Bayesian estimation of two-part joint models for a longitudinal semicontinuous biomarker and a terminal event with INLA: Interests for cancer clinical trial evaluation.

Two-part joint models for a longitudinal semicontinuous biomarker and a terminal event have been recently introduced based on frequentist estimation. The biomarker distribution is decomposed into a probability of positive value and the expected value among positive values. Shared random effects can represent the association structure between the biomarker and the terminal event. The computational burden increases compared to standard joint models with a single regression model for the biomarker. In this context, the frequentist estimation implemented in the R package frailtypack can be challenging for complex models (i.e., a large number of parameters and dimension of the random effects). As an alternative, we propose a Bayesian estimation of two-part joint models based on the Integrated Nested Laplace Approximation (INLA) algorithm to alleviate the computational burden and fit more complex models. Our simulation studies confirm that INLA provides accurate approximation of posterior estimates and to reduced computation time and variability of estimates compared to frailtypack in the situations considered. We contrast the Bayesian and frequentist approaches in the analysis of two randomized cancer clinical trials (GERCOR and PRIME studies), where INLA has a reduced variability for the association between the biomarker and the risk of event. Moreover, the Bayesian approach was able to characterize subgroups of patients associated with different responses to treatment in the PRIME study. Our study suggests that the Bayesian approach using the INLA algorithm enables to fit complex joint models that might be of interest in a wide range of clinical applications.

Discrete versus continuous domain models for disease mapping.

The main goal of disease mapping is to estimate disease risk and identify high-risk areas. Such analyses are hampered by the limited geographical resolution of the available data. Typically the available data are counts per spatial unit and the common approach is the Besag-York-Mollié (BYM) model. When precise geocodes are available, it is more natural to use Log-Gaussian Cox processes (LGCPs). In a simulation study mimicking childhood leukaemia incidence using actual residential locations of all children in the canton of Zürich, Switzerland, we compare the ability of these models to recover risk surfaces and identify high-risk areas. We then apply both approaches to actual data on childhood leukaemia incidence in the canton of Zürich during 1985-2015. We found that LGCPs outperform BYM models in almost all scenarios considered. Our findings suggest that there are important gains to be made from the use of LGCPs in spatial epidemiology.

Estimating multilevel regional variation in excess mortality of cancer patients using integrated nested Laplace approximation.

Models of excess mortality with random effects were used to estimate regional variation in relative or net survival of cancer patients. Statistical inference for these models based on the Markov chain Monte Carlo (MCMC) methods is computationally intensive and, therefore, not feasible for routine analyses of cancer register data. This study assessed the performance of the integrated nested Laplace approximation (INLA) in monitoring regional variation in cancer survival. Poisson regression model of excess mortality including both spatially correlated and unstructured random effects was fitted to the data of patients diagnosed with ovarian and breast cancer in Finland during 1955-2014 with follow up from 1960 through 2014 by using the period approach with five-year calendar time windows. We estimated standard deviations associated with variation (i) between hospital districts and (ii) between municipalities within hospital districts. Posterior estimates based on the INLA approach were compared to those based on the MCMC simulation. The estimates of the variation parameters were similar between the two approaches. Variation within hospital districts dominated in the total variation between municipalities. In 2000-2014, the proportion of the average variation within hospital districts was 68% (95% posterior interval: 35%-93%) and 82% (60%-98%) out of the total variation in ovarian and breast cancer, respectively. In the estimation of regional variation, the INLA approach was accurate, fast, and easy to implement by using the R-INLA package.

A note on intrinsic conditional autoregressive models for disconnected graphs.

In this note we discuss (Gaussian) intrinsic conditional autoregressive (CAR) models for disconnected graphs, with the aim of providing practical guidelines for how these models should be defined, scaled and implemented. We show how these suggestions can be implemented in two examples, on disease mapping.

Bayesian bivariate meta-analysis of diagnostic test studies with interpretable priors.

In a bivariate meta-analysis, the number of diagnostic studies involved is often very low so that frequentist methods may result in problems. Using Bayesian inference is particularly attractive as informative priors that add a small amount of information can stabilise the analysis without overwhelming the data. However, Bayesian analysis is often computationally demanding and the selection of the prior for the covariance matrix of the bivariate structure is crucial with little data. The integrated nested Laplace approximations method provides an efficient solution to the computational issues by avoiding any sampling, but the important question of priors remain. We explore the penalised complexity (PC) prior framework for specifying informative priors for the variance parameters and the correlation parameter. PC priors facilitate model interpretation and hyperparameter specification as expert knowledge can be incorporated intuitively. We conduct a simulation study to compare the properties and behaviour of differently defined PC priors to currently used priors in the field. The simulation study shows that the PC prior seems beneficial for the variance parameters. The use of PC priors for the correlation parameter results in more precise estimates when specified in a sensible neighbourhood around the truth. To investigate the usage of PC priors in practice, we reanalyse a meta-analysis using the telomerase marker for the diagnosis of bladder cancer and compare the results with those obtained by other commonly used modelling approaches. Copyright © 2017 John Wiley & Sons, Ltd.

Bayesian inference for generalized linear mixed models.

Generalized linear mixed models (GLMMs) continue to grow in popularity due to their ability to directly acknowledge multiple levels of dependency and model different data types. For small sample sizes especially, likelihood-based inference can be unreliable with variance components being particularly difficult to estimate. A Bayesian approach is appealing but has been hampered by the lack of a fast implementation, and the difficulty in specifying prior distributions with variance components again being particularly problematic. Here, we briefly review previous approaches to computation in Bayesian implementations of GLMMs and illustrate in detail, the use of integrated nested Laplace approximations in this context. We consider a number of examples, carefully specifying prior distributions on meaningful quantities in each case. The examples cover a wide range of data types including those requiring smoothing over time and a relatively complicated spline model for which we examine our prior specification in terms of the implied degrees of freedom. We conclude that Bayesian inference is now practically feasible for GLMMs and provides an attractive alternative to likelihood-based approaches such as penalized quasi-likelihood. As with likelihood-based approaches, great care is required in the analysis of clustered binary data since approximation strategies may be less accurate for such data.

Towards joint disease mapping.

This article discusses and extends statistical models to jointly analyse the spatial variation of rates of several diseases with common risk factors. We start with a review of methods for separate analyses of diseases, then move to ecological regression approaches, where the rates from one of the diseases enter as surrogate covariates for exposure. Finally, we propose a general framework for jointly modelling the variation of two or more diseases, some of which share latent spatial fields, but with possibly different risk gradients. In our application, we consider mortality data on oral, oesophagus, larynx and lung cancers for males in Germany, which all share smoking as a common risk factor. Furthermore, the first three cancers are also known to be related to excessive alcohol consumption. An empirical comparison of the different models based on a formal model criterion as well as on the posterior precision of the relative risk estimates strongly suggests that the joint modelling approach is a useful and valuable extension over individual analyses.

Effects of mRNA amplification on gene expression ratios in cDNA experiments estimated by analysis of variance.

BACKGROUND: A limiting factor of cDNA microarray technology is the need for a substantial amount of RNA per labeling reaction. Thus, 20-200 micro-grams total RNA or 0.5-2 micro-grams poly (A) RNA is typically required for monitoring gene expression. In addition, gene expression profiles from large, heterogeneous cell populations provide complex patterns from which biological data for the target cells may be difficult to extract. In this study, we chose to investigate a widely used mRNA amplification protocol that allows gene expression studies to be performed on samples with limited starting material. We present a quantitative study of the variation and noise present in our data set obtained from experiments with either amplified or non-amplified material. RESULTS: Using analysis of variance (ANOVA) and multiple hypothesis testing, we estimated the impact of amplification on the preservation of gene expression ratios. Both methods showed that the gene expression ratios were not completely preserved between amplified and non-amplified material. We also compared the expression ratios between the two cell lines for the amplified material with expression ratios between the two cell lines for the non-amplified material for each gene. With the aid of multiple t-testing with a false discovery rate of 5%, we found that 10% of the genes investigated showed significantly different expression ratios. CONCLUSION: Although the ratios were not fully preserved, amplification may prove to be extremely useful with respect to characterizing low expressing genes.