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.     

Quantifying multiple pressure interactions affecting populations of a recreationally and commercially important freshwater fish

The expanding human global footprint and growing demand for freshwater have placed tremendous stress on inland aquatic ecosystems. Aichi Target 10 of the Convention on Biological Diversity aims to minimize anthropogenic pressures affecting vulnerable ecosystems, and pressure interactions are increasingly being incorporated into environmental management and climate change adaptation strategies. In this study, we explore how climate change, overfishing, forest disturbance, and invasive species pressures interact to affect inland lake walleye (Sander vitreus) populations. Walleye support subsistence, recreational, and commercial fisheries and are one of most sought‐after freshwater fish species in North America. Using data from 444 lakes situated across an area of 475 000 km² in Ontario, Canada, we apply a novel statistical tool, R‐INLA, to determine how walleye biomass deficit (carrying capacity—observed biomass) is impacted by multiple pressures. Individually, angling activity and the presence of invasive zebra mussels (Dreissena polymorpha) were positively related to biomass deficits. In combination, zebra mussel presence interacted negatively and antagonistically with angling activity and percentage decrease in watershed mature forest cover. Velocity of climate change in growing degree days above 5°C and decrease in mature forest cover interacted to negatively affect walleye populations. Our study demonstrates how multiple pressure evaluations can be conducted for hundreds of populations to identify influential pressures and vulnerable ecosystems. Understanding pressure interactions is necessary to guide management and climate change adaptation strategies, and achieve global biodiversity targets.     

Temporal variability in the way local habitat affects duck population growth

Climate change is expected to lead to greater temporal climatic variability across broad spatial extents. A potential consequence is that shifts in climatic conditions might alter how local habitat affects the population growth of animals dependent on those habitats for at least part of their life cycle. We tested whether such a phenomenon occurred when the North American Prairie Pothole Region transitioned through periods of wet and dry conditions by modeling the population growth of seven duck species over 52 years (1961–2012). We found that the influence of local habitat quality—indexed by wetland availability—on duck population growth varied in magnitude and direction on an annual basis. While the effect of wetlands was relatively small in most years, there were some years in which wetlands strongly affected duck population growth in both positive and negative directions (e.g., negative in 2002 and positive in 2008). Contrary to our expectation, inter-annual variability in the effect of wetlands on duck population growth did not depend on regional precipitation. We also found that for two species—American Wigeon (Anas americana) and Green-winged Teal (A. carolinensis)—duck population growth in the presence of wetlands rarely differed from what would be expected solely under density dependence. Our study is the first to demonstrate that the effect of local habitat on population growth varies over time even if the cause of that variation remains unexplained. Consequently, any study that attempts to identify a species’ critical habitat using time series abundance data must consider that local relationships are non-stationary. More complicated measures of climate change may reveal how local drivers of population growth depend on broader temporal climatic patterns.     

Bayesian outbreak detection algorithm for monitoring reported cases of campylobacteriosis in Germany

In infectious disease epidemiology, statistical methods are an indispensable component for the automated detection of outbreaks in routinely collected surveillance data. So far, methodology in this area has been largely of frequentist nature and has increasingly been taking inspiration from statistical process control. The present work is concerned with strengthening Bayesian thinking in this field. We extend the widely used approach of Farrington et al. and Heisterkamp et al. to a modern Bayesian framework within a time series decomposition context. This approach facilitates a direct calculation of the decision‐making threshold while taking all sources of uncertainty in both prediction and estimation into account. More importantly, with the methodology it is now also possible to integrate covariate processes, e.g. weather influence, into the outbreak detection. Model inference is performed using fast and efficient integrated nested Laplace approximations, enabling the use of this method in routine surveillance at public health institutions. Performance of the algorithm was investigated by comparing simulations with existing methods as well as by analysing the time series of notified campylobacteriosis cases in Germany for the years 2002–2011, which include absolute humidity as a covariate process. Altogether, a flexible and modern surveillance algorithm is presented with an implementation available through the R package ‘surveillance’.     

tigaR: integrative significance analysis of temporal differential gene expression induced by genomic abnormalities

Background

To determine which changes in the host cell genome are crucial for cervical carcinogenesis, a longitudinal in vitro model system of HPV-transformed keratinocytes was profiled in a genome-wide manner. Four cell lines affected with either HPV16 or HPV18 were assayed at 8 sequential time points for gene expression (mRNA) and gene copy number (DNA) using high-resolution microarrays. Available methods for temporal differential expression analysis are not designed for integrative genomic studies.

Results

Here, we present a method that allows for the identification of differential gene expression associated with DNA copy number changes over time. The temporal variation in gene expression is described by a generalized linear mixed model employing low-rank thin-plate splines. Model parameters are estimated with an empirical Bayes procedure, which exploits integrated nested Laplace approximation for fast computation. Iteratively, posteriors of hyperparameters and model parameters are estimated. The empirical Bayes procedure shrinks multiple dispersion-related parameters. Shrinkage leads to more stable estimates of the model parameters, better control of false positives and improvement of reproducibility. In addition, to make estimates of the DNA copy number more stable, model parameters are also estimated in a multivariate way using triplets of features, imposing a spatial prior for the copy number effect.

Conclusion

With the proposed method for analysis of time-course multilevel molecular data, more profound insight may be gained through the identification of temporal differential expression induced by DNA copy number abnormalities. In particular, in the analysis of an integrative oncogenomics study with a time-course set-up our method finds genes previously reported to be involved in cervical carcinogenesis. Furthermore, the proposed method yields improvements in sensitivity, specificity and reproducibility compared to existing methods. Finally, the proposed method is able to handle count (RNAseq) data from time course experiments as is shown on a real data set.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-327) contains supplementary material, which is available to authorized users.     

Incorporating capture heterogeneity in the estimation of autoregressive coefficients of animal population dynamics using capture–recapture data

Population dynamic models combine density dependence and environmental effects. Ignoring sampling uncertainty might lead to biased estimation of the strength of density dependence. This is typically addressed using state‐space model approaches, which integrate sampling error and population process estimates. Such models seldom include an explicit link between the sampling procedures and the true abundance, which is common in capture–recapture settings. However, many of the models proposed to estimate abundance in the presence of capture heterogeneity lead to incomplete likelihood functions and cannot be straightforwardly included in state‐space models. We assessed the importance of estimating sampling error explicitly by taking an intermediate approach between ignoring uncertainty in abundance estimates and fully specified state‐space models for density‐dependence estimation based on autoregressive processes. First, we estimated individual capture probabilities based on a heterogeneity model for a closed population, using a conditional multinomial likelihood, followed by a Horvitz–Thompson estimate for abundance. Second, we estimated coefficients of autoregressive models for the log abundance. Inference was performed using the methodology of integrated nested Laplace approximation (INLA). We performed an extensive simulation study to compare our approach with estimates disregarding capture history information, and using R‐package VGAM, for different parameter specifications. The methods were then applied to a real data set of gray‐sided voles Myodes rufocanus from Northern Norway. We found that density‐dependence estimation was improved when explicitly modeling sampling error in scenarios with low process variances, in which differences in coverage reached up to 8% in estimating the coefficients of the autoregressive processes. In this case, the bias also increased assuming a Poisson distribution in the observational model. For high process variances, the differences between methods were small and it appeared less important to model heterogeneity.     

Assessing the impact of a movement network on the spatiotemporal spread of infectious diseases

Summary Linking information on a movement network with space-time data on disease incidence is one of the key challenges in infectious disease epidemiology. In this article, we propose and compare two statistical frameworks for this purpose, namely, parameter-driven (PD) and observation-driven (OD) models. Bayesian inference in PD models is done using integrated nested Laplace approximations, while OD models can be easily fitted with existing software using maximum likelihood. The predictive performance of both formulations is assessed using proper scoring rules. As a case study, the impact of cattle trade on the spatiotemporal spread of Coxiellosis in Swiss cows, 2004-2009, is finally investigated.