Intervention analysis for integer-valued autoregressive models

We study the problem of intervention effects generating various types of outliers in an integer-valued autoregressive model with Poisson innovations. We concentrate on outliers which enter the dynamics and can be seen as effects of extraordinary events. We consider three different scenarios, namely the detection of an intervention effect of a known type at a known time, the detection of an intervention effect of unknown type at a known time and the detection of an intervention effect when both the type and the time are unknown. We develop F-tests and score tests for the first scenario. For the second and third scenarios we rely on the maximum of the different F-type or score statistics. The usefulness of the proposed approach is illustrated using monthly data on human brucellosis infections in Greece.Comment: 70 pages, 15 figure

Detailed statistical assessment of the characteristics of the ESMO Magnitude of Clinical Benefit Scale (ESMO-MCBS) threshold rules

Background The European Society for Medical Oncology (ESMO) has developed the ESMO Magnitude of Clinical Benefit Scale (ESMO-MCBS), a tool to assess the magnitude of clinical benefit from new cancer therapies. Grading is guided by a dual rule comparing the relative benefit (RB) and the absolute benefit (AB) achieved by the therapy to prespecified threshold values. The ESMO-MCBS v1.0 dual rule evaluates the RB of an experimental treatment based on the lower limit of the 95%CI (LL95%CI) for the hazard ratio (HR) along with an AB threshold. This dual rule addresses two goals: inclusiveness: not unfairly penalising experimental treatments from trials designed with adequate power targeting clinically meaningful relative benefit; and discernment: penalising trials designed to detect a small inconsequential benefit. Methods Based on 50 000 simulations of plausible trial scenarios, the sensitivity and specificity of the LL95%CI rule and the ESMO-MCBS dual rule, the robustness of their characteristics for reasonable power and range of targeted and true HRs, are examined. The per cent acceptance of maximal preliminary grade is compared with other dual rules based on point estimate (PE) thresholds for RB. Results For particularly small or particularly large studies, the observed benefit needs to be relatively big for the ESMO-MCBS dual rule to be satisfied and the maximal grade awarded. Compared with approaches that evaluate RB using the PE thresholds, simulations demonstrate that the MCBS approach better exhibits the desired behaviour achieving the goals of both inclusiveness and discernment. Conclusions RB assessment using the LL95%CI for HR rather than a PE threshold has two advantages: it diminishes the probability of excluding big benefit positive studies from achieving due credit and, when combined with the AB assessment, it increases the probability of downgrading a trial with a statistically significant but clinically insignificant observed benefit.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Μοντέλα πολυμεταβλητών χρονολογικών σειρών για διακριτά δεδομένα

The study of time series models for count data has become a topic of special interest during the last years. However, while research on univariate time series for counts now flourishes, the literature on multivariate time series models for count data is notably more limited. The main reason for this is that the analysis of multivariate counting processes presents many more difficulties. Specifically, the need to account for both serial and cross-correlation complicates model specification, estimation and inference. This thesis deals with the class of INteger-valued AutoRegressive (INAR) processes, a recently popular class of models for time series of counts. The simple, univariate INAR(1) process is initially extended to the 2-dimensional space. In this way, a bivariate (BINAR(1)) process is introduced. Subsequently, the time invariant BINAR(1) model is generalized to a BINAR(1) regression model. Emphasis is given on models with bivariate Poisson and bivariate negative binomial innovations. The properties of the BINAR(1) model are studied and the methods of moments, Yule-Walker and conditional maximum likelihood are proposed for the estimation of its unknown parameters. Issues of diagnostics and forecasting are considered and predictions are produced by means of the conditional forecast distribution. A generalized specification of the BINAR(1) process, where cross-correlation between the two series receives contribution from two different sources, is also discussed. We mainly focus on the assumption of bivariate Poisson innovations. The resulting joint distribution of the bivariate series is identified as an 8-parameters bivariate Hermite. At a second stage, the BINAR(1) process is extended to the multi-dimensional space. Thus, we define a multivariate integer-valued autoregressive process of order 1 (MINAR(1)) and examine its basic statistical properties. Such an extension is not simple and we emphasize on problems that occur relating to selecting a reasonable innovation distribution as well as on problems related to inference. We also study two specific parametric cases that arise under the assumptions of a multivariate Poisson and a multivariate negative binomial distribution for the innovations. To overcome the computational difficulties of the maximum likelihood approach we suggest the method of composite likelihood. Extensions to incorporate covariance information are also discussed. The proposed models are illustrated on real data series.Η μελέτη στατιστικών μοντέλων χρονολογικών σειρών για διακριτά δεδομένα έχει συγκεντρώσει ιδιαίτερο ενδιαφέρον κατά τη διάρκεια των τελευταίων ετών. Ωστόσο, ενώ η βιβλιογραφία περιλαμβάνει πλήθος εργασιών σχετικών με μονομεταβλητές χρονολογικές σειρές, η μελέτη αντίστοιχων πολυμεταβλητών σειρών είναι σαφώς πιο περιορισμένη. Συγκεκριμένα, η ανάγκη συνυπολογισμού της σειριακής συσχέτισης των δεδομένων και της αυτοσυσχέτισης που αυτά παρουσιάζουν, περιπλέκουν τον ορισμό του μοντέλου, την εκτίμηση των παραμέτρων του και τη σχετική συμπερασματολογία. Η παρούσα διατριβή ασχολείται με την κατηγορία των Διακριτών Αυτοπαλίνδρομων ακολουθιών (INteger-valued AutoRegressive (INAR) processes), μία προσφάτως δημοφιλή κατηγορία μοντέλων για διακριτές χρονολογικές σειρές. Αρχικά, το απλό INAR μοντέλο πρώτης τάξης (INAR(1)) επεκτείνεται στις δύο διαστάσεις, ορίζοντας κατ' αυτό τον τρόπο μία Διδιάστατη (Bivariate) INAR ακολουθία (BINAR(1)). Το χρονικά αμετάβλητο BINAR(1) μοντέλο γενικεύεται επίσης σε ένα μοντέλο παλινδρόμησης. Ιδιαίτερη έμφαση δίνεται στη μελέτη των μοντέλων που προκύπτουν υποθέτοντας ότι οι 'αφίξεις' (innovations) του συστήματος ακολουθούν μία διδιάστατη Poisson ή αρνητική διωνυμική κατανομή. Για την εκτίμηση των παραμέτρων του BINAR(1) μοντέλου προτείνονται οι μέθοδοι των ροπών, Yule-Walker και μέγιστης πιθανοφάνειας. Επίσης διερευνώνται διαγνωστικές μέθοδοι και η δεσμευμένη κατανομή πρόγνωσης. Ένας γενικευμένος ορισμός της BINAR(1) ακολουθίας όπου η σειριακή συσχέτιση διαμορφώνεται από δύο πηγές ταυτόχρονα, επίσης διερευνάται. Το βασικό ενδιαφέρον επικεντρώνεται στο μοντέλο που προκύπτει κάτω από την υπόθεση ότι οι αφίξεις ακολουθούν μία διδιάστατη κατανομή Poisson. Όπως προκύπτει, η από κοινού κατανομή της διδιάστατης σειράς είναι μία διδιάστατη Hermite κατανομή. Εν συνεχεία, η BINAR(1) ακολουθία γενικεύεται στον πολυδιάστατο χώρο. Συγκεκριμένα ορίζουμε ένα Πολυμεταβλητό (Multivariate) INAR μοντέλο πρώτης τάξης (MINAR(1)) και εξετάζουμε τις βασικές στατιστικές του ιδιότητες. Επίσης μελετάμε τις παραμετρικές περιπτώσεις που προκύπτουν υποθέτοντας μία πολυδιάστατη κατανομή Poisson και μία πολυδιάστατη αρνητική διωνυμική για τις αφίξεις του συστήματος. Προκειμένου να αντιμετωπιστούν οι πρακτικές υπολογιστικές δυσκολίες της μεθόδου μεγίστης πιθανοφάνειας, προτείνεται η μέθοδος της σύνθετης πιθανοφάνειας (composite likelihood). Τα προτεινόμενα μοντέλα εφαρμόζονται σε πραγματικά δεδομένα πολυμεταβλητών χρονολογικών σειρών

Pairwise likelihood estimation of latent autoregressive count models

Latent autoregressive models are useful time series models for the analysis of infectious disease data. Evaluation of the likelihood function of latent autoregressive models is intractable and its approximation through simulation-based methods appears as a standard practice. Although simulation methods may make the inferential problem feasible, they are often computationally intensive and the quality of the numerical approximation may be difficult to assess. We consider instead a weighted pairwise likelihood approach and explore several computational and methodological aspects including estimation of robust standard errors and the role of numerical integration. The suggested approach is illustrated using monthly data on invasive meningococcal disease infection in Greece and Italy

lacm: Latent Autoregressive Count Models

Pairwise likelihood inference in latent autoregressive count model