Frequentist estimation of an epidemic's spreading potential
when observations are scarce

J 2014

Frequentist estimation of an epidemic's spreading potential when observations are scarce

KRAUS, Andrea a VM PANARETOS

Základní údaje

Originální název

Frequentist estimation of an epidemic's spreading potential when observations are scarce

Autoři

KRAUS, Andrea a VM PANARETOS

Vydání

Biometrika, Oxford, Oxford Univ Press, 2014, 0006-3444

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 1.418

DOI

http://dx.doi.org/10.1093/biomet/ast049

UT WoS

000332328400009

Klíčová slova anglicky

Birth and death process; Explosion; Malthusian parameter; Markov process; Marked point process; Martingale; Partial observation; Quasilikelihood

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 12. 1. 2016 23:13, Mgr. Andrea Kraus, M.Sc., Ph.D.

Anotace

V originále

We consider the problem of inferring the potential of an epidemic for escalating into a pandemic on the basis of limited observations in its initial stages. Classical results of Becker & Hasofer (J. R. Statist. Soc. B, 59, 415-29) illustrate that frequentist estimation of the complete set of parameters of an epidemic modelled as a birth and death process remains feasible even when one is able to observe only the deaths and the total number of births. These assumptions on the observation mechanism, however, are too strong to be met in practice. We consider a more realistic scenario where only temporally aggregated random proportions of the deaths are observed over time. We demonstrate that the frequentist estimation of the Malthusian parameter governing the growth of the epidemic is still feasible in this context. We construct explicit straightforwardly calculable estimators motivated heuristically by the martingale dynamics of the process, and show that they admit a rigorous quasilikelihood interpretation. We establish the consistency and asymptotic normality of these estimators, allowing for the construction of approximate confidence intervals that can be used to infer the spreading potential of the epidemic. A simulation study and an application to the initial outbreak data of the 2009 H1N1 influenza pandemic illustrate that the method can be expected to give reasonable results in practice.

Citovat

KRAUS, Andrea a VM PANARETOS. Frequentist estimation of an epidemic's spreading potential when observations are scarce. Biometrika. Oxford: Oxford Univ Press, 2014, roč. 101, č. 1, s. 141-154. ISSN 0006-3444. Dostupné z: https://dx.doi.org/10.1093/biomet/ast049.

@article{1324043,
   author = {Kraus, Andrea and Panaretos, VM},
   article_location = {Oxford},
   article_number = {1},
   doi = {http://dx.doi.org/10.1093/biomet/ast049},
   keywords = {Birth and death process; Explosion; Malthusian parameter; Markov process; Marked point process; Martingale; Partial observation; Quasilikelihood},
   language = {eng},
   issn = {0006-3444},
   journal = {Biometrika},
   title = {Frequentist estimation of an epidemic's spreading potential when observations are scarce},
   volume = {101},
   year = {2014}
}

TY  - JOUR
ID  - 1324043
AU  - Kraus, Andrea - Panaretos, VM
PY  - 2014
TI  - Frequentist estimation of an epidemic's spreading potential when observations are scarce
JF  - Biometrika
VL  - 101
IS  - 1
SP  - 141-154
EP  - 141-154
PB  - Oxford Univ Press
SN  - 00063444
KW  - Birth and death process
KW  - Explosion
KW  - Malthusian parameter
KW  - Markov process
KW  - Marked point process
KW  - Martingale
KW  - Partial observation
KW  - Quasilikelihood
N2  - We consider the problem of inferring the potential of an epidemic for escalating into a pandemic on the basis of limited observations in its initial stages. Classical results of Becker & Hasofer (J. R. Statist. Soc. B, 59, 415-29) illustrate that frequentist estimation of the complete set of parameters of an epidemic modelled as a birth and death process remains feasible even when one is able to observe only the deaths and the total number of births. These assumptions on the observation mechanism, however, are too strong to be met in practice. We consider a more realistic scenario where only temporally aggregated random proportions of the deaths are observed over time. We demonstrate that the frequentist estimation of the Malthusian parameter governing the growth of the epidemic is still feasible in this context. We construct explicit straightforwardly calculable estimators motivated heuristically by the martingale dynamics of the process, and show that they admit a rigorous quasilikelihood interpretation. We establish the consistency and asymptotic normality of these estimators, allowing for the construction of approximate confidence intervals that can be used to infer the spreading potential of the epidemic. A simulation study and an application to the initial outbreak data of the 2009 H1N1 influenza pandemic illustrate that the method can be expected to give reasonable results in practice.
ER  -

KRAUS, Andrea a VM PANARETOS. Frequentist estimation of an epidemic's spreading potential when observations are scarce. \textit{Biometrika}. Oxford: Oxford Univ Press, 2014, roč.~101, č.~1, s.~141-154. ISSN~0006-3444. Dostupné z: https://dx.doi.org/10.1093/biomet/ast049.

Podrobný výpis o publikaci