To account for measurement error (ME) in explanatory variables, Bayesian approaches provide a flexible framework, as expert knowledge can be incorporated in the prior distributions. Recently, integrated nested Laplace approximations have been proven to be a computationally convenient alternative to sampling approaches for Bayesian inference in latent Gaussian models. We show how the most common approaches to adjust for ME, the classical and the Berkson ME, fit into this framework. This is achieved through a reformulation with augmented pseudo-observations and a suitable extension of the latent Gaussian field. Two specific classes are described, which allow for a particularly simple implementation using integrated nested Laplace approximations. We present three applications within the framework of generalized linear (mixed) models with ME. To illustrate the practical feasibility, R code is provided in on-line supplementary material.

Novel molecularly targeted agents (MTAs) have emerged as valuable alternatives or complements to traditional cytotoxic agents in the treatment of cancer. Clinicians are combining cytotoxic agents with MTAs in a single trial to achieve treatment synergism and better outcomes for patients. An important feature of such combinational trials is that, unlike the efficacy of the cytotoxic agent, that of the MTA may initially increase at low dose levels and then approximately plateau at higher dose levels as MTA saturation levels are reached. Therefore, the goal of the trial is to find the optimal dose combination that yields the highest efficacy with the lowest toxicity and meanwhile satisfies a certain safety requirement. We propose a Bayesian phase I–II design to find the optimal dose combination. We model toxicity by using a logistic regression and propose a novel proportional hazard model for efficacy, which accounts for the plateau in the MTA dose–efficacy curve. We evaluate the operating characteristics of the proposed design through simulation studies under various practical scenarios. The results show that the design proposed performs well and selects the optimal dose combination with high probability.

We propose and fit a Bayesian model to infer palaeoclimate over several thousand years. The data that we use arise as ancient pollen counts taken from sediment cores together with radiocarbon dates which provide (uncertain) ages. When combined with a modern pollen–climate data set, we can calibrate ancient pollen into ancient climate. We use a normal–inverse Gaussian process prior to model the stochastic volatility of palaeoclimate over time, and we present a novel modularized Markov chain Monte Chain algorithm to enable fast computation. We illustrate our approach with a case-study from Sluggan Moss, Northern Ireland, and provide an R package, Bclim, for use at other sites.

The paper develops hypothesis testing procedures for the stratified mark-specific proportional hazards model in the presence of missing marks. The motivating application is preventive human immunodeficiency virus (HIV) vaccine efficacy trials, where the mark is the genetic distance of an infecting HIV sequence to an HIV sequence represented inside the vaccine. The test statistics are constructed on the basis of two-stage efficient estimators, which utilize auxiliary predictors of the missing marks. The asymptotic properties and finite sample performances of the testing procedures are investigated, demonstrating double robustness and effectiveness of the predictive auxiliaries to recover efficiency. The methods are applied to the RV144 vaccine trial.

We discuss two-sample global permutation tests for sets of multivariate ordinal data in possibly high dimensional set-ups, motivated by the analysis of data collected by means of the World Health Organization's ‘International classification of functioning, disability and health’. The tests do not require any modelling of the multivariate dependence structure. Specifically, we consider testing for marginal inhomogeneity and direction-independent marginal order. As opposed to max-*T*-tests, which are known to have good power against alternatives with few strong individual effects, the tests proposed have good power against alternatives with many weak individual effects. Permutation tests are valid only if the two multivariate distributions are identical under the null hypothesis. By means of simulations, we examine the practical effect of violations of this exchangeability condition. Our simulations suggest that theoretically invalid permutation tests can still be ‘practically valid’. In particular, they suggest that the degree of the permutation procedure's failure may be considered as a function of the difference in group-specific covariance matrices, the proportion between group sizes, the number of variables in the set, the test statistic used and the number of levels per variable.

We consider an application in electricity grid load prediction, where generalized additive models are appropriate, but where the data set's size can make their use practically intractable with existing methods. We therefore develop practical generalized additive model fitting methods for large data sets in the case in which the smooth terms in the model are represented by using penalized regression splines. The methods use iterative update schemes to obtain factors of the model matrix while requiring only subblocks of the model matrix to be computed at any one time. We show that efficient smoothing parameter estimation can be carried out in a well-justified manner. The grid load prediction problem requires updates of the model fit, as new data become available, and some means for dealing with residual auto-correlation in grid load. Methods are provided for these problems and parallel implementation is covered. The methods allow estimation of generalized additive models for large data sets by using modest computer hardware, and the grid load prediction problem illustrates the utility of reduced rank spline smoothing methods for dealing with complex modelling problems.

We consider a problem of reducing the expected number of treatment failures in trials where the probability of response to treatment is close to 1 and treatments are compared on the basis of the log-odds ratio. We propose a new class of urn designs for randomization of patients in a clinical trial. The new urn designs target a number of allocation proportions including the allocation proportion that yields the same power as equal allocation but significantly less expected treatment failures. The new design is compared with the doubly adaptive biased coin design, the efficient randomized adaptive design and with equal allocation. The properties of the new class of designs are studied by embedding them in a family of continuous time stochastic processes.

The Lyon–Fedder–Mobarry global magnetosphere–ionosphere coupled model LFM-MIX is used to study Sun–Earth interactions by simulating geomagnetic storms. This work focuses on relating the multifidelity output from LFM-MIX to field observations of ionospheric conductance. Given a set of input values and solar wind data, LFM-MIX numerically solves the magnetohydrodynamic equations and outputs a bivariate spatiotemporal field of ionospheric energy and flux. Of particular interest here are LFM-MIX input settings required to match corresponding output with field observations. To estimate these input settings, a multivariate spatiotemporal statistical LFM-MIX emulator is constructed. The statistical emulator leverages the multiple fidelities such that the less computationally demanding yet lower fidelity LFM-MIX is used to provide estimates of the higher fidelity output. The higher fidelity LFM-MIX output is then used for calibration by using additive and non-linear discrepancy functions.

In observational studies, interest mainly lies in estimation of the population level relationship between the explanatory variables and dependent variables, and the estimation is often undertaken by using a sample of longitudinal data. In some situations, the longitudinal data sample features biases and loss of estimation efficiency due to non-random dropout. However, inclusion of population level information can increase estimation efficiency. We propose an empirical-likelihood-based method to incorporate population level information in a longitudinal study with dropout. The population level information is incorporated via constraints on functions of the parameters, and non-random dropout bias is corrected by using a weighted generalized estimating equations method. We provide a three-step estimation procedure that makes computation easier. Some commonly used methods are compared in simulation studies, which demonstrate that our proposed method can correct the non-random dropout bias and increase the estimation efficiency, especially for small sample sizes or when the missing proportion is high. In some situations, the improvement in efficiency is substantial. Finally, we apply the method to an Alzheimer's disease study.

Weather predictions are uncertain by nature. This uncertainty is dynamically assessed by a finite set of trajectories, called ensemble members. Unfortunately, ensemble prediction systems underestimate the uncertainty and thus are unreliable. Statistical approaches are proposed to post-process ensemble forecasts, including Bayesian model averaging and the Bayesian processor of output. We develop a methodology, called the Bayesian processor of ensemble members, from a hierarchical model and combining the two aforementioned frameworks to calibrate ensemble forecasts. The Bayesian processor of ensemble members is compared with Bayesian model averaging and the Bayesian processor of output by calibrating surface temperature forecasting over eight stations in the province of Quebec (Canada). Results show that ensemble forecast skill is improved by the method developed.

Motivated by a study exploring geographic disparities in test scores among fourth graders in North Carolina, we develop a multivariate mixture model for the spatial analysis of correlated continuous outcomes. The responses are modelled as a finite mixture of multivariate normal distributions, which accommodates a wide range of marginal response distributions and allows investigators to examine covariate effects within subpopulations of interest. The model has a hierarchical structure incorporating both individual and areal level predictors as well as spatial random effects for each mixture component. Conditional auto-regressive priors on the random effects provide spatial smoothing and allow the shape of the multivariate distribution to vary flexibly across geographic regions. By integrating over this distribution, we obtain region-specific joint, marginal and conditional inferences of interest. We adopt a Bayesian modelling approach and develop an efficient posterior sampling algorithm that relies primarily on closed form full conditionals. Our results show that students in the central and coastal counties of North Carolina demonstrate higher achievement on average than students in the other parts of the state. These findings can be used to guide county level initiatives, such as school-based literacy programmes, to improve elementary education.

In a longitudinal metabolomics study, multiple metabolites are measured from several observations at many time points. Interest lies in reducing the dimensionality of such data and in highlighting influential metabolites which change over time. A dynamic probabilistic principal components analysis model is proposed to achieve dimension reduction while appropriately modelling the correlation due to repeated measurements. This is achieved by assuming an auto-regressive model for some of the model parameters. Linear mixed models are subsequently used to identify influential metabolites which change over time. The model proposed is used to analyse data from a longitudinal metabolomics animal study.

We present a novel analysis of a landmark table of dose–response mortality counts from lung cancer in men. The data were originally collected by Doll and Hill. Our inferences are based on Poisson models for which the rates of occurrence are partially ordered according to two covariates. The partial ordering of the mortality rates enforces the well-established knowledge that lung cancer mortality rates are higher for older men and for heavier smokers. The ordered group reference priors that we use in our analyses generalize a class of reference priors that we previously derived for models of count data in which the rates of occurrence in different categories are completely ordered with respect to the values of a single covariate. The reference models for the lung cancer data based on the proposed priors are more flexible than and can be superior, in terms of goodness of fit, to a Bayesian version of several parametric models derived from a mathematical theory of carcinogenesis that have appeared in the literature.

Downscaled rainfall projections from climate models are essential for many meteorological and hydrological applications. The technique presented utilizes an approach that efficiently parameterizes spatiotemporal dynamic models in terms of the close association between mean sea level pressure patterns and rainfall during winter over south-west Western Australia by means of Bayesian hierarchical modelling. This approach allows us to understand characteristics of the spatiotemporal variability of the mean sea level pressure patterns and the associated rainfall patterns. An application is presented to show the effectiveness of the technique to reconstruct present day rainfall and to predict future rainfall.

In the quantitative analysis of dynamic contrast-enhanced magnetic resonance imaging compartment models allow the uptake of contrast medium to be described with biologically meaningful kinetic parameters. As simple models often fail to describe adequately the observed uptake behaviour, more complex compartment models have been proposed. However, the non-linear regression problem arising from more complex compartment models often suffers from parameter redundancy. We incorporate spatial smoothness on the kinetic parameters of a two-tissue compartment model by imposing Gaussian Markov random-field priors on them. We analyse to what extent this spatial regularization helps to avoid parameter redundancy and to obtain stable parameter point estimates per voxel. Choosing a full Bayesian approach, we obtain posteriors and point estimates by running Markov chain Monte Carlo simulations. The approach proposed is evaluated for simulated concentration time curves as well as for *in vivo* data from a breast cancer study.

We develop methods for analysing the spatial pattern of events, classified into several types, that occur on a network of lines. The motivation is the study of small protrusions called ‘spines’ which occur on the dendrite network of a neuron. The spatially varying density of spines is modelled by using relative distributions and regression trees. Spatial correlations are investigated by using counterparts of the *K*-function and pair correlation function, where the main problem is to compensate for the network geometry. This application illustrates the need for careful analysis of spatial variation in the intensity of points, before assessing any evidence of clustering.

A major issue in non-inferiority trials is the controversial assumption of constancy, namely that the active control has the same effect relative to placebo as in previous studies comparing the active control with placebo. The constancy assumption is often in doubt, which has motivated various methods that ‘discount’ the control effect estimate from historical data as well as methods that adjust for imbalances in observed covariates. We develop a new approach to deal with residual inconstancy, i.e. possible violations of the constancy assumption due to imbalances in unmeasured covariates after adjusting for the measured covariates. We characterize the extent of residual inconstancy under a generalized linear model framework and use the results to obtain fully adjusted estimates of the control effect in the current study based on plausible assumptions about an unmeasured covariate. Because such assumptions may be difficult to justify, we propose a sensitivity analysis approach that covers a range of situations. This approach is developed for indirect comparison with placebo and effect retention, and implemented through additive and multiplicative adjustments. The approach proposed is applied to two examples concerning benign prostate hyperplasia and human immunodeficiency virus infection, and evaluated in simulation studies.

Our application data are produced from a scalable, on-line expert elicitation process that incorporates hundreds of participating raters to score the importance of research goals for the prevention of suicide with the purpose of informing policy making. We develop a Bayesian formulation for analysis of ordinal multirater data motivated by our application. Our model employs a non-parametric mixture distribution over rater-indexed parameters for a latent continuous response under a Poisson–Dirichlet process mixing measure that allows inference about distinct rater behavioural and learning typologies from realized clusters.

Despite the widespread use of equal randomization in clinical trials, response-adaptive randomization has attracted considerable interest. There is typically a prerun of equal randomization before the implementation of response-adaptive randomization, although it is often not clear how many subjects are needed in this prephase, and in practice the number of patients in the equal randomization stage is often arbitrary. Another concern that is associated with realtime response-adaptive randomization is that trial conduct often requires patients' responses to be immediately available after the treatment, whereas clinical responses may take a relatively long period of time to exhibit. To resolve these two issues, we propose a two-stage procedure to achieve a balance between power and response, which is equipped with a likelihood ratio test before skewing the allocation probability towards a better treatment. Furthermore, we develop a non-parametric fractional model and a parametric survival design with an optimal allocation scheme to tackle the common problem caused by delayed response. We evaluate the operating characteristics of the two-stage designs through extensive simulation studies and illustrate them with a human immunodeficiency virus clinical trial. Numerical results show that the methods proposed satisfactorily resolve the arbitrary size of the equal randomization phase and the delayed response problem in response-adaptive randomization.

Stable isotope sourcing is used to estimate proportional contributions of sources to a mixture, such as in the analysis of animal diets and plant nutrient use. Statistical methods for inference on the diet proportions by using stable isotopes have focused on the linear mixing model. Existing frequentist methods assume that the diet proportion vector can be uniquely solved for in terms of one or two isotope ratios. We develop large sample methods that apply to an arbitrary number of isotope ratios, assuming that the linear mixing model has a unique solution or is overconstrained. We generalize these methods to allow temporal modelling of the population mean diet, assuming that isotope ratio response data are collected over time. The methodology is motivated by a study of the diet of dunlin, a small migratory seabird.

The analysis of genomics alterations that may occur in nature when segments of chromosomes are copied (known as copy number alterations) has been a focus of research to identify genetic markers of cancer. One high throughput technique that has recently been adopted is the use of molecular inversion probes to measure probe copy number changes. The resulting data consist of high dimensional copy number profiles that can be used to ascertain probe-specific copy number alterations in correlative studies with patient outcomes to guide risk stratification and future treatment. We propose a novel Bayesian variable selection method, the hierarchical structured variable selection method, which accounts for the natural gene and probe-within-gene architecture to identify important genes and probes associated with clinically relevant outcomes. We propose the hierarchical structured variable selection model for grouped variable selection, where simultaneous selection of both groups and within-group variables is of interest. The hierarchical structured variable selection model utilizes a discrete mixture prior distribution for group selection and group-specific Bayesian lasso hierarchies for variable selection within groups. We provide methods for accounting for serial correlations within groups that incorporate Bayesian fused lasso methods for within-group selection. Through simulations we establish that our method results in lower model errors than other methods when a natural grouping structure exists. We apply our method to a molecular inversion probe study of breast cancer and show that it identifies genes and probes that are significantly associated with clinically relevant subtypes of breast cancer.

In recent decades there has been an increase in the reported incidence of clinical pertussis in many countries. Estimation of the true circulation of the bacterium *Bordetella pertussis* is most reliably made on the basis of studies that measure antibody concentrations against pertussis toxin. Antibody levels decay over time and provide a fading memory of the infection. We develop a discrete bivariate mixture model for paired antibody levels in a cohort of 1002 Mexican adolescents who were followed over the 2008–2009 school year. This model postulates three groups of children based on past pertussis infection; never, prior and new. On the basis of this model we directly estimate incidence and prevalence, and select a diagnostic cut-off for classifying children as recently infected. We also discuss a relatively simple approach that uses only ‘discordant’ children who test positively on one visit and negatively on the other. The discordant approach provides inferences that are very similar to those of the full model when the data follow the assumed full model. Additionally, the discordant method is much more robust to model misspecification than the full model which has substantial problems with optimization. We estimate the school year incidence of pertussis to be about 3% and the prevalence to be about 8%. A cut-off of 50 was estimated to have about 99.5% specificity and 68% sensitvity.

We propose a method for assessing variable importance in matched case–control investigations and other highly stratified studies characterized by high dimensional data (*p*>>*n*). In simulated and real data sets, we show that the algorithm proposed performs better than a conventional univariate method (conditional logistic regression) and a popular multivariable algorithm (random forests) that does not take the matching into account. The methods are applicable to wide ranging, high impact clinical studies including metabolomic, proteomic studies and neuroimaging analyses, such as those assessing stroke and Alzheimer's disease. The methods proposed have been implemented in a freely available R library (http://cran.r-project.org/web/packages/RPCLR/index.html).

Using data collected from the ‘Sequenced treatment alternatives to relieve depression’ study, we use logistic regression to predict whether a patient will respond to treatment on the basis of early symptom change and patient characteristics. Model selection criteria such as the Akaike information criterion AIC and mean-squared-error of prediction MSEP may not be appropriate if the aim is to predict with a high degree of certainty who will respond or not respond to treatment. Towards this aim, we generalize the definition of the positive and negative predictive value curves to the case of multiple predictors. We point out that it is the ordering rather than the precise values of the response probabilities which is important, and we arrive at a unified approach to model selection via two-sample rank tests. To avoid overfitting, we define a cross-validated version of the positive and negative predictive value curves and compare these curves after smoothing for various models. When applied to the study data, we obtain a ranking of models that differs from those based on AIC and MSEP, as well as a tree-based method and regularized logistic regression using a lasso penalty. Our selected model performs consistently well for both 4-week-ahead and 7-week-ahead predictions.