performed through efficient MCMC algorithms. We illustrate the approach through simulations and medical applications involving recurrent hospitalizations of cancer patients and successive urinary tract infections.

A comparative review of network meta-analysis models in longitudinal randomized controlled trial.

Network meta-analysis (NMA) technique extends the standard meta-analysis methods, allowing pairwise comparison of all treatments in a network in the absence of head-to-head comparisons. Traditional NMA models consider a single endpoint for each trial. However, in many cases, trials in the network have different durations and/or report data at multiple time points. Moreover, these time points are often not the same for all trials. In this work, we review the most relevant methods that incorporate multiple time points and allow indirect comparisons of treatment effects across different longitudinal studies. In particular, we focus on the mixed treatment comparison developed by Dakin et al,[10] on the Bayesian evidence synthesis techniques-integrated two-component prediction developed by Ding et al,[11] and on the more recent method based on fractional polynomials by Jansen et al.[12] We highlight the main features of each model and illustrate them in simulations and in a real data application. Our study shows that methods based on fractional polynomials offer a flexible modeling strategy in most applications.