The aim of this work is the comparison of the performance of the three popular software platforms JAGS, NIMBLE and Stan. These probabilistic programming languages are able to automatically generate samples from the posterior distribution of interest using MCMC algorithms, starting from the specification of a Bayesian model, i.e. the likelihood and the prior. The final goal is to present a detailed analysis of their strengths and weaknesses to statisticians or applied scientists. In this way, we wish to contribute to make them fully aware of the pros and cons of this software. We carry out a systematic comparison of the three platforms on a wide class of models, prior distributions, and data generating mechanisms. Our extensive simulation studies evaluate the quality of the MCMC chains produced, the efficiency of the software and the goodness of fit of the output. We also consider the efficiency of the parallelization made by the three platforms.

JAGS, NIMBLE, Stan: a detailed comparison among Bayesian MCMC software

A Gaussian copula joint model for longitudinal and time-to-event data with random effects

Many clinical trials generate both longitudinal biomarker and time-to-event data. We might be interested in their relationship, as in the case of tumor size and overall survival in oncology drug development. Many well-established methods exist for analyzing such data either sequentially (two-stage models) or simultaneously (joint models). Two-stage modeling (2stgM) has been challenged (i) for not acknowledging that biomarkers are endogenous covariable to the survival submodel and (ii) for not propagating the uncertainty of the longitudinal biomarker submodel to the survival submodel. On the other hand, joint modeling (JM), which properly circumvents both problems, has been criticized for being time-consuming, and difficult to use in practice. In this paper, we explore a third approach, referred to as a novel two-stage modeling (N2stgM). This strategy reduces the model complexity without compromising the parameter estimate accuracy. The three approaches (2stgM, JM, and N2stgM) are formulated, and a Bayesian framework is considered for their implementation. Both real and simulated data were used to analyze the performance of such approaches. In all scenarios, our proposal estimated the parameters approximately as JM but without being computationally expensive, while 2stgM produced biased results.

Bridging the gap between two-stage and joint models: The case of tumor growth inhibition and overall survival models.

The PAIN-CONTRoLS trial compared four medications in treating Cryptogenic sensory polyneuropathy. The primary outcome was a utility function that combined two outcomes, patients’ pain score reduction and patients’ quit rate. However, additional analysis of the individual outcomes could also be leveraged to inform selecting an optimal medication for future patients. We demonstrate how joint modeling of longitudinal and time-to-event data from PAIN-CONTRoLS can be used to predict the effects of medication in a patient-specific manner and helps to make patient-focused decisions. A joint model was used to evaluate the two outcomes while accounting for the association between the longitudinal process and the time-to-event processes. Results suggested no significant association between the patients’ pain scores and time to the medication quit in the PAIN-CONTRoLS study, but the joint model still provided robust estimates and a better model fit. Using the model estimates, given patients’ baseline characteristics, a drug profile on both the pain reduction and medication time could be obtained for each drug, providing information on how likely they would quit and how much pain reduction they should expect. Our analysis suggested that drugs viable for one patient may not be beneficial for others. 

Using a Bayesian model of the joint distribution of pain and time on medication to decide on pain medication for neuropathy

A bivariate functional copula joint model, which models the repeatedly measured longitudinal outcome at each time point with the survival data, jointly by both random eﬀects and bivariate functional copulas, is proposed in this paper. A regular joint model normally supposes there are some subject-speciﬁc latent random eﬀects or classes shared by the longitudinal and time-to-event processes and they are assumed to be conditionally independent given these latent random variables. Under this assumption, the joint likelihood of the two processes can be easily derived and the association between them, as well as heterogeneity among population are naturally introduced by the unobservable latent random variables. However, because of the unobservable nature of these latent variables, the conditional independence assumption is diﬃcult to verify. Therefore, a bivariate functional copula is introduced into a regular joint model to account for the cases where there could be extra association between the two processes which cannot be captured by the latent random variables. Our proposed model includes a regular joint model as a special case when the correlation function, which is modelled continuously by B-spline basis functions as a function of time t, is constant at 0 under the bivariate Gaussian copula. Simulation studies and dynamic prediction of survival probabilities are conducted to compare the performance of the proposed model with the regular joint model and a real data application on the Primary biliary cirrhosis (PBC) data is performed.

A bivariate functional copula joint model for longitudinal measurements and time-to-event data

Over the last 20 or more years a lot of clinical applications and methodological development in the area of joint models of longitudinal and time-to-event outcomes have come up. In these studies, p...

/pdf/joint-modelling-of-longitudinal-response-and-time-to-event-3f431dfvo2.pdf

Joint modelling of longitudinal response and time-to-event data using conditional distributions: a Bayesian perspective

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Joint modelling of longitudinal response and time-to-event data using conditional distributions: a Bayesian perspective