A Non-parametric Frailty Model for Temporally Clustered Multivariate Failure Times

Abstract A model is introduced here for multivariate failure time data arising from heterogenous populations. In particular, we consider a situation in which the failure times of individual subjects are often temporally clustered, so that many failures occur during a relatively short age interval. The clustering is modelled by assuming that the subjects can be divided into ‘internally homogenous’ latent classes, each such class being then described by a time‐dependent frailty profile function. As an example, we reanalysed the dental caries data presented earlier in Härkänen et al. [Scand. J. Statist. 27 (2000) 577], as it turned out that our earlier model could not adequately describe the observed clustering.     

Scheduling algorithms for computer-aided line balancing in printed circuit board assembly

Generalized flexible flow line (GFFL) is a scheduling environment comprising several machine banks which the products visit in the same order but can skip some machine banks. The type of machines in a bank can differ but they are suitable for performing the same manufacturing tasks. To change one product to another demands a set-up operation of the machine. This paper describes several scheduling algorithms for the GFFL problem. The overall structure of these algorithms is similar, consisting of machine allocation and sequencing phases. The algorithms have been integrated into an interactive production scheduling system for electronics assembly. Sample cases are used to illustrate the operation of the system in practice.     

Systematic handling of missing data in complex study designs – experiences from the Health 2000 and 2011 Surveys

We present a systematic approach to the practical and comprehensive handling of missing data motivated by our experiences of analyzing longitudinal survey data. We consider the Health 2000 and 2011 Surveys (BRIF8901) where increased non-response and non-participation from 2000 to 2011 was a major issue. The model assumptions involved in the complex sampling design, repeated measurements design, non-participation mechanisms and associations are presented graphically using methodology previously defined as a causal model with design, i.e. a functional causal model extended with the study design. This tool forces the statistician to make the study design and the missing-data mechanism explicit. Using the systematic approach, the sampling probabilities and the participation probabilities can be considered separately. This is beneficial when the performance of missing-data methods are to be compared. Using data from Health 2000 and 2011 Surveys and from national registries, it was found that multiple imputation removed almost all differences between full sample and estimated prevalences. The inverse probability weighting removed more than half and the doubly robust method 60% of the differences. These findings are encouraging since decreasing participation rates are a major problem in population surveys worldwide.     

Measurement and socio-demographic variation of social capital in a large population-based survey

Objectives The main objective of this study was to describe the variation of individual social capital according to socio-demographic factors, and to develop a suitable way to measure social capital for this purpose. The similarity of socio-demographic variation between the genders was also assessed. Data and methods The study applied cross-sectional data from the national Finnish Health 2000 survey (n = 8,028) which represents the adult population, aged 30 years and over. Several variables indicating social capital were condensed to dimensions on the basis of factor analysis. Participants were categorized into tertiles in each dimension of social capital by means of factor scores. The multinomial logistic regression model was used to produce the adjusted prevalences for the dimensions of social capital according to socio-demographic categories (age, gender, education, living arrangements, income, and type of region). Results Three dimensions of social capital were distinguished: social support, social participation and networks, and trust and reciprocity. Age had an inverse association with social support as well as participation and networks, and a curvilinear association between age and trust and reciprocity, the oldest age groups showing the highest level of trust. Married persons and those in the highest educational and income groups tended to have more social capital than other persons. Residents of urban and rural regions did not systematically differ from each other in their level of social capital although residents of urban regions participated less and showed less trust than people living in semi-urban or rural regions. Social support varied significantly with gender. The decline of social support by age was steeper in women than in men. Social participation and networks increased with education, the gradient appearing steeper among men. The difference between married and cohabiting men was substantial compared to women when it came to trust. Conclusions People who are young, married, educated, and well-off have plenty of social capital. This information might help various services to concentrate the actions on the people in danger of social exclusion. Our results also form a basis for the future by allowing the changes in social capital to be examined over time and over different studies.     

Elevator planning with stochastic multicriteria acceptability analysis

Modern elevator systems in high-rise buildings consist of groups of elevators with centralized control. The goal in elevator planning is to configure a suitable elevator group to be built. The elevator group must satisfy specific minimum requirements for a number of standard performance criteria. In addition, it is desirable to optimize the configuration in terms of other criteria related to the performance, economy and service level of the elevator group. Different stakeholders involved in the planning phase emphasize different criteria. Most of the criteria measurements are by nature uncertain. Some criteria can be estimated by using analytical models, while others, especially those related to the service level in different traffic patterns, require simulations.     

Algorithmic parameterization of mixed treatment comparisons

Mixed Treatment Comparisons (MTCs) enable the simultaneous meta-analysis (data pooling) of networks of clinical trials comparing ??2 alternative treatments. Inconsistency models are critical in MTC to assess the overall consistency between evidence sources. Only in the absence of considerable inconsistency can the results of an MTC (consistency) model be trusted. However, inconsistency model specification is non-trivial when multi-arm trials are present in the evidence structure. In this paper, we define the parameterization problem for inconsistency models in mathematical terms and provide an algorithm for the generation of inconsistency models. We evaluate running-time of the algorithm by generating models for 15 published evidence structures.     

Tractable Bayesian learning of tree belief networks

In this paper we present decomposable priors, a family of priors over structure and parameters of tree belief nets for which Bayesian learning with complete observations is tractable, in the sense that the posterior is also decomposable and can be completely determined analytically in polynomial time. Our result is the first where computing the normalization constant and averaging over a super-exponential number of graph structures can be performed in polynomial time. This follows from two main results: First, we show that factored distributions over spanning trees in a graph can be integrated in closed form. Second, we examine priors over tree parameters and show that a set of assumptions similar to Heckerman, Geiger and Chickering (1995) constrain the tree parameter priors to be a compactly parametrized product of Dirichlet distributions. Besides allowing for exact Bayesian learning, these results permit us to formulate a new class of tractable latent variable models in which the likelihood of a data point is computed through an ensemble average over tree structures.     

Bayesian parameter estimation via variational methods

We consider a logistic regression model with a Gaussian prior distribution over the parameters. We show that an accurate variational transformation can be used to obtain a closed form approximation to the posterior distribution of the parameters thereby yielding an approximate posterior predictive model. This approach is readily extended to binary graphical model with complete observations. For graphical models with incomplete observations we utilize an additional variational transformation and again obtain a closed form approximation to the posterior. Finally, we show that the dual of the regression problem gives a latent variable density model, the variational formulation of which leads to exactly solvable EM updates.     

Caries on Permanent Teeth: A Non-parametric Bayesian Analysis

Most earlier epidemiological investigations of dental caries have been based on cross-sectional data. Subject-specific information of dental caries in the past, and the duration of exposure of each tooth to the oral environment, are obviously important factors also influencing the presence of dental caries in the future. This has led us to consider multivariate survival models in which the information about the tooth eruption and failure times are combined to assess caries risk. A non-parametric Bayesian intensity model is presented, reflecting, on the one hand, the within subject and between subject sources of variability, and a corresponding split of variability when considering the 28 permanent teeth. We analyse a data set consisting of the dental history of 240 boys, where the observations are based on predetermined dental examinations taking place approximately once every year. Markov chain Monte Carlo integration techniques are applied in the numerical work.     

Non‐parametric Bayesian Intensity Model: Exploring Time‐to‐Event Data on Two Time Scales

Time‐to‐event data have been extensively studied in many areas. Although multiple time scales are often observed, commonly used methods are based on a single time scale. Analysing time‐to‐event data on two time scales can offer a more extensive insight into the phenomenon. We introduce a non‐parametric Bayesian intensity model to analyse two‐dimensional point process on Lexis diagrams. After a simple discretization of the two‐dimensional process, we model the intensity by a one‐dimensional piecewise constant hazard functions parametrized by the change points and corresponding hazard levels. Our prior distribution incorporates a built‐in smoothing feature in two dimensions. We implement posterior simulation using the reversible jump Metropolis–Hastings algorithm and demonstrate the applicability of the method using both simulated and empirical survival data. Our approach outperforms commonly applied models by borrowing strength in two dimensions.