A latent class model for competing risks.

Survival data analysis becomes complex when the proportional hazards assumption is violated at population level or when crude hazard rates are no longer estimators of marginal ones. We develop a Bayesian survival analysis method to deal with these situations, on the basis of assuming that the complexities are induced by latent cohort or disease heterogeneity that is not captured by covariates and that proportional hazards hold at the level of individuals. This leads to a description from which risk-specific marginal hazard rates and survival functions are fully accessible, 'decontaminated' of the effects of informative censoring, and which includes Cox, random effects and latent class models as special cases. Simulated data confirm that our approach can map a cohort's substructure and remove heterogeneity-induced informative censoring effects. Application to data from the Uppsala Longitudinal Study of Adult Men cohort leads to plausible alternative explanations for previous counter-intuitive inferences on prostate cancer. The importance of managing cardiovascular disease as a comorbidity in women diagnosed with breast cancer is suggested on application to data from the Swedish Apolipoprotein Mortality Risk Study. Copyright © 2017 John Wiley & Sons, Ltd.

Quantifying noise in mass spectrometry and yeast two-hybrid protein interaction detection experiments.

Protein interaction networks (PINs) are popular means to visualize the proteome. However, PIN datasets are known to be noisy, incomplete and biased by the experimental protocols used to detect protein interactions. This paper aims at understanding the connection between true protein interactions and the protein interaction datasets that have been obtained using the most popular experimental techniques, i.e. mass spectronomy and yeast two-hybrid. We start from the observation that the adjacency matrix of a PIN, i.e. the binary matrix which defines, for every pair of proteins in the network, whether or not there is a link, has a special form, that we call separable. This induces precise relationships between the moments of the degree distribution (i.e. the average number of links that a protein in the network has, its variance, etc.) and the number of short loops (i.e. triangles, squares, etc.) along the links of the network. These relationships provide powerful tools to test the reliability of datasets and hint at the underlying biological mechanism with which proteins and complexes recruit each other.

Unbiased degree-preserving randomization of directed binary networks.

Randomizing networks using a naive "accept-all" edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with nontrivial acceptance probabilities for directed graphs, which converges to a strictly uniform measure and is based on edge swaps that conserve all in and out degrees. The acceptance probabilities can also be generalized to define Markov chains that target any alternative desired measure on the space of directed graphs in order to generate graphs with more sophisticated topological features. This is demonstrated by defining a process tailored to the production of directed graphs with specified degree-degree correlation functions. The theory is implemented numerically and tested on synthetic and biological network examples.

Direct Response Analysis in cellular signalling networks.

Direct Response Analysis is a general computational tool for quantifying direct functional interactions between components in cellular signalling systems from experimental perturbations and measurements alone. This paper aims to reveal the biological meaning of the direct response coefficients obtained upon applying DRA to simple Michaelis-Menten type proteomic and gene regulatory systems. These systems describe dimer formation and dissociation, protein preduction and decay, and transcription. We derive explicit formulae for the direct response coefficients in terms of biochemical reaction rates, and clarify the potential and limitations of the DRA method. We find that response coefficients are strongly asymmetric, and that they balance persistent characteristics of reactions (e.g. the ratios of on- and off rates) against the time-scales over which these reactions act; fast reactions give stronger response coefficients. The direct interactions between protein species, caused by dimer formation, are effectively negative. We illustrate our results with numerical simulations.

Evaluating acute medical admissions through emergency departments in Hong Kong: can one adjust for case-mix variation?

BACKGROUND: Healthcare systems are under pressure to efficiently and safely reduce acute care admissions to hospital. There is a need to develop a standardised system for assessing emergency department performance which takes into account case-mix variation. The objective of this study was to derive and validate a standardised tool for assessing variations in medical admissions through emergency departments in Hong Kong. METHODS: Retrospective study of patients attending emergency departments of 14 acute hospitals in Hong Kong. Data were retrieved from a centralised administrative database. RESULTS: Of 2,531,225 patients who attended emergency departments between 1 January 2001 and 31 December 2003, 780,444 (30.8%) were admitted to medical wards. A model derived from 2001 data shows well-calibrated admission probabilities, with an area under the receiver operating characteristic curve for probability of admission of 90.3 (95% CI ±0.11). The areas under the receiver operating characteristic curves for 2002 and 2003 validation sets were 89.9 (95% CI ±0.11) and 89.0 (95% CI ±0.12), respectively. With an averaged benchmark, reductions in medical admissions of up to 19% could be achieved, while under the most optimistic assumption, reductions of up 36% could be achieved. CONCLUSIONS: A tool for benchmarking hospital medical admissions and minimising case-mix variation has been derived and validated in Hong Kong, but it requires further validation in other healthcare systems given the wide variations in admission thresholds internationally. This may be used as one potential method to evaluate the performance of emergency departments against a common standard.

What you see is not what you get: how sampling affects macroscopic features of biological networks.

We use mathematical methods from the theory of tailored random graphs to study systematically the effects of sampling on topological features of large biological signalling networks. Our aim in doing so is to increase our quantitative understanding of the relation between true biological networks and the imperfect and often biased samples of these networks that are reported in public data repositories and used by biomedical scientists. We derive exact explicit formulae for degree distributions and degree correlation kernels of sampled networks, in terms of the degree distributions and degree correlation kernels of the underlying true network, for a broad family of sampling protocols that include random and connectivity-dependent node and/or link undersampling as well as random and connectivity-dependent link oversampling. Our predictions are in excellent agreement with numerical simulations.

A Bayesian method for single molecule, fluorescence burst analysis.

There is currently great interest in determining physical parameters, e.g. fluorescence lifetime, of individual molecules that inform on environmental conditions, whilst avoiding the artefacts of ensemble averaging. Protein interactions, molecular dynamics and sub-species can all be studied. In a burst integrated fluorescence lifetime (BIFL) experiment, identification of fluorescent bursts from single molecules above background detection is a problem. This paper presents a Bayesian method for burst identification based on model selection and demonstrates the detection of bursts consisting of 10% signal amplitude. The method also estimates the fluorescence lifetime (and its error) from the burst data.

Dynamical replica analysis of disordered Ising spin systems on finitely connected random graphs.

We study the dynamics of macroscopic observables such as the magnetization and the energy per degree of freedom in Ising spin models on random graphs of finite connectivity, with random bonds and/or heterogeneous degree distributions. To do so, we generalize existing versions of dynamical replica theory and cavity field techniques to systems with strongly disordered and locally treelike interactions. We illustrate our results via application to, e.g., +/-J spin glasses on random graphs and of the overlap in finite connectivity Sourlas codes. All results are tested against Monte Carlo simulations.

Statistical mechanics beyond the Hopfield model: solvable problems in neural network theory.

We present four 'case study' examples of solvable problems in the theory of recurrent neural networks, which are relevant to our understanding of information processing in the brain, but which are also interesting from a purely statistical mechanical point of view, even at the level of simple models (which helps in stimulating interdisciplinary work). The examples concern issues in network dynamics, network connectivity, spike timing and synaptic plasticity.

Dynamics of the batch minority game with inhomogeneous decision noise.

We study the dynamics of a version of the batch minority game, with random external information and with different types of inhomogeneous decision noise (additive and multiplicative), using generating functional techniques à la De Dominicis. The control parameters in this model are the ratio alpha=p/N of the number p of possible values for the external information over the number N of trading agents, and the statistical properties of the agents' decision noise parameters. The presence of decision noise is found to have the general effect of damping macroscopic oscillations, which explains why in certain parameter regions it can effectively reduce the market volatility, as observed in earlier studies. In the limit N-->infinity we (i) solve the first few time steps of the dynamics (for any alpha), (ii) calculate the location alpha(c) of the phase transition (signaling the onset of anomalous response), and (iii) solve the statics for alpha>alpha(c). We find that alpha(c) is not sensitive to additive decision noise, but we arrive at nontrivial phase diagrams in the case of multiplicative noise. Our theoretical results find excellent confirmation in numerical simulations.

Generating functional analysis of the dynamics of the batch minority game with random external information.

We study the dynamics of the batch minority game, with random external information, using generating functional techniques introduced by De Dominicis. The relevant control parameter in this model is the ratio alpha=p/N of the number p of possible values for the external information over the number N of trading agents. In the limit N-->infinity we calculate the location alphac of the phase transition (signaling the onset of anomalous response), and solve the statics for alpha>alphac exactly. The temporal correlations in global market fluctuations turn out not to decay to zero for infinitely widely separated times. For alpha0 we analyze our equations in leading order in alpha, and find asymptotic solutions with diverging volatility sigma=O(alpha(-1/2)) (as regularly observed in simulations), but also asymptotic solutions with vanishing volatility sigma=O(alpha(1/2)). The former, however, are shown to emerge only if the agents' initial strategy valuations are below a specific critical value.

Autonomous development of decorrelation filters in neural networks with recurrent inhibition.

We perform a quantitative analysis of information processing in a simple neural network model with recurrent inhibition. We postulate that both excitatory and inhibitory synapses continually adapt according to the following Hebbian-type rules: for excitatory synapses correlated pre- and post-synaptic activity induces enhanced excitation; for inhibitory synapses it induces enhanced inhibition. Following synaptic equilibration in unsupervised learning processes, the model is found to perform a novel type of principal-component analysis which involves filtering and decorrelation. In the light of these results we discuss the possible role of the granule-/Golgi-cell subnetwork in the cerebellum.

Sequences of smoothly correlated patterns in neural networks with random transmission delays.

A neural network with a broad distribution of transmission delays was used to study numerically the retrieval of sequences having several types of correlations between successive patterns. In the case of sequences consisting of patterns correlated for finite time, the quality of retrieval was found to be (more or less) independent of the pattern correlation width and the delay distribution. On the other hand the quality of retrieval is dependent on these factors in the case of sequences with pattern correlation functions with long time 'tails'. Finally we have studied to what extent the storage capacity depends on the pattern correlation function and the delay distribution.

Kinetics of human cone photopigments explained with a Rushton-Henry model.

Densitrometric measurements of the regeneration of cone visual photopigments have shown effects that cannot be explained by the existing quantitative models. Regeneration from a fully bleached state seems to depend on how this state has been reached and the shape of the regeneration curve cannot be produced by a first order reaction. Rushton and Henry (1968) proposed a store of 11-cis-retinal to explain rapid regeneration after a short bleach. We elaborated this idea into a quantitative model. Regeneration after three different bleach histories and steady state behaviour of the pigments was measured using the Utrecht densitometer. The Rushton-Henry model gives a good fit to the data and is clearly superior to the classical Rushton model in describing densitometric measurements.