# Nowcasting pandemic influenza A/H1N1 2009 hospitalizations in the Netherlands

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## Abstract

During emerging epidemics of infectious diseases, it is vital to have up-to-date information on epidemic trends, such as incidence or health care demand, because hospitals and intensive care units have limited excess capacity. However, real-time tracking of epidemics is difficult, because of the inherent delay between onset of symptoms or hospitalizations, and reporting. We propose a robust algorithm to correct for reporting delays, using the observed distribution of reporting delays. We apply the algorithm to pandemic influenza A/H1N1 2009 hospitalizations as reported in the Netherlands. We show that the proposed algorithm is able to provide unbiased predictions of the actual number of hospitalizations in real-time during the ascent and descent of the epidemic. The real-time predictions of admissions are useful to adjust planning in hospitals to avoid exceeding their capacity.

## Keywords

Influenza Epidemiology Hospitalization Estimation techniques Disease notification## Introduction

A hallmark of influenza A pandemics is their unpredictability, not only with respect to the timing of their occurrence but also with respect to their size, duration, and severity. With the benefit of hindsight it is now clear that the 2009 pandemic influenza A/H1N1 has been relatively mild, both in terms of the fraction of the population that has developed influenza-like illness, and the overall severity of the disease [1, 2, 3]. Nevertheless, demand for high care hospital beds has been high compared to the available number of beds [4, 5].

Excess high care hospital capacity is limited [6]. For instance, in the Netherlands intensive care capacity is approximately 10 beds per 100,000 persons, of which less than 2 per 100,000 may be available to meet sudden increases in demand [7]. It is therefore vital that trends of rapidly increasing incidence and health care demand (especially hospitalizations requiring intensive care) are noticed early so that there may be time to increase operational capacity by strict triaging and by postponement of non-critical operations [8].

Real-time tracking of hospital admissions during epidemics is difficult because of the inherent delay in reporting of cases or hospital admissions. Reasons for such delays include the time to complete diagnostic tests, logistics, and overwhelmed surveillance systems. A number of studies have addressed the problem of reporting delay, and recently the term ‘nowcasting’ has been coined for attempts to assess the current situation based on imperfect information [9, 10, 11].

Here we propose an algorithm to correct for delays in reporting, and infer the number of admissions from incoming reports. We have applied this nowcasting method to track the 2009 influenza A/H1N1 hospitalizations in the Netherlands, using a complete set of dates of hospital admissions and associated reporting delays. Now the pandemic has passed, we can assess retrospectively the precision of our nowcasting estimates of the number of hospital admissions during the pandemic.

## Methods

### Surveillance system

From April 25, 2009, both general practitioners and hospitals were required to notify to the municipal health services patients with influenza like symptoms. Laboratory tests were performed at the National Influenza Centre (represented by the National Institute for Public Health and the Environment, RIVM, and the Erasmus Medical Centre), using RT-PCR. Anonymized data about confirmed cases, including date of admission and travel history, was entered into a web-based database by the municipal health services and collected at the RIVM. On August 3 it was announced that the novel influenza A/H1N1 would no longer be a notifiable disease, which stopped the registration of cases. From that day on, only hospitalized cases that fulfilled the case definition [12] were reported by the hospitals to the municipal health services.

### Reporting probability

We reconstructed the number of hospitalized patients on each day of the epidemic. The reporting delay was measured as the difference between the date of admission of a patient and the date of reporting. We observed the reporting delays for all cases from June 5 to measure the distribution of reporting delays. The cumulative frequency distribution of reporting delays gives the probability of a case having been reported *i* days after the day of onset of symptoms, ρ_{ i }. The 95% reporting horizon is the delay where this cumulative distribution surpasses 0.95.

### Estimation of the actual number of cases

We set the current day as day 0. Our goal is to estimate the number of admissions *i* days ago, *N* _{ i }. We denote the number of admissions on that day that have been reported up to the current day by *C* _{ i }. We denote the probability that an admission on that day has been reported before or during that day by ρ_{ i }. We are looking for the actual number of admissions *i* days ago, *N* _{ i }, given the number of reported cases for that day so far, *C* _{ i }.

_{ i }and the actual number of cases

*N*

_{ i }:

*C*

_{ i }= ρ

_{ i }

*N*

_{ i }. Rearranging gives an estimator for the actual number of cases

### Maximum likelihood estimator and 95% confidence interval

*N*

_{ i }independent trials where the probability of success is ρ

_{ i }. The probability of observing

*C*

_{ i }cases is

*N*

_{ i }given the number of observed cases

*C*

_{ i }and probability of reporting ρ

_{ i }is, up to a constant, given by

We construct a confidence interval by the profile likelihood method. We accept values of *N* _{ i } that have a likelihood ratio of \(\lambda = {\frac{L(N_i)}{L(\hat{N}_i)}}\) in the acceptance region specified by the likelihood ratio test with α = 0.05, that is −2 log λ ≤ χ^{2} _{1:0.05}. This means that the confidence interval includes all values *N* _{ i } that have a likelihood higher than 1/6.8 of the maximum likelihood.

## Results

## Discussion

In emerging outbreaks, it is important to have up-to-date information on the spread of the disease, and growth of the epidemic, because the number of cases can increase dramatically in a matter of days. Hospitalizations, and intensive care admissions in particular, should be tracked promptly, because excess capacity is small most of the time. However, surveillance systems suffer from delayed reporting of cases. This delay causes an apparent decrease in number of cases in the most recent part of the epidemic, and should therefore be taken into consideration when interpreting epidemic curves.

We have shown how routinely collected surveillance data can be used to obtain precise estimates of the actual number of hospitalized patients during an outbreak. Despite considerable reporting delays, the estimates were close to the actual numbers of daily hospitalized patients, up to 1 day before the observation.

The estimator has a number of limitations that should be addressed. First, patients that are reported after a very long time have not yet been included in the delay distribution. This truncation of data can be adjusted for [13], but we believe that little additional precision can be obtained by such more complicated analyses. Second, we assume that the distribution of delays is at least approximately stationary. If there is evidence of significant changes in the delay distribution over time, the different phases of the epidemic should be analyzed separately to reduce bias in the estimation, at the expense of a loss of precision. Third, the reporting delay will typically differ between weekdays, because hospitalizations are generally not reported during the weekends. If the difference between weekdays is large, the number that is still to be reported for each day of the week should be analyzed separately. Again, this reduces bias at the expense of a loss of precision.

The application of the nowcasting algorithm to pandemic influenza A/H1N1 2009 hospitalizations in the Netherlands provides an example where the limitations as described above, have been checked carefully. The scale of the delay distribution is much shorter than the scale of the epidemic. The reporting delay differed between weekdays but not enough to cause a substantial bias. Our analysis of the pandemic influenza A/H1N1 2009 hospitalizations may have profited from the relatively long period between the first reported cases and the start of the epidemic growth in the Netherlands. The Dutch hospitals and health services had ample time to prepare for the epidemic, and diagnostic tests were available throughout the epidemic. These preparations resulted in the relatively stable reporting delay distribution throughout the epidemic. Whereas a shorter period, such as in the UK, USA or Australia, could have overwhelmed the health services, causing larger fluctuations in the reporting delay. This, in turn, could result in less precise estimations.

The method presented here enables estimation of the current number of cases, and is not intended to predict the development of the epidemic. To that end, real-time prediction models are available that use the numbers of reported cases in combination with simple mathematical models to project the trajectory of the epidemic [14, 15, 16]. These models usually assume that cases are reported instantaneously, which is hardly ever the case in practice. We believe that a two-pronged approach in which our nowcasting estimator is used in conjunction with real-time prediction models could substantially improve prospects for the practical application of predicting the future course of an epidemic.

Concluding, we combined surveillance data to estimate the number of hospitalizations during the pandemic influenza A/H1N1 2009 outbreak, to track the actual health care demand. The method reliably predicts both increasing and decreasing trends in the number of hospitalizations. The nowcasting tool holds considerable promise for gauging actual number of hospitalizations in the presence of reporting delays.

## Notes

### Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

## References

- 1.Fraser C, Donnelly CA, Cauchemez S, Hanage WP, Van Kerkhove MD, Hollingsworth TD, et al. (2009) Pandemic potential of a strain of influenza A (H1N1): early findings. Science. 2009;324(5934):1557–61.PubMedCrossRefGoogle Scholar
- 2.Presanis AM, De Angelis D, Hagy A, Reed C, Riley S, Cooper BS, et al. (2009) The severity of pandemic H1N1 influenza in the United States, from April to July 2009: a Bayesian analysis. PLoS Med. 2009;6(12):e1000207.PubMedCrossRefGoogle Scholar
- 3.Wu JT, Cowling BJ, Lau EHY, Ip DKM, Ho LM, Tsang T, et al. (2010) School closure and mitigation of pandemic (H1N1) 2009, Hong Kong. Emer Infect Dis. 2010;16(3):538–41.Google Scholar
- 4.Domínguez-Cherit G, Lapinsky SE, Macias AE, Pinto R, Espinosa-Perez L, de la Torre A, et al. Critically Ill patients with 2009 influenza A(H1N1) in Mexico. JAMA. 2009;302(17):1880–7.PubMedCrossRefGoogle Scholar
- 5.Kumar A, Zarychanski R, Pinto R, Cook DJ, Marshall J, Lacroix J, et al. (2009) Critically ill patients with 2009 influenza A(H1N1) infection in Canada. JAMA. 2009;302(17):1872–9.PubMedCrossRefGoogle Scholar
- 6.Carr BG, Addyson DK, Kahn JM. Variation in critical care beds per capita in the United States: implications for pandemic and disaster planning. JAMA. 2010;303(14):1371–2.CrossRefGoogle Scholar
- 7.Hansen J, Van Der Velden LFJ, Hingstman L. Intensive care needs assessment for adults 2006–2016 (Behoefteraming Intensive Care voor Volwassenen 2006–2016). 2008.Google Scholar
- 8.White DB, Angus DC. Preparing for the sickest patients with 2009 influenza A(H1N1). JAMA. 2009;302(17):1905–6.PubMedCrossRefGoogle Scholar
- 9.Farrington CP, Andrews NJ, Beale AD, Catchpole MA. A statistical algorithm for the early detection of outbreaks of infectious disease. J R Stat Soci Ser A (Stat Soci). 1996;159(3):547–63.CrossRefGoogle Scholar
- 10.Garske T, Legrand J, Donnelly CA, Ward H, Cauchemez S, Fraser C, et al. Assessing the severity of the novel influenza A/H1N1 pandemic. BMJ. 2009;339:b2840.PubMedCrossRefGoogle Scholar
- 11.Nicoll A, Ammon A, Amato Gauci A, Amato A, Ciancio B, Zucs P, et al. Experience and lessons from surveillance and studies of the 2009 pandemic in Europe. Public Health. 2010;124(1):14–23.PubMedCrossRefGoogle Scholar
- 12.Hahné S, Donker T, Meijer A, Van Steenbergen J, Osterhaus A, Van Der Sande M, et al. Epidemiology and control of influenza A(H1N1)v in the Netherlands: the first 115 cases. Eurosurveillance. 2009;14(27):1–4.Google Scholar
- 13.Hubbard AE, Van der Laan MJ, Enanoria W, Colford JM. Nonparametric survival estimation when death is reported with delay. Lifetime Data Anal. 2000;6(3):237–50.PubMedCrossRefGoogle Scholar
- 14.Hall IM, Gani R, Hughes HE, Leach S. Real-time epidemic forecasting for pandemic influenza. Epidemiol Infect. 2007;135(3):372–85.PubMedCrossRefGoogle Scholar
- 15.Ong JB, Chen MI, Cook AR, Lee HC, Lee VJ, Lin RT, et al. Real-time epidemic monitoring and forecasting of H1N1-2009 using influenza-like illness from general practice and family doctor clinics in Singapore. PloS One. 2010;5(4):e10036.PubMedCrossRefGoogle Scholar
- 16.Nishiura H. Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009). Biomedical engineering online. 2011;10(1).Google Scholar