Modelling Under-Reported Data: Pitfalls of Naïve Approaches and a New Statistical Framework for Epidemic Curve Reconstruction
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912585415131136 |
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| author | Slater, Justin J. Bebeziqi, Sindi |
| author_facet | Slater, Justin J. Bebeziqi, Sindi |
| contents | Count-valued autoregressions are widely used to analyse time-series of reported infectious-disease cases because of their close connection with discrete-time transmission models. However, when such models are applied directly to under-reported case counts, their mechanistic interpretation can break down. We establish new theoretical results quantifying the consequences of ignoring under-reporting in these models. To address this issue, reported cases are often modelled as a binomially thinned version of an underlying count process, but such models are difficult to fit because the unobserved true counts are serially correlated and integer-valued. We develop a new statistical framework for under-reported infectious-disease data that uses a normal-normal approximation to a broad class of thinned count autoregressions and then accurately maps this continuous process back to the integers. Through simulations and applications to rotavirus incidence in a German state and Covid-19 incidence in English conurbations, we demonstrate that our approach both retains the mechanistic appeal of thinned autoregressions and substantially simplifies inference. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10668 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modelling Under-Reported Data: Pitfalls of Naïve Approaches and a New Statistical Framework for Epidemic Curve Reconstruction Slater, Justin J. Bebeziqi, Sindi Applications Count-valued autoregressions are widely used to analyse time-series of reported infectious-disease cases because of their close connection with discrete-time transmission models. However, when such models are applied directly to under-reported case counts, their mechanistic interpretation can break down. We establish new theoretical results quantifying the consequences of ignoring under-reporting in these models. To address this issue, reported cases are often modelled as a binomially thinned version of an underlying count process, but such models are difficult to fit because the unobserved true counts are serially correlated and integer-valued. We develop a new statistical framework for under-reported infectious-disease data that uses a normal-normal approximation to a broad class of thinned count autoregressions and then accurately maps this continuous process back to the integers. Through simulations and applications to rotavirus incidence in a German state and Covid-19 incidence in English conurbations, we demonstrate that our approach both retains the mechanistic appeal of thinned autoregressions and substantially simplifies inference. |
| title | Modelling Under-Reported Data: Pitfalls of Naïve Approaches and a New Statistical Framework for Epidemic Curve Reconstruction |
| topic | Applications |
| url | https://arxiv.org/abs/2509.10668 |