A unification of models for meta-analysis of diagnostic accuracy studies

Studies of diagnostic accuracy require more sophisticated methods for their meta-analysis than studies of therapeutic interventions. A number of different, and apparently divergent, methods for meta-analysis of diagnostic studies have been proposed, including two alternative approaches that are statistically rigorous and allow for between-study variability: the hierarchical summary receiver operating characteristic (ROC) model (Rutter and Gatsonis, 2001) and bivariate random-effects meta-analysis (van Houwelingen and others, 1993), (van Houwelingen and others, 2002), (Reitsma and others, 2005). We show that these two models are very closely related, and define the circumstances in which they are identical. We discuss the different forms of summary model output suggested by the two approaches, including summary ROC curves, summary points, confidence regions, and prediction regions.

Statistical evaluation of alternative models of human evolution

An appropriate model of recent human evolution is not only important to understand our own history, but it is necessary to disentangle the effects of demography and selection on genome diversity. Although most genetic data support the view that our species originated recently in Africa, it is still unclear if it completely replaced former members of the Homo genus, or if some interbreeding occurred during its range expansion. Several scenarios of modern human evolution have been proposed on the basis of molecular and paleontological data, but their likelihood has never been statistically assessed. Using DNA data from 50 nuclear loci sequenced in African, Asian and Native American samples, we show here by extensive simulations that a simple African replacement model with exponential growth has a higher probability (78%) as compared with alternative multiregional evolution or assimilation scenarios. A Bayesian analysis of the data under this best supported model points to an origin of our species approximately 141 thousand years ago (Kya), an exit out-of-Africa approximately 51 Kya, and a recent colonization of the Americas approximately 10.5 Kya. We also find that the African replacement model explains not only the shallow ancestry of mtDNA or Y-chromosomes but also the occurrence of deep lineages at some autosomal loci, which has been formerly interpreted as a sign of interbreeding with Homo erectus.

Bayesian statistics in oncology: a guide for the clinical investigator

The rise of evidence-based medicine as well as important progress in statistical methods and computational power have led to a second birth of the >200-year-old Bayesian framework. The use of Bayesian techniques, in particular in the design and interpretation of clinical trials, offers several substantial advantages over the classical statistical approach. First, in contrast to classical statistics, Bayesian analysis allows a direct statement regarding the probability that a treatment was beneficial. Second, Bayesian statistics allow the researcher to incorporate any prior information in the analysis of the experimental results. Third, Bayesian methods can efficiently handle complex statistical models, which are suited for advanced clinical trial designs. Finally, Bayesian statistics encourage a thorough consideration and presentation of the assumptions underlying an analysis, which enables the reader to fully appraise the authors' conclusions. Both Bayesian and classical statistics have their respective strengths and limitations and should be viewed as being complementary to each other; we do not attempt to make a head-to-head comparison, as this is beyond the scope of the present review. Rather, the objective of the present article is to provide a nonmathematical, reader-friendly overview of the current practice of Bayesian statistics coupled with numerous intuitive examples from the field of oncology. It is hoped that this educational review will be a useful resource to the oncologist and result in a better understanding of the scope, strengths, and limitations of the Bayesian approach.

Hierarchical modeling gave plausible estimates of associations between metabolic syndrome and components of antiretroviral therapy

OBJECTIVE: Hierarchical modeling has been proposed as a solution to the multiple exposure problem. We estimate associations between metabolic syndrome and different components of antiretroviral therapy using both conventional and hierarchical models. STUDY DESIGN AND SETTING: We use discrete time survival analysis to estimate the association between metabolic syndrome and cumulative exposure to 16 antiretrovirals from four drug classes. We fit a hierarchical model where the drug class provides a prior model of the association between metabolic syndrome and exposure to each antiretroviral. RESULTS: One thousand two hundred and eighteen patients were followed for a median of 27 months, with 242 cases of metabolic syndrome (20%) at a rate of 7.5 cases per 100 patient years. Metabolic syndrome was more likely to develop in patients exposed to stavudine, but was less likely to develop in those exposed to atazanavir. The estimate for exposure to atazanavir increased from hazard ratio of 0.06 per 6 months' use in the conventional model to 0.37 in the hierarchical model (or from 0.57 to 0.81 when using spline-based covariate adjustment). CONCLUSION: These results are consistent with trials that show the disadvantage of stavudine and advantage of atazanavir relative to other drugs in their respective classes. The hierarchical model gave more plausible results than the equivalent conventional model.

Representation via Probabilities: Models of Probabilistic Modeling

How do probabilistic models represent their targets and how do they allow us to learn about them? The answer to this question depends on a number of details, in particular on the meaning of the probabilities involved. To classify the options, a minimalist conception of representation (Su\'arez 2004) is adopted: Modelers devise substitutes (``sources'') of their targets and investigate them to infer something about the target. Probabilistic models allow us to infer probabilities about the target from probabilities about the source. This leads to a framework in which we can systematically distinguish between different models of probabilistic modeling. I develop a fully Bayesian view of probabilistic modeling, but I argue that, as an alternative, Bayesian degrees of belief about the target may be derived from ontic probabilities about the source. Remarkably, some accounts of ontic probabilities can avoid problems if they are supposed to apply to sources only.

Chow–Liu trees are sufficient predictive models for reproducing key features of functional networks of periictal EEG time-series

Seizure freedom in patients suffering from pharmacoresistant epilepsies is still not achieved in 20–30% of all cases. Hence, current therapies need to be improved, based on a more complete understanding of ictogenesis. In this respect, the analysis of functional networks derived from intracranial electroencephalographic (iEEG) data has recently become a standard tool. Functional networks however are purely descriptive models and thus are conceptually unable to predict fundamental features of iEEG time-series, e.g., in the context of therapeutical brain stimulation. In this paper we present some first steps towards overcoming the limitations of functional network analysis, by showing that its results are implied by a simple predictive model of time-sliced iEEG time-series. More specifically, we learn distinct graphical models (so called Chow–Liu (CL) trees) as models for the spatial dependencies between iEEG signals. Bayesian inference is then applied to the CL trees, allowing for an analytic derivation/prediction of functional networks, based on thresholding of the absolute value Pearson correlation coefficient (CC) matrix. Using various measures, the thus obtained networks are then compared to those which were derived in the classical way from the empirical CC-matrix. In the high threshold limit we find (a) an excellent agreement between the two networks and (b) key features of periictal networks as they have previously been reported in the literature. Apart from functional networks, both matrices are also compared element-wise, showing that the CL approach leads to a sparse representation, by setting small correlations to values close to zero while preserving the larger ones. Overall, this paper shows the validity of CL-trees as simple, spatially predictive models for periictal iEEG data. Moreover, we suggest straightforward generalizations of the CL-approach for modeling also the temporal features of iEEG signals.

European summer temperatures since Roman times

The spatial context is critical when assessing present-day climate anomalies, attributing them to potential forcings and making statements regarding their frequency and severity in a long-term perspective. Recent international initiatives have expanded the number of high-quality proxy-records and developed new statistical reconstruction methods. These advances allow more rigorous regional past temperature reconstructions and, in turn, the possibility of evaluating climate models on policy-relevant, spatio-temporal scales. Here we provide a new proxy-based, annually-resolved, spatial reconstruction of the European summer (June–August) temperature fields back to 755 CE based on Bayesian hierarchical modelling (BHM), together with estimates of the European mean temperature variation since 138 BCE based on BHM and composite-plus-scaling (CPS). Our reconstructions compare well with independent instrumental and proxy-based temperature estimates, but suggest a larger amplitude in summer temperature variability than previously reported. Both CPS and BHM reconstructions indicate that the mean 20th century European summer temperature was not significantly different from some earlier centuries, including the 1st, 2nd, 8th and 10th centuries CE. The 1st century (in BHM also the 10th century) may even have been slightly warmer than the 20th century, but the difference is not statistically significant. Comparing each 50 yr period with the 1951–2000 period reveals a similar pattern. Recent summers, however, have been unusually warm in the context of the last two millennia and there are no 30 yr periods in either reconstruction that exceed the mean average European summer temperature of the last 3 decades (1986–2015 CE). A comparison with an ensemble of climate model simulations suggests that the reconstructed European summer temperature variability over the period 850–2000 CE reflects changes in both internal variability and external forcing on multi-decadal time-scales. For pan-European temperatures we find slightly better agreement between the reconstruction and the model simulations with high-end estimates for total solar irradiance. Temperature differences between the medieval period, the recent period and the Little Ice Age are larger in the reconstructions than the simulations. This may indicate inflated variability of the reconstructions, a lack of sensitivity and processes to changes in external forcing on the simulated European climate and/or an underestimation of internal variability on centennial and longer time scales.

Internal Models, Vestibular Cognition, and Mental Imagery: Conceptual Considerations

Vestibular cognition has recently gained attention. Despite numerous experimental and clinical demonstrations, it is not yet clear what vestibular cognition really is. For future research in vestibular cognition, adopting a computational approach will make it easier to explore the underlying mech- anisms. Indeed, most modeling approaches in vestibular science include a top-down or a priori component. We review recent Bayesian optimal observer models, and discuss in detail the conceptual value of prior assumptions, likelihood and posterior estimates for research in vestibular cognition. We then consider forward models in vestibular processing, which are required in order to distinguish between sensory input that is induced by active self-motion, and sensory input that is due to passive self-motion. We suggest that forward models are used not only in the service of estimating sensory states but they can also be drawn upon in an offline mode (e.g., spatial perspective transformations), in which interaction with sensory input is not desired. A computational approach to vestibular cogni- tion will help to discover connections across studies, and it will provide a more coherent framework for investigating vestibular cognition.

Disentangling mental imagery and perceptual expectation

Mental imagery and perception are thought to rely on similar neural circuits, and many recent behavioral studies have attempted to demonstrate interactions between actual physical stimulation and sensory imagery in the corresponding sensory modality. However, there has been a lack of theoretical understanding of the nature of these interactions, and both interferential and facilitatory effects have been found. Facilitatory effects appear strikingly similar to those that arise due to experimental manipulations of expectation. Using a self-motion discrimination task, we try to disentangle the effects of mental imagery from those of expectation by using a hierarchical drift diffusion model to investigate both choice data and response times. Manipulations of expectation are reasonably well understood in terms of their selective influence on parameters of the drift diffusion model, and in this study, we make the first attempt to similarly characterize the effects of mental imagery. We investigate mental imagery within the computational framework of control theory and state estimation. • Mental imagery and perception are thought to rely on similar neural circuits; however, on more theoretical grounds, imagery seems to be closely related to the output of forward models (sensory predictions). • We reanalyzed data from a study of imagined self-motion. • Bayesian modeling of response times may allow us to disentangle the effects of mental imagery on behavior from other cognitive (top-down) effects, such as expectation.