In the estimation of a lifetime distribution from regular interval-censored data with an additional censoring variable, we focus on the case where (contrary to the actuarial method) both events (interest and censorship) can occur on a given individual in the same interval and, thus, are observed simultaneously. Specifically, we consider a population where individuals pass through a finite number of successive stages during their growth and are threatened by a disease. First, we estimate the lifetime and time-to-disease distributions in each developmental stage from such censored data. Using data that were recorded on a cohort of individuals followed over a long period of time, we propose a non-parametric, yet continuously differentiable and piecewise quadratic polynomial, estimator for the survival function of each of these distributions. We applied it to estimate, from weekly field observations in Mbankomo (Cameroon), the lifetime and time-to-disease distributions of cocoa fruits in each of their three developmental stages before maturity. It is found that on average a healthy cocoa fruit spends only weeks in its first stage (cherelle), compared with nearly 9 weeks as a young pod and weeks as an adult pod. In a second phase, however, adapting our methodology to competing risks estimation, we observed that, owing to the severe rate of attacks, the fruits' effective lifetime expectancy in farmland is much shorter. Indeed, in that part of Cameroon, the cumulative risk of an attack on cocoa fruits in farmland, especially by pod rot disease, far outweighs their chances of reaching maturity.

Motivated by the need to understand the dynamics of relationship formation and dissolution over time in real world social networks we develop a new longitudinal model for transitions in the relationship status of pairs of individuals (‘dyads’). We first specify a model for the relationship status of a single dyad and then extend it to account for important interdyad dependences (e.g. transitivity—‘a friend of a friend is a friend’) and heterogeneity. Model parameters are estimated by using Bayesian analysis implemented via Markov chain Monte Carlo sampling. We use the model to perform novel analyses of two diverse longitudinal friendship networks: an excerpt of the Teenage Friends and Lifestyle Study (a moderately sized network) and the Framingham Heart Study (a large network).

There is growing interest in understanding the heterogeneity of treatment effects (HTE), which has important implications in treatment evaluation and selection. The standard approach to assessing HTE (i.e. subgroup analyses based on known effect modifiers) is informative about the heterogeneity between subpopulations but not within. It is arguably more informative to assess HTE in terms of individual treatment effects, which can be defined by using potential outcomes. However, estimation of HTE based on potential outcomes is challenged by the lack of complete identifiability. The paper proposes methods to deal with the identifiability problem by using relevant information in baseline covariates and repeated measurements. If a set of covariates is sufficient for explaining the dependence between potential outcomes, the joint distribution of potential outcomes and hence all measures of HTE will then be identified under a conditional independence assumption. Possible violations of this assumption can be addressed by including a random effect to account for residual dependence or by specifying the conditional dependence structure directly. The methods proposed are shown to reduce effectively the uncertainty about HTE in a trial of human immunodeficiency virus.

The paper develops a framework for volatility graphics in financial time series analysis which allows exploration of the time progression of volatility and the dependence of volatility on past behaviour. It is particularly suitable for identifying volatility structure to be incorporated in specific volatility models. Plotting techniques are identified on the basis of a general time series volatility model and are illustrated on the Financial Times Stock Exchange 100-Share Index financial time series. They are statistically validated by bootstrapping and application to simulated volatile and non-volatile series, generated by both conditionally heteroscedastic and stochastic volatility models. An important point is that volatility can only be properly visualized and analysed for linearly uncorrelated or decorrelated series.

We explore a particular fully parametric approach to quantile regression and show that this approach can be very successful. Motivated by the provision of reference charts, we work in the specific context of a positive response variable, whose conditional distribution is modelled by the generalized gamma distribution, and a single covariate, the dependence of parameters of the generalized gamma distribution on which is through simple linear and log-linear forms. With only six parameters at most, such models allow a perhaps surprisingly wide range of distributional shapes that seems adequate for many practical situations. We show that maximum likelihood estimation of the models is computationally quite straightforward, that the estimated quantiles behave well, that use of standard maximum likelihood asymptotics to perform likelihood ratio tests of the number of parameters needed and to give pointwise confidence bands based on the expected information matrix are reliable in this context, and we more tentatively provide a simple goodness-of-fit test of the whole model. Two data analyses, from the health and environmental spheres, are included, along with simulation results. We claim that quite a direct parametric maximum likelihood approach like this—which also obviates the problem of quantile crossing—is adequate for many situations, and there is less need than one might think to resort to more complicated semiparametric and non-parametric approaches to quantile regression in practice.

To investigate interactions between parasite species in a host, a population of field voles was studied longitudinally, with presence or absence of six different parasites measured repeatedly. Although trapping sessions were regular, a different set of voles was caught at each session, leading to incomplete profiles for all subjects. We use a discrete time hidden Markov model for each disease with transition probabilities dependent on covariates via a set of logistic regressions. For each disease the hidden states for each of the other diseases at a given time point form part of the covariate set for the Markov transition probabilities from that time point. This allows us to gauge the influence of each parasite species on the transition probabilities for each of the other parasite species. Inference is performed via a Gibbs sampler, which cycles through each of the diseases, first using an adaptive Metropolis–Hastings step to sample from the conditional posterior of the covariate parameters for that particular disease given the hidden states for all other diseases and then sampling from the hidden states for that disease given the parameters. We find evidence for interactions between several pairs of parasites and of an acquired immune response for two of the parasites.

Acute infectious diseases are transmitted over networks of social contacts. Epidemic models are used to predict the spread of emergent pathogens and to compare intervention strategies. Many of these models assume equal probability of contact within mixing groups (homes, schools, etc.), but little work has inferred the actual contact network, which may influence epidemic estimates. We develop a penalized likelihood method to infer contact networks within households, which are a key area for disease transmission. Using egocentric surveys of contact behaviour in Belgium, we estimate within-household contact networks for six different age compositions. Our estimates show dependence in contact behaviour and vary substantively by age composition, with fewer contacts in older households. Our results are relevant for epidemic models that are used to make policy recommendations.

Secondary ion mass spectrometry is a popular physical technique that allows learning elemental and chemical compositions of various substances. In some cases, the mass spectrum of the sample studied is not observable without that of the liquid solution in which the investigated substance must be placed. To separate the informative part of the observed mixed spectrum from the irrelevant liquid solution part, we develop an approach that is based on finite mixtures. Finite mixture modelling is a statistical technique that is capable of accounting for various shapes and patterns in data. We discuss a mixture model constructed with bell-shaped discrete component distributions that can be employed in the mass spectrometry framework for extracting the informative part of the mixed spectrum of organic objects. The results for assessing variability in the mass spectrum extracted are derived. The procedure is thoroughly illustrated on simulated data sets and applied to several real life problems that are concerned with complex organic dyes placed in a glycerol liquid matrix. The results obtained have clear chemical interpretation and suggest that the approach proposed is very promising.

Conditional auto-regressive models are commonly used to capture spatial cor relation in areal unit data, as part of a hierarchical Bayesian model. The spatial correlation structure that is induced by these models is determined by geographical adjacency, but this is too simplistic for some real data sets, which can visually exhibit subregions of strong correlation as well as locations at which the response exhibits a step change. An example of this, and the motivation for the paper, is the spatial pattern in respiratory disease risk in the 271 intermed iate geographies in the Greater Glasgow and Clyde Health Board in 2005. The methodology proposed is an extension to the class of conditional auto-regressive priors, which allow them to capture such localized spatial correlation and to identify step changes. The approach takes the form of an iterative algorithm, which sequentially updates the spatial correlation structure that is assumed by the model in addition to estimating the remaining parameters. The efficacy of the approach is assessed by simulation, before being applied to the motivating Greater Glasgow application.

Ecological momentary assessment is a method for collecting realtime data in subjects' environments. It often uses electronic devices to obtain information on psychological state through administration of questionnaires at times that are selected from a probability-based sampling design. This information can be used to model the effect of momentary variation in psychological state on the lifetimes to events such as smoking lapse. Motivated by this, a probability sampling framework is proposed for estimating the effect of time varying covariates on the lifetimes to events. Presented as an alternative to joint modelling of the covariate process as well as event lifetimes, this framework calls for sampling covariates at the event lifetimes and at times that are selected according to a probability-based sampling design. A design-unbiased estimator for the cumulative hazard is substituted into the log-likelihood, and the resulting objective function is maximized to obtain the proposed estimator. This estimator has two quantifiable sources of variation: that due to the survival model and that due to sampling the covariates. Data from a nicotine patch trial are used to illustrate the approach proposed.