MULTILEVEL DISCRETE‐TIME EVENT HISTORY MODELS WITH APPLICATIONS TO THE ANALYSIS OF RECURRENT EMPLOYMENT TRANSITIONS

Data on the timing of events such as births, residential moves and changes in employment status are collected in many longitudinal surveys. These data often have a highly complex structure, with events of several types occurring repeatedly over time to an individual and interdependences between different event processes (e.g. births and employment transitions). The aim of this paper is to review a general class of multilevel discrete‐time event history models for handling recurrent events and transitions between multiple states. It is also shown how standard methods can be extended to allow for time‐varying covariates that are outcomes of an event process that is jointly determined with the process of interest. The considerable potential of these methods for studying transitions through the life course is illustrated in analyses of the effect of the presence and age of children on women's employment transitions, using data from the British Household Panel Survey.     

Monitoring point patterns for the development of space–time clusters

Existing statistical methods for the detection of space–time clusters of point events are retrospective, in that they are used to ascertain whether space–time clustering exists among a fixed number of past events. In contrast, prospective methods treat a series of observations sequentially, with the aim of detecting quickly any changes that occur in the series. In this paper, cumulative sum methods of monitoring are adapted for use with Knox's space–time statistic. The result is a procedure for the rapid detection of any emergent space–time interactions for a set of sequentially monitored point events. The approach relies on a 'local' Knox statistic that is useful in retrospective analyses to detect when and where space–time interaction occurs. The distribution of the local Knox statistic under the null hypothesis of no space–time interaction is derived. The retrospective local statistic and the prospective cumulative sum monitoring method are illustrated by using previously published data on Burkitt's lymphoma in Uganda.     

Regression analysis for discrete event history or failure time data

The paper deals with discrete-time regression models to analyze multistate—multiepisode models for event history data or failure time data collected in follow-up studies, retrospective studies, or longitudinal panels. The models are applicable if the events are not dated exactly but only a time interval is recorded. The models include individual specific parameters to account for unobserved heterogeneity. The explantory variables may be time-varying and random with distributions depending on the observed history of the process. Different estimation procedures are considered: Estimation of structural as well as individual specific parameters by maximization of a joint likelihood function, estimation of the structural parameters by maximization of a conditional likelihood function conditioning on a set of sufficient statistics for the individual specific parameters, and estimation of the structural parameters by maximization of a marginal likelihood function assuming that the individual specific parameters follow a distribution. The advantages and limitations of the different approaches are discussed.     

A Further Study on Reliable Life Estimation under Ranked Set Sampling

This article considers nonparametric estimation of reliable life based on ranked set sampling and its properties. It is proven analytically that the large sample efficiency of the reliable life estimator under the balanced ranked set sampling is higher than that under the simple random sampling of the same size, but the relative efficiency damps away as the reliable life moves away from the median on both directions. To improve the efficiency for the estimation of extreme reliable life, we then propose a reliable life estimator under a modified ranked set sampling protocol, its strong consistency and asymptotic normality are established. The proposed sampling is shown to be superior to the balanced ranked set sampling, and the relative advantage improves as the reliable life moves away from median. Finally, results of simulation studies for small sample as well as an application to a real data set are presented to illustrate some of the theoretical findings.     

Intertemporal consumer behaviour under structural changes in income

In this paper we analyze models of forward looking consumer behaviour and give empirical evidence for aggregate quarterly data for the Netherlands, 1967-1984. Special attention is devoted to the implications of unanticipated structural changes in the income process, which because of replanning, will have an impact on the consumption decision. We start with the life cycle hypothesis. Since the fall in aggregate consumption in the Netherlands in the eighties can not be explained by the life cycle model, the theory is reformulated by assuming that the planning horizon of the consumers moves ahead as time goes on. As a result, an error correction mechanism has to be introduced in the consumption function.The modified model is found to be in agreement with the data.     

BACKWARD ESTIMATION OF STOCHASTIC PROCESSES WITH FAILURE EVENTS AS TIME ORIGINS

Stochastic processes often exhibit sudden systematic changes in pattern a short time before certain failure events. Examples include increase in medical costs before death and decrease in CD4 counts before AIDS diagnosis. To study such terminal behavior of stochastic processes, a natural and direct way is to align the processes using failure events as time origins. This paper studies backward stochastic processes counting time backward from failure events, and proposes one-sample nonparametric estimation of the mean of backward processes when follow-up is subject to left truncation and right censoring. We will discuss benefits of including prevalent cohort data to enlarge the identifiable region and large sample properties of the proposed estimator with related extensions. A SEER-Medicare linked data set is used to illustrate the proposed methodologies.     

Bayesian analysis of zero-inflated regression models

In modeling defect counts collected from an established manufacturing processes, there are usually a relatively large number of zeros (non-defects). The commonly used models such as Poisson or Geometric distributions can underestimate the zero-defect probability and hence make it difficult to identify significant covariate effects to improve production quality. This article introduces a flexible class of zero inflated models which includes other familiar models such as the Zero Inflated Poisson (ZIP) models, as special cases. A Bayesian estimation method is developed as an alternative to traditionally used maximum likelihood based methods to analyze such data. Simulation studies show that the proposed method has better finite sample performance than the classical method with tighter interval estimates and better coverage probabilities. A real-life data set is analyzed to illustrate the practicability of the proposed method easily implemented using WinBUGS.     

Assessing Type I error and power of multistate Markov models for panel data—A simulation study

Ordinal outcomes collected at multiple follow-up visits are common in clinical trials. Sometimes, one visit is chosen for the primary analysis and the scale is dichotomized amounting to loss of information. Multistate Markov models describe how a process moves between states over time. Here, simulation studies are performed to investigate the Type I error and power characteristics of multistate Markov models for panel data with limited non-adjacent state transitions. The results suggest that the multistate Markov models preserve the Type I error and adequate power is achieved with modest sample sizes for panel data with limited non-adjacent state transitions.     

Outcome Prediction for Heart Failure Telemonitoring Via Generalized Linear Models with Functional Covariates

An effective methodology for dealing with data extracted from clinical surveys on heart failure linked to the Public Health Database is proposed. A model for recurrent events is used for modelling the occurrence of hospital readmissions in time, thus deriving a suitable way to compute individual cumulative hazard functions. Estimated cumulative hazard trajectories are then treated as functional data, and they are used as covariates along with clinical survey data within the framework of generalized linear models with functional covariates.     

Earthquakes occurrences estimation through a parametric semi-Markov approach

The estimation of earthquakes’ occurrences prediction in seismic areas is a challenging problem in seismology and earthquake engineering. Indeed, the prevention and the quantification of possible damage provoked by destructive earthquakes are directly linked to this kind of prevision. In our paper, we adopt a parametric semi-Markov approach. This model assumes that a sequence of earthquakes is seen as a Markov process and besides it permits to take into consideration the more realistic assumption of events’ dependence in space and time. The elapsed time between two consecutive events is modeled as a general Weibull distribution. We determine then the transition probabilities and the so-called crossing states probabilities. We conclude then with a Monte Carlo simulation and the model is validated through a large database containing real data.     

Multi-state Models: A Review

Multi-state models are models for a process, for example describing a life history of an individual, which at any time occupies one of a few possible states. This can describe several possible events for a single individual, or the dependence between several individuals. The events are the transitions between the states. This class of models allows for an extremely flexible approach that can model almost any kind of longitudinal failure time data. This is particularly relevant for modeling different events, which have an event-related dependence, like occurrence of disease changing the risk of death. It can also model paired data. It is useful for recurrent events, but has limitations. The Markov models stand out as much simpler than other models from a probability point of view, and this simplifies the likelihood evaluation. However, in many cases, the Markov models do not fit satisfactorily, and happily, it is reasonably simple to study non-Markov models, in particular the Markov extension models. This also makes it possible to consider, whether the dependence is of short-term or long-term nature. Applications include the effect of heart transplantation on the mortality and the mortality among Danish twins.     

Expressing Estimators of Expected Quality Adjusted Survival as Functions of Nelson-Aalen Estimators

Quality adjusted survival has been increasingly advocated in clinical trials to be assessed as a synthesis of survival and quality of life. We investigate nonparametric estimation of its expectation for a general multistate process with incomplete follow-up data. Upon establishing a representation of expected quality adjusted survival through marginal distributions of a set of defined events, we propose two estimators for expected quality adjusted survival. Expressed as functions of Nelson-Aalen estimators, the two estimators are strongly consistent and asymptotically normal. We derive their asymptotic variances and propose sample-based variance estimates, along with evaluation of asymptotic relative efficiency. Monte Carlo studies show that these estimation procedures perform well for practical sample sizes. We illustrate the methods using data from a national, multicenter AIDS clinical trial.     

Modelling spatio-temporal air pollution data from a mobile monitoring station

ABSTRACT

Environmental data is typically indexed in space and time. This work deals with modelling spatio-temporal air quality data, when multiple measurements are available for each space-time point. Typically this situation arises when different measurements referring to several response variables are observed in each space-time point, for example, different pollutants or size resolved data on particular matter. Nonetheless, such a kind of data also arises when using a mobile monitoring station moving along a path for a certain period of time. In this case, each spatio-temporal point has a number of measurements referring to the response variable observed several times over different locations in a close neighbourhood of the space-time point. We deal with this type of data within a hierarchical Bayesian framework, in which observed measurements are modelled in the first stage of the hierarchy, while the unobserved spatio-temporal process is considered in the following stages. The final model is very flexible and includes autoregressive terms in time, different structures for the variance-covariance matrix of the errors, and can manage covariates available at different space-time resolutions. This approach is motivated by the availability of data on urban pollution dynamics: fast measures of gases and size resolved particulate matter have been collected using an Optical Particle Counter located on a cabin of a public conveyance that moves on a monorail on a line transect of a town. Urban microclimate information is also available and included in the model. Simulation studies are conducted to evaluate the performance of the proposed model over existing alternatives that do not model data over the first stage of the hierarchy.     

Extraction of sea temperature in the Barents Sea by a scale space multiresolution method – prospects for Atlantic salmon

Variation of marine temperature at different time scales is a central environmental factor in the life cycle of marine organisms, and may have particular importance for various life stages of anadromous species, for example, Atlantic salmon. To understand the salient features of temperature variation we employ scale space multiresolution analysis, that uses differences of smooths of a time series to decompose it as a sum of scale-dependent components. The number of resolved components can be determined either automatically or by exploring a map that visualizes the structure of the time series. The statistical credibility of the features of the components is established with Bayesian inference. The method was applied to analyze a marine temperature time series measured from the Barents Sea and its correlation with the abundance of Atlantic salmon in three Barents Sea rivers. Besides the annual seasonal variation and a linear trend, the method revealed mid time-scale (～10 years) and long time-scale (～30 years) variation. The 10-year quasi-cyclical component of the temperature time series appears to be connected with a similar feature in Atlantic salmon abundance. These findings can provide information about the environmental factors affecting seasonal and periodic variation in survival and migrations of Atlantic salmon and other migratory fish.     

Analysis of longitudinal health-related quality of life data with terminal events

Longitudinal health-related quality of life data arise naturally from studies of progressive and neurodegenerative diseases. In such studies, patients’ mental and physical conditions are measured over their follow-up periods and the resulting data are often complicated by subject-specific measurement times and possible terminal events associated with outcome variables. Motivated by the “Predictor’s Cohort” study on patients with advanced Alzheimer disease, we propose in this paper a semiparametric modeling approach to longitudinal health-related quality of life data. It builds upon and extends some recent developments for longitudinal data with irregular observation times. The new approach handles possibly dependent terminal events. It allows one to examine time-dependent covariate effects on the evolution of outcome variable and to assess nonparametrically change of outcome measurement that is due to factors not incorporated in the covariates. The usual large-sample properties for parameter estimation are established. In particular, it is shown that relevant parameter estimators are asymptotically normal and the asymptotic variances can be estimated consistently by the simple plug-in method. A general procedure for testing a specific parametric form in the nonparametric component is also developed. Simulation studies show that the proposed approach performs well for practical settings. The method is applied to the motivating example.     

Retrospective Reporting of Household Wealth: Evidence From the 1983–1989 Survey of Consumer Finances

One way to obtain panel-like information on household wealth is to ask households about changes in their asset holdings. Yet the reliability of retrospective data is unclear, considering the potential for recall error. This article examines the reliability of retrospective reporting, using data from the 1983–1989 Survey of Consumer Finances. We find substantial inconsistencies between reported net investments in assets with measured changes in holdings. Inconsistencies are less severe for salient transactions like home sales and more severe for aggregated items like financial assets.     

The complexity of school and neighbourhood effects and movements of pupils on school differences in models of educational achievement

Summary.  Traditional studies of school differences in educational achievement use multilevel modelling techniques to take into account the nesting of pupils within schools. However, educational data are known to have more complex non-hierarchical structures. The potential importance of such structures is apparent when considering the effect of pupil mobility during secondary schooling on educational achievement. Movements of pupils between schools suggest that we should model pupils as belonging to the series of schools that are attended and not just their final school. Since these school moves are strongly linked to residential moves, it is important to explore additionally whether achievement is also affected by the history of neighbourhoods that are lived in. Using the national pupil database, this paper combines multiple membership and cross-classified multilevel models to explore simultaneously the relationships between secondary school, primary school, neighbourhood and educational achievement. The results show a negative relationship between pupil mobility and achievement, the strength of which depends greatly on the nature and timing of these moves. Accounting for pupil mobility also reveals that schools and neighbourhoods are more important than shown by previous analysis. A strong primary school effect appears to last long after a child has left that phase of schooling. The additional effect of neighbourhoods, in contrast, is small. Crucially, the rank order of school effects across all types of pupil is sensitive to whether we account for the complexity of the multilevel data structure.     

Economic design of quick switching sampling system for assuring Weibull distributed mean life

In this paper, we propose the quick switching sampling system for assuring mean life of a product under time truncated life test where the lifetime of the product follows the Weibull distribution and the mean life is considered as the quality of the product. The optimal parameters of the proposed system are determined using two points on the operating characteristic curve approach for various combinations of consumer's risk and ratio of true mean life time and specified life time. Tables are constructed to determine the optimal parameters for specified acceptable quality level and limiting quality level along with the corresponding probabilities of acceptance. The proposed system is compared with other existing sampling plans under Weibull lifetime model. In addition, an economical design of the proposed system is also discussed.     

Robust variable selection with application to quality of life research

A large database containing socioeconomic data from 60 communities in Austria and Germany has been built, stemming from 18,000 citizens’ responses to a survey, together with data from official statistical institutes about these communities. This paper describes a procedure for extracting a small set of explanatory variables to explain response variables such as the cognition of quality of life. For better interpretability, the set of explanatory variables needs to be very small and the dependencies among the selected variables need to be low. Due to possible inhomogeneities within the data set, it is further required that the solution is robust to outliers and deviating points. In order to achieve these goals, a robust model selection method, combined with a strategy to reduce the number of selected predictor variables to a necessary minimum, is developed. In addition, this context-sensitive method is applied to obtain responsible factors describing quality of life in communities.