JOURNAL OF EMERGING AND RARE DISEASES (ISSN:2517-7397)

Daily COVID-19 related hospitalizations have been used in monitoring the trends of the COVID-19 pandemic. However, the daily hospitalizations can be under-reported due to lags in reporting. The impact of this under-reporting on estimating the growth rate of hospitalizations has not been evaluated. Our aims of this study are 1) to investigate the under-reporting of hospitalizations in Colorado State; 2) to examine the impact of underreporting on estimating growth rates of hospitalizations; 3) to propose a method to adjust for the under-reporting when estimating growth rates. We found that under-reporting of daily hospitalizations was severe in the early days of the pandemic, with the percentage of under-reporting as high as 59%. We also demonstrated that the under-reporting of the daily hospitalizations had the greatest impact on estimating the most recent growth rates. For the period between April 9th and April 15^th, the growth rate was -0.079 (95% CIs=(-0.118, -0.041)) on report date April 15^th, 2020 and it became -0.008 (95% CIs=(-0.038, 0.054)) on report date April 29^th, 2020. We recommend either removal of recent data or consideration of adjusting for the under-reporting of the daily hospitalizations in estimating growth rates. 

As of June 7^th, 2020, COVID-19 has infected more than 4 million people globally and killed more than 400,000. In the United States of America (USA) over 1.9 million Americans tested positive and over tens of thousands lost their lives to the disease [1]. Since the middle of March, many state governments have issued social distancing guidelines including school and non-essential business closures [2]. These mitigation measures helped flatten the curve of the pandemic, evidenced by lower daily COVID-19 hospitalizations and lower daily deaths. New York, for instance, was able to make enough progress to begin reopening their businesses on June 8^th, 2020. However, some states that reopened (e.g., Texas and Arizona) saw surges in COVID-19 cases and hospitalizations two weeks after Memorial Day [3]. The numbers coming out of these states have not been the only setback. Large gatherings of demonstrators demanding social justice for African Americans across the USA have also posed a risk for increased COVID-19 transmission [4]. Given all these threats to progress on beating the epidemic, monitoring the trends of the pandemic is crucial.

The growth rate of COVID-19 cases has been used to monitor trends of the pandemic [5,6] and to evaluate the impact of social distancing guidelines in USA [7]. However, COVID-19 testing has been challenged in the USA due to the shortages in testing components. Thus, COVID-19 cases were not ideal for estimating growth rates [6]. As an alternative reliable metric, the number of COVID-19 hospitalizations was considered. Monitoring the growth rates of the hospitalizations became important for health systems to prepare and allocate limited resources [8-10].

Although some states’ Department of Public Health websites report COVID-19 hospitalizations, the recent hospitalizations were often underrepresented due to lags in reporting. The objectives of this study are 1) to evaluate the under-reporting of hospitalizations; 2) to assess the impact of the under-reporting on estimating the growth rate of hospitalizations; 3) to measure the under-reporting of hospitalizations and adjust for the under-reporting of hospitalizations in estimating the growth rate.

Population and data resource 

The Colorado Department of Public Health and Evaluation (CDPHE) has been collecting the cumulative numbers for COVID-19 cases, hospitalizations, and deaths on a daily basis. As of June 6^th, 2020, among 5.8 million Coloradans, 210,285 people were tested; among those tested, 27,848 were COVID-19 positive, 4,480 were hospitalized, and 1,274 were dead due to COVID-19 [11]. The CDPHE made these data available to public through a portal, which has been updated daily [12]. We considered the cumulative number of hospitalizations reported from the CDPHE as the actual numbers for those dates in Colorado.

However, due to lags in reporting from the CDPHE’s partners, a cumulative number of hospitalizations for a given date was usually reported two days later. Then, it would get repeated updates over a period of time. The daily number of hospitalizations was derived by subtracting the cumulative number in the previous day from the number at the current day. We used “report date” to denote the time that the number of hospitalizations for a specific date was updated. For example, the daily numbers of hospitalizations for April 1^st, 2020 were 60, 63, 70, and 80 on report dates April 3^rd, 4^th, 5^th, and 6^th, 2020, respectively. In this paper, we analyzed the numbers of hospitalizations from March 9^th to June 4^th, 2020. 

To assess the extent of under-reporting, we first identified the time it took for the daily number of hospitalizations to reach a plateau. We then calculated the percentage of under-reporting during “the report dates” before reaching the plateau. Finally, we proposed an approach to estimate recent growth rates while adjusting for the under-reporting.

A nonlinear model to identify the time for the daily number of hospitalizations to reach a plateau 

While analyzing COVID-19 hospitalizations for estimating a growth rate and doubling time [10], we observed that the cumulative number of hospitalizations was updated daily since April 1st by the CDPHE. In general, the daily number of hospitalizations increased for several days after it was first reported on the data portal. We proposed a nonlinear model to identify the time that it took (in days) for the daily number of hospitalizations to reach a plateau. The time to reach a plateau is represented by the variable t _c .

Let y _it be the daily number of hospitalizations for day i and reported on day t where i=March 9th to June 4^th, t being the days from the date when it y was first reported (t =1). For example, on April 6^th, 30 hospitalizations for April 4th was first reported (a delay of 2 days). Over successive days, the number of hospitalizations for April 4^th was updated as more reporting occurred. Finally, on May 5^th, 29 days after it was first reported, the number of hospitalizations for April 4^th reached its plateau. We fit separate piece-wise quadratic models to identify the time to reach a plateau ( t _(ic)) for each daily number of hospitalizations y _i. [13-16],

Note that the recent daily numbers of hospitalizations may have not reached a plateau because there were more updates to come.

The percentages of under-reporting daily hospitalizations over report time, a Beta distribution and the adjusted daily number of hospitalizations for recent days

In the days before the daily hospitalizations reached a plateau, the percentage of under-reporting over time was estimated as:

Because of lags in reporting hospitalizations, y _{it (ic)} > y _it when t < t _(ic) ; thus, π _i (t) is between 0 and 1. For each value of t , we assumed a Beta distribution for the percentages of the under-reporting across values of i ,

where a t(t) and b t(t ) were the two positive shape parameters at time t for a Beta distribution [14]. It can be shown that the adjusted daily hospitalizations before reaching a plateau is

Growth rate of the daily hospitalizations

Previously, a growth model was proposed for estimating growth rates and doubling times of the daily hospitalizations [10]. Because the growth rates and doubling times changed over time, a rolling growth curve approach (RGCA) was used with a period of 7 days. The RGCA approach excluded the recent 1-2 days’ hospitalization data due to the under-reporting of hospitalizations [10]. However, that adjustment was not enough. The hospitalization data older than two days were still under-reported. Here, we propose a modified growth curve model to adjust for the under-reporting.

First without considering the lags in reporting, suppose we seek to estimate the growth rate over n days from day i (start day) to day 

(i n + −1). Let y _{(i +j-1)} denote the daily hospitalizations at day ( i + j- 1),

1≤ ≤j n . Based on a growth model, we have [10]:

where r is the growth rate during day i to day (i n + −1).

where r_a is the growth rate after adjusting for the under-reporting of hospitalizations; I _(1+f-1)t is a binary indicator equal to 1 after y_(i+j-t)t  has reached a plateau and equal to zero if y_(i+j-t)t has not reached a plateau; I _it is a different binary indicator equal to when y _it has reached a plateau and equal to zero if y _it has not reached a plateau.

To estimate r _a and obtain its 95% confidence intervals (CIs), we employed the Monte Carlo (MC) simulation approach. We simulated 1000 values of π (t) based on a Beta distribution using the shape parameters estimated in equation (1). This provided 1000 values of r _a The average of these 1000 values of r _a The 2.5^th and the 97.5^th percentiles were considered as r_a ’s 95% CIs.

Although not reported in this study, the doubling time D_a or half time H_a can be estimated by replacing r_a in equation (3) with

The daily number of hospitalizations before March 21^st remained the same since they were first reported on the CDPHE portal on April 1^st. As a result, the data before March 21^st were not included in identifying the time to plateau, and not included in calculating the percentages of the under-reporting (π (t)), but were included in estimating growth rates.

Figure 1a showed the daily numbers of hospitalizations for April 4^th, 5^th and 6th (i ) over report dates. Figure 1b showed the daily numbers of hospitalizations for May 23^rd, 24^th, and 25^th. For the daily numbers of hospitalizations before May 5^th, there were significant increases on May 5th, indicating a possible addition of partner(s) with CDPHE (Figure 1a). Both figures 1a and 1b showed a significant under-reporting of hospitalizations in the early days of reporting. 

The time for the daily hospitalizations to reach a plateau was shown in groups by weeks where i date fell in (Table 1). In the early stages of the pandemic, it took a longer time for the daily hospitalizations to reach a plateau. For example, during the week of March 21-March 27, it took 37.5 days on average for the daily hospitalizations to reach a plateau; after May 2^nd, it took fewer than 10 days on average for the daily hospitalizations to reach a plateau, indicating an improved reporting of daily hospitalizations in Colorado.

The percentages of under-reporting of the daily hospitalizations (π (t) ) due to lags in reporting over 15 days are presented in Table 2. When daily hospitalizations were first reported on the CDPHE portal, on average they were under-reported by 59%. The percentages of under-reporting of daily hospitalizations decreased over report dates. However, even 10 days after the first reporting on the portal, the percentages of under-reporting of daily hospitalizations were still about 10%. This is an indication of the importance of adjusting for the under-reporting of recent hospitalizations for estimating recent growth rates. The two shape parameters of a Beta distribution for the percentages of under-reporting are also presented in Table 2.

In estimating the growth rates, we used the RGCA approach with a period of 7 days as described before [10]. For the daily hospitalizations in Colorado, we estimated the growth rates for the following periods during March 9th – June 4^th: March 9^th -15^th,16^th - 22^th, 15^th - 21^st ,…, and May 29th-June 4^th. First, we estimated the growth rates of the daily hospitalizations without adjusting for the under-reporting. Figure 2 shows the growth rates of four selected middle dates of a period of seven days over report dates. It took over two weeks for the growth rate of a seven-day period with a middle date of April 12^th to stabilize: the growth rate was -0.079 (95% CIs=(- 0.118, -0.041)) on report date April 15^th 2020 and increased to -0.008 (95% CIs=(-0.038, 0.054)) on report date April 29^th. The growth rates for the middle dates of May 27^th and May 28^th had not stabilized as of June 4^th.

We then estimated the growth rates of the daily hospitalizations, adjusting for the under-reporting as proposed in METHODS. We only present the growth rates after 5/27/2020. The results were compared to those using the daily hospitalizations reported on June 6^th that had hospitalization data up to June 4^th. The growth rates before 5/27/2020 were the same with and without adjusting for the under-reporting because the daily hospitalizations reached a plateau and the same data were used for both approaches. The difference in growth rates was greatest for the most recent period May 29th-June 4^th, 2020, the unadjusted growth rate r = −0.14 (95% CIs=(-0.25, -0.04)), and the adjusted growth rate r_a =0.10 (95% CIs=(0.00, 0.27)) (Table 3).

During the early days of the COVID-19 pandemic, many forecasting models painted a horrific picture for the US including Colorado [15,16]. Although those predictions did not come true, these daunting death tolls pushed local and federal governments to form and implement social distancing guidelines which in turn helped flatten the pandemic curves in states such as Colorado, New York, and other states. When COVID-19 cases increased in the US, some researchers started to use available data to inform models so that their forecasts were more relevant to the US population. However, these numbers can be under-reported and this underreporting may have contributed to the inaccuracy of forecasting. To our knowledge, this is the first study that has examined the underreporting of COVID-19 related hospitalizations and its impact on estimating growth rates.

There are several limitations in this study. First, we used only Colorado’s hospitalization data and the results may not be generalizable to other regions. However, we expect similar underreporting issues in other states. Second, the percentages of the under-reporting of daily hospitalizations (π (t)) were estimated using data including those from the early pandemic when the underreporting was severe. They may not represent the under-reporting of recent daily hospitalizations. As a result, the recent growth rates may be overcorrected. A solution is to use the more recent data (e.g., data during May 2020) to estimate the percentages of the under-reporting (π (t)).

We conclude that it is crucial to adjust for the under-reporting of hospitalizations to monitor the trend of the pandemic in real-time. If it takes a few days for the daily hospitalization number to reach a plateau, we recommend removal of recent data in estimating growth rates; if it takes a longer time for number to reach their final values, we recommend estimating the percentages of under-reporting of daily hospitalizations and application of the newly proposed approach; if the percentages of under-reporting of hospitalizations changes over time, we recommend use of recent data to estimate the percentages of under-reporting of daily hospitalizations and application of the newly proposed approach.

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