Linking fast and slow: The case for generative models

A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable longer, more naturalistic neuronal recordings. The implicit opportunity for understanding the self-organised brain calls for new analysis methods that link temporal scales: from the order of milliseconds over which neuronal dynamics evolve, to the order of minutes, days, or even years over which experimental observations unfold. This review article demonstrates how hierarchical generative models and Bayesian inference help to characterise neuronal activity across different time scales. Crucially, these methods go beyond describing statistical associations among observations and enable inference about underlying mechanisms. We offer an overview of fundamental concepts in state-space modeling and suggest a taxonomy for these methods. Additionally, we introduce key mathematical principles that underscore a separation of temporal scales, such as the slaving principle, and review Bayesian methods that are being used to test hypotheses about the brain with multiscale data. We hope that this review will serve as a useful primer for experimental and computational neuroscientists on the state of the art and current directions of travel in the complex systems modelling literature.

Should I use fixed effects or random effects when I have fewer than five levels of a grouping factor in a mixed-effects model?

As linear mixed-effects models (LMMs) have become a widespread tool in ecology, the need to guide the use of such tools is increasingly important. One common guideline is that one needs at least five levels of the grouping variable associated with a random effect. Having so few levels makes the estimation of the variance of random effects terms (such as ecological sites, individuals, or populations) difficult, but it need not muddy one's ability to estimate fixed effects terms-which are often of primary interest in ecology. Here, I simulate datasets and fit simple models to show that having few random effects levels does not strongly influence the parameter estimates or uncertainty around those estimates for fixed effects terms-at least in the case presented here. Instead, the coverage probability of fixed effects estimates is sample size dependent. LMMs including low-level random effects terms may come at the expense of increased singular fits, but this did not appear to influence coverage probability or RMSE, except in low sample size (N = 30) scenarios. Thus, it may be acceptable to use fewer than five levels of random effects if one is not interested in making inferences about the random effects terms (i.e. when they are 'nuisance' parameters used to group non-independent data), but further work is needed to explore alternative scenarios. Given the widespread accessibility of LMMs in ecology and evolution, future simulation studies and further assessments of these statistical methods are necessary to understand the consequences both of violating and of routinely following simple guidelines.

How does interspecific competition modify the response of grass plants against herbicide treatment? A hierarchical concentration-response approach

Ecological interactions are rarely taken into account in environmental risk assessment. The objective of this work was to assess how interspecific competition affects the way plant species react to herbicides and more specifically how it modifies the concentration-response curves that can be built using ecotoxicological bioassays. To do this, we relied on the results of ecotoxicological bioassays on six herbaceous species exposed to isoproturon under two conditions: in presence and in absence of a competitor. At the end of the experiments, eleven endpoints were measured. We modelled these data using a hierarchical modelling framework designed to assess the effects of competition on each of the four parameters of the concentration response curves (e.g. the level of response at the control or the concentration at the inflection point of the curve) simultaneously for the six species. The modelled effects could be of three types, 1) competition had no effect on the parameter, 2) competition had the same effect on the parameter for all species and 3) competition had a different effect on the parameter for each species. Our main hypothesis was that different species would react differently to competition. Results showed that about a half of the estimated parameters showed a modification under competition pressure among which only a fourth showed a species-specific effect, the three other fourth showing the same effect between the different species. Our initial hypothesis was thus not supported as species tended to react in the same way to competition. The competition effect on plants was mainly negative, thus showing that they were more affected by isoproturon under competition pressure. This study therefore establishes how competition modifies plant responses to chemical stress and how this interaction varies from one species to the other.

Bayesian statistics in the design and analysis of cluster randomised controlled trials and their reporting quality: a methodological systematic review

BACKGROUND

In a cluster randomised controlled trial (CRCT), randomisation units are "clusters" such as schools or GP practices. This has methodological implications for study design and statistical analysis, since clustering often leads to correlation between observations which, if not accounted for, can lead to spurious conclusions of efficacy/effectiveness. Bayesian methodology offers a flexible, intuitive framework to deal with such issues, but its use within CRCT design and analysis appears limited. This review aims to explore and quantify the use of Bayesian methodology in the design and analysis of CRCTs, and appraise the quality of reporting against CONSORT guidelines.

METHODS

We sought to identify all reported/published CRCTs that incorporated Bayesian methodology and papers reporting development of new Bayesian methodology in this context, without restriction on publication date or location. We searched Medline and Embase and the Cochrane Central Register of Controlled Trials (CENTRAL). Reporting quality metrics according to the CONSORT extension for CRCTs were collected, as well as demographic data, type and nature of Bayesian methodology used, journal endorsement of CONSORT guidelines, and statistician involvement.

RESULTS

Twenty-seven publications were included, six from an additional hand search. Eleven (40.7%) were reports of CRCT results: seven (25.9%) were primary results papers and four (14.8%) reported secondary results. Thirteen papers (48.1%) reported Bayesian methodological developments, the remaining three (11.1%) compared different methods. Four (57.1%) of the primary results papers described the method of sample size calculation; none clearly accounted for clustering. Six (85.7%) clearly accounted for clustering in the analysis. All results papers reported use of Bayesian methods in the analysis but none in the design or sample size calculation.

CONCLUSIONS

The popularity of the CRCT design has increased rapidly in the last twenty years but this has not been mirrored by an uptake of Bayesian methodology in this context. Of studies using Bayesian methodology, there were some differences in reporting quality compared to CRCTs in general, but this study provided insufficient data to draw firm conclusions. There is an opportunity to further develop Bayesian methodology for the design and analysis of CRCTs in order to expand the accessibility, availability, and, ultimately, use of this approach.

Different statistical techniques dealing with confounding in observational research: measuring the effect of breast-conserving therapy and mastectomy on survival

PURPOSE

Propensity trimming, hierarchical modelling and instrumental variable (IV) analysis are statistical techniques dealing with confounding, cluster-related variation or confounding by severity. This study aimed to explain (dis)advantages of these techniques in estimating the effect of breast-conserving therapy (BCT) and mastectomy on 10-year distant metastasis-free survival (DMFS).

METHODS

All women diagnosed in 2005 with primary T1-2N0-1 breast cancer treated with BCT or mastectomy were selected from the Netherlands Cancer Registry. We used multivariable Cox regression to correct for confounding. Propensity trimming was used to create a more homogeneous population for which the treatment choice was not self-evident. Hospital of surgery was used as hierarchical level to handle hospital-related variation, and as IV to deal with unmeasured confounding.

RESULTS

Multivariable Cox regression showed higher 10-year DMFS for BCT than mastectomy [HR 0.70 (95% CI 0.60-82)]. Propensity trimming on the 10-90th and the 20-80th percentile of the propensity score distribution and hierarchical modelling showed similar HRs. IV analysis showed no significant difference between BCT and mastectomy.

CONCLUSION

Unmeasured confounding is very difficult to eliminate in observational research. We cannot conclude that BCT or mastectomy has a causal relationship with 10-year DMFS. It is crucial to critically evaluate all model's assumptions, and to be careful in drawing firm conclusions.

Association between Rift Valley fever virus seroprevalences in livestock and humans and their respective intra-cluster correlation coefficients, Tana River County, Kenya

We implemented a cross-sectional study in Tana River County, Kenya, a Rift Valley fever (RVF)-endemic area, to quantify the strength of association between RVF virus (RVFv) seroprevalences in livestock and humans, and their respective intra-cluster correlation coefficients (ICCs). The study involved 1932 livestock from 152 households and 552 humans from 170 households. Serum samples were collected and screened for anti-RVFv immunoglobulin G (IgG) antibodies using inhibition IgG enzyme-linked immunosorbent assay (ELISA). Data collected were analysed using generalised linear mixed effects models, with herd/household and village being fitted as random variables. The overall RVFv seroprevalences in livestock and humans were 25.41% (95% confidence interval (CI) 23.49–27.42%) and 21.20% (17.86–24.85%), respectively. The presence of at least one seropositive animal in a household was associated with an increased odds of exposure in people of 2.23 (95% CI 1.03–4.84). The ICCs associated with RVF virus seroprevalence in livestock were 0.30 (95% CI 0.19–0.44) and 0.22 (95% CI 0.12–0.38) within and between herds, respectively. These findings suggest that there is a greater variability of RVF virus exposure between than within herds. We discuss ways of using these ICC estimates in observational surveys for RVF in endemic areas and postulate that the design of the sentinel herd surveillance should consider patterns of RVF clustering to enhance its effectiveness as an early warning system for RVF epidemics.

Using an onset-anchored Bayesian hierarchical model to improve predictions for amyotrophic lateral sclerosis disease progression

BACKGROUND

Amyotrophic Lateral Sclerosis (ALS), also known as Lou Gehrig's disease, is a rare disease with extreme between-subject variability, especially with respect to rate of disease progression. This makes modelling a subject's disease progression, which is measured by the ALS Functional Rating Scale (ALSFRS), very difficult. Consider the problem of predicting a subject's ALSFRS score at 9 or 12 months after a given time-point.

METHODS

We obtained ALS subject data from the Pooled Resource Open-Access ALS Clinical Trials Database, a collection of data from various ALS clinical trials. Due to the typical linearity of the ALSFRS, we consider several Bayesian hierarchical linear models. These include a mixture model (to account for the two potential classes of "fast" and "slow" ALS progressors) as well as an onset-anchored model, in which an additional artificial data-point, using time of disease onset, is utilized to improve predictive performance.

RESULTS

The onset-anchored model had a drastically reduced posterior predictive mean-square-error distributions, when compared to the Bayesian hierarchical linear model or the mixture model under a cross-validation approach. No covariates, other than time of disease onset, consistently improved predictive performance in either the Bayesian hierarchical linear model or the onset-anchored model.

CONCLUSIONS

Augmenting patient data with an additional artificial data-point, or onset anchor, can drastically improve predictive modelling in ALS by reducing the variability of estimated parameters at the cost of a slight increase in bias. This onset-anchored model is extremely useful if predictions are desired directly after a single baseline measure (such as at the first day of a clinical trial), a feat that would be very difficult without the onset-anchor. This approach could be useful in modelling other diseases that have bounded progression scales (e.g. Parkinson's disease, Huntington's disease, or inclusion-body myositis). It is our hope that this model can be used by clinicians and statisticians to improve the efficacy of clinical trials and aid in finding treatments for ALS.

Predicting survival of pancreatic cancer patients treated with gemcitabine using longitudinal tumour size data

Purpose

Measures derived from longitudinal tumour size data have been increasingly utilised to predict survival of patients with solid tumours. The aim of this study was to examine the prognostic value of such measures for patients with metastatic pancreatic cancer undergoing gemcitabine therapy.

Methods

The control data from two Phase III studies were retrospectively used to develop (271 patients) and validate (398 patients) survival models. Firstly, 31 baseline variables were screened from the training set using penalised Cox regression. Secondly, tumour shrinkage metrics were interpolated for each patient by hierarchical modelling of the tumour size time-series. Subsequently, survival models were built by applying two approaches: the first aimed at incorporating model-derived tumour size metrics in a parametric model, and the second simply aimed at identifying empirical factors using Cox regression. Finally, the performance of the models in predicting patient survival was evaluated on the validation set.

Results

Depending on the modelling approach applied, albumin, body surface area, neutrophil, baseline tumour size and tumour shrinkage measures were identified as potential prognostic factors. The distributional assumption on survival times appeared to affect the identification of risk factors but not the ability to describe the training data. The two survival modelling approaches performed similarly in predicting the validation data.

Conclusions

A parametric model that incorporates model-derived tumour shrinkage metrics in addition to other baseline variables could predict reasonably well survival of patients with metastatic pancreatic cancer. However, the predictive performance was not significantly better than a simple Cox model that incorporates only baseline characteristics.

Electronic supplementary material

The online version of this article (doi:10.1007/s00280-016-2994-x) contains supplementary material, which is available to authorized users.

Bayesian model reduction and empirical Bayes for group (DCM) studies

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction.

Multicenter trials, guidelines, and uncertainties - Do we know as much as we think we do?

There is an uncritical belief that "positive" large scale multicenter randomized clinical trials provide a definitive window to the "truth". The limitations and difficulties in performing large trials are discussed herein and the need to fully and transparently acknowledge residual uncertainties is stressed. For example, the failure to consider the regional variations that may arise with the "outsourcing" of trials may lead to false estimates of precision. As large trials form the backbone of guidelines, failure to critically evaluate the importance of evidential limitations may see a minimization of residual uncertainties and lead to inappropriate recommendations.

Is prospective memory related to depression and anxiety? A hierarchical MPT modelling approach

Prospective memory (PM) refers to remembering to perform an action in the future. One hundred and twenty-nine students completed a laboratory event-based PM task as well as depression and anxiety questionnaires. The data were analysed with the beta-MPT version of the multinomial processing tree model of event-based PM. Thereby, the prospective and retrospective components of PM were estimated for each participant and were then correlated with depression and anxiety. State anxiety was negatively correlated with the prospective component of PM. Neither depression nor trait anxiety were related to either component of PM.