arXiv subjects

Leonhard Held

Publications and source records attributed to Leonhard Held.

50 records · Page 3Linked to original sources

arXiv2018

Power Priors Based on Multiple Historical Studies for Binary Outcomes

Incorporating historical information into the design and analysis of a new clinical trial has been the subject of much recent discussion. For example, in the context of clinical trials of antibiotics for drug resistant infections, where patients with specific infections can be difficult to recruit, there is often only limited and heterogeneous information available from the historical trials. To make the best use of the combined information at hand, we consider an approach based on the multiple power prior which allows the prior weight of each historical study to be chosen adaptively by empirical Bayes. This choice of weight has advantages in that it varies commensurably with differences in the historical and current data and can choose weights near 1 if the data from the corresponding historical study are similar enough to the data from the current study. Fully Bayesian approaches are also considered. The methods are applied to data from antibiotics trials. An analysis of the operating characteristics in a binomial setting shows that the proposed empirical Bayes adaptive method works well, compared to several alternative approaches, including the meta-analytic prior.

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arXiv2017

Periodically stationary multivariate autoregressive models

A class of multivariate periodic autoregressive models is proposed where coupling between time series is achieved through linear mean functions. Various response distributions with quadratic mean-variance relationships fit into the framework, including the negative binomial, gamma and Gaussian distributions. We develop an iterative algorithm to obtain unconditional means, variances and auto-/cross-covariances for models with higher order lags. Analytical solutions are given for the univariate model with lag one and multivariate models with linear mean-variance relationship. A special case of the model class is an established framework for modelling multivariate time series of counts from routine surveillance of infectious diseases. We extend this model class to allow for distributed lags and apply it to a dataset on norovirus gastroenteritis in two German states. The availability of unconditional moments and auto/cross-correlations enhances model assessment and interpretation.

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arXiv2017

p-Values for Credibility

Analysis of credibility is a reverse-Bayes technique that has been proposed by Matthews (2001) to overcome some of the shortcomings of significance tests. A significant result is deemed credible if current knowledge about the effect size is in conflict with any sceptical prior that would make the effect non-significant. In this paper I formalize the approach and propose to use Bayesian predictive tail probabilities to quantify the evidence for credibility. This gives rise to a p-value for extrinsic credibility, taking into account both the internal and the external evidence for an effect. The assessment of intrinsic credibility leads to a new threshold for ordinary significance that is remarkably close to the recently proposed 0.005 level. Finally, a p-value for intrinsic credibility is proposed that is a simple function of the ordinary p-value for significance and has a direct frequentist interpretation in terms of the replication probability that a future study under identical conditions will give an estimated effect in the same direction as the first study.

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arXiv2017

Fast and accurate Bayesian model criticism and conflict diagnostics using R-INLA

Bayesian hierarchical models are increasingly popular for realistic modelling and analysis of complex data. This trend is accompanied by the need for flexible, general, and computationally efficient methods for model criticism and conflict detection. Usually, a Bayesian hierarchical model incorporates a grouping of the individual data points, for example individuals in repeated measurement data. In such cases, the following question arises: Are any of the groups "outliers", or in conflict with the remaining groups? Existing general approaches aiming to answer such questions tend to be extremely computationally demanding when model fitting is based on MCMC. We show how group-level model criticism and conflict detection can be done quickly and accurately through integrated nested Laplace approximations (INLA). The new method is implemented as a part of the open source R-INLA package for Bayesian computing (http://r-inla.org).

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arXiv2016

Incorporating social contact data in spatio-temporal models for infectious disease spread

Routine public health surveillance of notifiable infectious diseases gives rise to weekly counts of reported cases -- possibly stratified by region and/or age group. We investigate how an age-structured social contact matrix can be incorporated into a spatio-temporal endemic-epidemic model for infectious disease counts. To illustrate the approach, we analyze the spread of norovirus gastroenteritis over 6 age groups within the 12 districts of Berlin, 2011-2015, using contact data from the POLYMOD study. The proposed age-structured model outperforms alternative scenarios with homogeneous or no mixing between age groups. An extended contact model suggests a power transformation of the survey-based contact matrix towards more within-group transmission.

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arXiv2016

Model-based testing for space-time interaction using point processes: An application to psychiatric hospital admissions in an urban area

Spatio-temporal interaction is inherent to cases of infectious diseases and occurrences of earthquakes, whereas the spread of other events, such as cancer or crime, is less evident. Statistical significance tests of space-time clustering usually assess the correlation between the spatial and temporal (transformed) distances of the events. Although appealing through simplicity, these classical tests do not adjust for the underlying population nor can they account for a distance decay of interaction. We propose to use the framework of an endemic-epidemic point process model to jointly estimate a background event rate explained by seasonal and areal characteristics, as well as a superposed epidemic component representing the hypothesis of interest. We illustrate this new model-based test for space-time interaction by analysing psychiatric inpatient admissions in Zurich, Switzerland (2007-2012). Several socio-economic factors were found to be associated with the admission rate, but there was no evidence of general clustering of the cases.

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arXiv2015

Spatio-Temporal Analysis of Epidemic Phenomena Using the R Package surveillance

The availability of geocoded health data and the inherent temporal structure of communicable diseases have led to an increased interest in statistical models and software for spatio-temporal data with epidemic features. The open source R package surveillance can handle various levels of aggregation at which infective events have been recorded: individual-level time-stamped geo-referenced data (case reports) in either continuous space or discrete space, as well as counts aggregated by period and region. For each of these data types, the surveillance package implements tools for visualization, likelihoood inference and simulation from recently developed statistical regression frameworks capturing endemic and epidemic dynamics. Altogether, this paper is a guide to the spatio-temporal modeling of epidemic phenomena, exemplified by analyses of public health surveillance data on measles and invasive meningococcal disease.

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arXiv2015

Approximate Bayesian Model Selection with the Deviance Statistic

Bayesian model selection poses two main challenges: the specification of parameter priors for all models, and the computation of the resulting Bayes factors between models. There is now a large literature on automatic and objective parameter priors in the linear model. One important class are $g$-priors, which were recently extended from linear to generalized linear models (GLMs). We show that the resulting Bayes factors can be approximated by test-based Bayes factors (Johnson [Scand. J. Stat. 35 (2008) 354-368]) using the deviance statistics of the models. To estimate the hyperparameter $g$, we propose empirical and fully Bayes approaches and link the former to minimum Bayes factors and shrinkage estimates from the literature. Furthermore, we describe how to approximate the corresponding posterior distribution of the regression coefficients based on the standard GLM output. We illustrate the approach with the development of a clinical prediction model for 30-day survival in the GUSTO-I trial using logistic regression.

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arXiv2014

Power-law models for infectious disease spread

Short-time human travel behaviour can be described by a power law with respect to distance. We incorporate this information in space-time models for infectious disease surveillance data to better capture the dynamics of disease spread. Two previously established model classes are extended, which both decompose disease risk additively into endemic and epidemic components: a spatio-temporal point process model for individual-level data and a multivariate time-series model for aggregated count data. In both frameworks, a power-law decay of spatial interaction is embedded into the epidemic component and estimated jointly with all other unknown parameters using (penalised) likelihood inference. Whereas the power law can be based on Euclidean distance in the point process model, a novel formulation is proposed for count data where the power law depends on the order of the neighbourhood of discrete spatial units. The performance of the new approach is investigated by a reanalysis of individual cases of invasive meningococcal disease in Germany (2002-2008) and count data on influenza in 140 administrative districts of Southern Germany (2001-2008). In both applications, the power law substantially improves model fit and predictions, and is reasonably close to alternative qualitative formulations, where distance and order of neighbourhood, respectively, are treated as a factor. Implementation in the R package surveillance allows the approach to be applied in other settings.

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arXiv2013

Sensitivity analysis for Bayesian hierarchical models

Prior sensitivity examination plays an important role in applied Bayesian analyses. This is especially true for Bayesian hierarchical models, where interpretability of the parameters within deeper layers in the hierarchy becomes challenging. In addition, lack of information together with identifiability issues may imply that the prior distributions for such models have an undesired influence on the posterior inference. Despite its relevance, informal approaches to prior sensitivity analysis are currently used. They require repetitive re-runs of the model with ad-hoc modified base prior parameter values. Other formal approaches to prior sensitivity analysis suffer from a lack of popularity in practice, mainly due to their high computational cost and absence of software implementation. We propose a novel formal approach to prior sensitivity analysis which is fast and accurate. It quantifies sensitivity without the need for a model re-run. We develop a ready-to-use priorSens package in R for routine prior sensitivity investigation by R-INLA. Throughout a series of examples we show how our approach can be used to detect high prior sensitivities of some parameters as well as identifiability issues in possibly over-parametrized Bayesian hierarchical models.

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arXiv2013

Bayesian analysis of measurement error models using INLA

To account for measurement error (ME) in explanatory variables, Bayesian approaches provide a flexible framework, as expert knowledge about unobserved covariates can be incorporated in the prior distributions. However, given the analytic intractability of the posterior distribution, model inference so far has to be performed via time-consuming and complex Markov chain Monte Carlo implementations. In this paper we extend the Integrated nested Laplace approximations (INLA) approach to formulate Gaussian ME models in generalized linear mixed models. We present three applications, and show how parameter estimates are obtained for common ME models, such as the classical and Berkson error model including heteroscedastic variances. To illustrate the practical feasibility, R-code is provided.

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arXiv2012

Mixtures of g-Priors for Generalised Additive Model Selection with Penalised Splines

We propose an objective Bayesian approach to the selection of covariates and their penalised splines transformations in generalised additive models. Specification of a reasonable default prior for the model parameters and combination with a multiplicity-correction prior for the models themselves is crucial for this task. Here we use well-studied and well-behaved continuous mixtures of g-priors as default priors. We introduce the methodology in the normal model and extend it to non-normal exponential families. A simulation study and an application from the literature illustrate the proposed approach. An efficient implementation is available in the R-package "hypergsplines".

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arXiv2012

Estimation and extrapolation of time trends in registry data---Borrowing strength from related populations

To analyze and project age-specific mortality or morbidity rates age-period-cohort (APC) models are very popular. Bayesian approaches facilitate estimation and improve predictions by assigning smoothing priors to age, period and cohort effects. Adjustments for overdispersion are straightforward using additional random effects. When rates are further stratified, for example, by countries, multivariate APC models can be used, where differences of stratum-specific effects are interpretable as log relative risks. Here, we incorporate correlated stratum-specific smoothing priors and correlated overdispersion parameters into the multivariate APC model, and use Markov chain Monte Carlo and integrated nested Laplace approximations for inference. Compared to a model without correlation, the new approach may lead to more precise relative risk estimates, as shown in an application to chronic obstructive pulmonary disease mortality in three regions of England and Wales. Furthermore, the imputation of missing data for one particular stratum may be improved, since the new approach takes advantage of the remaining strata if the corresponding observations are available there. This is shown in an application to female mortality in Denmark, Sweden and Norway from the 20th century, where we treat for each country in turn either the first or second half of the observations as missing and then impute the omitted data. The projections are compared to those obtained from a univariate APC model and an extended Lee--Carter demographic forecasting approach using the proper Dawid--Sebastiani scoring rule.

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arXiv2010

Hyper-g Priors for Generalized Linear Models

We develop an extension of the classical Zellner's g-prior to generalized linear models. The prior on the hyperparameter g is handled in a flexible way, so that any continuous proper hyperprior f(g) can be used, giving rise to a large class of hyper-g priors. Connections with the literature are described in detail. A fast and accurate integrated Laplace approximation of the marginal likelihood makes inference in large model spaces feasible. For posterior parameter estimation we propose an efficient and tuning-free Metropolis-Hastings sampler. The methodology is illustrated with variable selection and automatic covariate transformation in the Pima Indians diabetes data set.

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