Statistical Modelling

This article considers some simple observation-driven time series models for counts. We provide a brief description of the class of integer-valued autoregressive (INAR) and integer-valued moving average (INMA) processes. These classes of models may be attractive when the data exhibit a significant serial dependence structure. We, therefore, briefly review various testing procedures useful for assessing the serial correlation in the data. Once it is established that the data are not serially independent, suitable INAR or INMA processes may be employed to model the data. In the important first order INAR model, we discuss various methods of estimating the structural parameters of the process. We also give a short account of the extension of some of these estimation procedures to second order INAR models. Moving average counterparts of both models are also entertained. Throughout, the models and methods are illustrated in the context of a famous data set from the branching process literature that turns out to be surprisingly difficult to model satisfactorily.

We propose a modeling framework for ultra-high-frequency data on financial asset price movements. The models proposed belong to the class of the doubly stochastic Poisson processes with marks and allow an interpretation of the changes in price volatility and trading activity in terms of news or information arrival. Assuming that the intensity process underlying event arrivals is unobserved by market agents, we propose a signal extraction (filtering) method based on the reversible jump Markov chain Monte Carlo algorithm. Moreover, given a realization of the price process, inference on the parameters can be performed by appealing to stochastic versions of the expectation-maximization algorithm. The simulation methods proposed will be applied to the computation of hedging strategies and derivative prices.

In this article, the author provides an econometric approach for comparing vocational training courses, and aims to study how courses affect individual behaviour. Given the hierarchical nature of the data and the purposes of the analysis, he proposes the application of a discrete-time multilevel hazard model. The variable of interest is the duration (in months) of the first job-search after the end of the course. The author focusses on contextual and correlated (course) effects and comments on the results also in terms of school effectiveness. The approach may be easily applied to several other clustered structures.

Many clinical trials enrol patients from different medical centres. Multi-centre studies are particularly helpful in cancer research as they allow researchers to evaluate the efficacy of a therapy in a variety of patients and settings, making it possible to investigate the effect of treatments in those cases when it is difficult, or even impossible, for a single centre to recruit the required number of patients. It is often argued, however, that despite agreement among different centres to follow common standardized protocols, variation may occur in both baseline characteristics of the recruited patients and in treatment effects. This heterogeneity should be detected and, if present, accounted for in the data analysis. Furthermore, the longitudinal nature of these types of experimental studies raises the problem of attrition, that is, patients may dropout of the study for a number of reasons mainly death or disease progression. In this paper, we consider the health related quality of life of advanced melanoma patients in a longitudinal multi-centre randomized clinical trial comparing two different anti-tumoural treatments. We propose a Heckman type model to account for the possibility that patients dropout according to a non-ignorable mechanism. The model is extended to a multilevel setting to account both for the longitudinal nature and the multi-centre structure of the design. We found a strong variation across centres in the quality of life evaluation. The effect of centres on the dropout was not found to be relevant in the considered data although dropout does depend on patient′s characteristics.

The ecological association between ‘low educational level′ and lung cancer mortality, both recorded at municipality level, is investigated. Six birth cohorts were retained from 1905 to 1940. Education data were derived from censuses of the period 1921-91. The education score was defined as prevalence of less educated people and was measured on a relative scale, defining a different threshold for ‘low educational level′ at each census. Four potentially relevant ages at first exposure were defined (20, 30, 40,50) to explore the temporal pattern of the disease. Thus, mortality in each cohort was matched to relative education at different periods corresponding to different ages at first exposure. The relevance of each age at first exposure and the degree of association between education and lung cancer mortality (males, Tuscany, 1971-99) were evaluated, defining a set of hierarchical Bayesian models, each corresponding to a different aetiologic hypothesis. Results show an inverse relationship between low education score and mortality for lung cancer, whose intensity decreases by cohort and becomes positive in the last one. This association was more evident for age at first exposure in the range 20-30 years. These results are consistent with the epidemiological transition of risk factors among socioeconomic classes and are coherent with the biological model of initiating carcinogen agents.

This study evaluates changes over time in occupational exposure to n-hexane by longitudinal repeated measurements analysis of data from the Biological Monitoring Registry from 1991 to 1998. The main sources of variability in n-hexane exposure among manufacturing workers in Florence province (Italy) are inspected. The 2,5-hexanedione concentrations in urine of industrial workers are explained by structural, individual and factory information. Here we analyse the effectiveness of a 1994 law on workplace conditions based on variability decomposition of measured 2,5-hexanedione concentrations.

We propose a hierarchical Bayesian model which takes into account the different levels of aggregation of data. The results show that for leather and shoe factories, the within-subject and within-factory variance components remain the most important over the time of study, whereas the between-factory components decreased in accordance with the expected effect of the new legislation.