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@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.
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