Summary. To assess the value of a continuous marker in predicting the risk of a disease, a graphical tool called the predictiveness curve has been proposed. It characterizes the marker's predictiveness, or capacity to stratify risk for the population, by displaying the distribution of risk endowed by the marker. Methods for making inference about the curve and for comparing curves in a general population have been developed. However, knowledge about a marker's performance in the general population only is not enough. Since a marker's effect on the risk model and its distribution can both differ across subpopulations, its predictiveness may vary when applied to different subpopulations. Moreover, information about the predictiveness of a marker conditional on baseline covariates is valuable for individual decision-making about having the marker measured or not. Therefore, to realize the usefulness of a risk prediction marker fully, it is important to study its performance conditional on covariates. We propose semiparametric methods for estimating covariate-specific predictiveness curves for a continuous marker. Unmatched and matched case[ndash]control study designs are accommodated. We illustrate application of the methodology by evaluating serum creatinine as a predictor of risk of renal artery stenosis.

Summary. Statistical methodology for the analysis of proteomic mass spectrometry data is proposed using mixed effects models. Each high dimensional spectrum is represented by using a near orthogonal low dimensional representation with a basis of Gaussian mixture functions. Linear mixed effect models are proposed in the lower dimensional space. In particular, differences between groups are investigated by using fixed effect parameters, and individual variability of spectra is modelled by using random effects. A deterministic peak fitting algorithm provides estimates of the near orthogonal Gaussian basis. The mixed effects model is fitted by using restricted maximum likelihood, and a parallel fitting procedure is used for computational convenience. The methodology is applied to proteomic mass spectrometry data from serum samples from melanoma patients who were categorized as stage I or stage IV, and significant locations of peaks are identified.

Summary. The paper discusses techniques for analysis of sequential data from variable processes, particularly techniques that can be used even when the data are not equally spaced in time. The techniques are based on models which use continuous time Brownian motion and its integrals to describe the pattern of variation in an underlying physical process and use white noise to describe variation due to measurement processes. The paper concentrates on making statements about what has been happening in the region that is covered by the data rather than on making predictions about regions that are far from the data. It is argued that the continuous time integrated Brownian motion plus white noise model is always preferable to its discrete time analogue: the local linear trend model. Further integrals of Brownian motion can be fitted as an alternative to using splines. All of these continuous time Brownian motion models can be fitted to data that are associated with a time interval (interval data) as well as to data that are associated with a single time (spot data). They can be fitted by using mixed model methodology as well as by using Kalman filtering and smoothing.

Summary. Persistent disturbing behaviour refers to a chronic condition in highly unstable, therapy resistant psychiatric patients. Because these patients are difficult to maintain in their natural living environment and even in hospital wards, purposely designed residential psychiatric facilities need to be established. Therefore, it is important to define and circumscribe the group carefully. Serroyen and co-workers, starting from the longitudinal analysis of a score based on data from the Belgian national psychiatric registry, undertook a discriminant analysis to distinguish persistent disturbing behaviour patients from a control group. They also indicated that there is scope for further subdividing the persistent disturbing behaviour patients into two subgroups, using conventional cluster analysis techniques. We employ a variety of novel longitudinal-data-based cluster analysis techniques. These are based on either conventional growth models, growth[ndash]mixture models or latent class growth models. Unlike in earlier analyses, where some evidence for two groups was found, there now is an indication of three groups, which is a finding with high practical and organizational relevance.

Summary. The self-controlled case series model may be used to analyse recurrent events when event times are conditionally independent given fixed or random individual effects. To test the hypothesis of within-individual independence, the model is augmented by an association parameter for diagonal dependence, which provides the focus for a test of independence. Estimation methods are described, and simulations are presented to illustrate the power of the method in relevant scenarios, and to quantify the bias resulting from failure of the independence assumption. The methods are applied to two data sets, relating to a rare bleeding disorder and to myocardial infarction.

Summary. The hypobaric decompression sickness data study was conducted by the National Aeronautics and Space Administration to investigate the risk of decompression sickness in hypobaric environments. The quantity of interest is the time to onset of grade IV venous gas emboli, which was mixed case interval censored because of measurement limitations. In the study, some subjects participated in multiple experiments, leading to repeated and correlated measurements on those subjects. In addition, it has been suggested that some subjects had a much lower risk of developing grade IV venous gas emboli than others, i.e. those subjects were immune from the event of interest (or 'cured'). We propose to use two-part models, where the first part describes the probability of cure and the second part describes the survival for susceptible subjects. We use two random effects to account for the correlated nature of measurements. A leverage bootstrap approach is proposed for model diagnosis. A simulation study shows satisfactory performance of the estimation and diagnosis approaches proposed. Model estimation and evaluation of the hypobaric decompression sickness data are carefully investigated.

Summary. In meteorology, the traditional approach to forecasting employs deterministic models mimicking atmospheric dynamics. Forecast uncertainty due to partial knowledge of the initial conditions is tackled by ensemble predictions systems. Probabilistic forecasting is a relatively new approach which may properly account for all sources of uncertainty. We propose a hierarchical Bayesian model which develops this idea and makes it possible to deal with ensemble predictions systems with non-identifiable members by using a suitable definition of the second level of the model. An application to Italian small-scale temperature data is shown.

Summary. Sample selection models attempt to correct for non-randomly selected data in a two-model hierarchy where, on the first level, a binary selection equation determines whether a particular observation will be available for the second level, i.e. in the outcome equation. Ignoring the non-random selection mechanism that is induced by the selection equation may result in biased estimation of the coefficients in the outcome equation. In the application that motivated this research, we analyse relief supply in earthquake-affected communities in Pakistan, where the decision to deliver goods represents the dependent variable in the selection equation whereas factors that determine the amount of goods supplied are analysed in the outcome equation. In this application, the inclusion of spatial effects is necessary since the available covariate information on the community level is rather scarce. Moreover, the high temporal dynamics underlying the immediate delivery of relief supply after a natural disaster calls for non-linear, time varying effects. We propose a geoadditive sample selection model that allows us to address these issues in a general Bayesian framework with inference being based on Markov chain Monte Carlo simulation techniques. The model proposed is studied in simulations and applied to the relief supply data from Pakistan.

Summary. In some assays, a diluted suspension of infected cells is plated onto multiple wells. In each well the number of genome copies of virus, Y, is recorded, but interest focuses on the number of infected cells, X, and the number of genome copies in the infected cells, W1,[hellip],WX. The statistical problem is to recover the distribution or at least moments of X and W on the basis of the convolution Y. We evaluate various parametric statistical models for this 'mixture'- type problem and settle on a flexible robust approach where X follows a two-component Poisson mixture model and W is a shifted negative binomial distribution. Data analysis and simulations reveal that the means and occasionally variances of X and W can be reliably captured by the model proposed. We also identify the importance of selecting an appropriate dilution for a reliable assay.

Summary. We analyse the effects of various treatments on cotton aphids (Aphis gossypii). The standard analysis of count data on cotton aphids determines parameter values by assuming a deterministic growth model and combines these with the corresponding stochastic model to make predictions on population sizes, depending on treatment. Here, we use an integrated stochastic model to capture the intrinsic stochasticity, of both observed aphid counts and unobserved cumulative population size for all treatment combinations simultaneously. Unlike previous approaches, this allows us to explore explicitly and more accurately to assess treatment interactions. Markov chain Monte Carlo methods are used within a Bayesian framework to integrate over uncertainty that is associated with the unobserved cumulative population size and estimate parameters. We restrict attention to data on aphid counts in the Texas High Plains obtained for three different levels of irrigation water, nitrogen fertilizer and block, but we note that the methods that we develop can be applied to a wide range of problems in population ecology.

Summary. Many popular estimators for duration models require independent competing risks or independent censoring. In contrast, copula-based estimators are also consistent in the presence of dependent competing risks. We suggest a computationally convenient extension of the copula graphic estimator to a model with more than two dependent competing risks. We analyse the applicability of this estimator by means of simulations and unemployment duration data from Germany. We obtain evidence that our estimator yields nice results if the dependence structure is known and that it is a powerful tool for the assessment of the relevance of (in-)dependence assumptions in applied duration research.