Determinants of COVID-19 Hospitalizations in Slovakia Martin Šuster1 , Katarína Bod’ová2 , Vladimír Nosál’3 , and Richard Kollár2 1 National Bank of Slovakia 2 Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia 3 Jessenius Faculty of Medicine in Martin, Comenius University, Slovakia Abstract: Prediction of COVID-19 related hospital ad- missions, especially in the conditions where testing strate- gies are changing due to introduction of mass rapid anti- gen testing without their PCR confirmation is very impor- tant. We introduce simple, short time prediction model for hospital admissions, where positive PCR and AG tests are used. 1 Introduction The COVID-19 pandemic is overwhelming hospital ca- pacities all over the world. Slovakia is a small country with 5.5 million inhabitants and limited resources of health- care system (Figure 1). Slovakia has fared very well dur- ing the first wave of the COVID-19 pandemic but was hit much harder in the second wave. Expecting second wave of the pandemic, 1000 new ventilators were procured. Despite that, healthcare workers are significantly under- staffed, especially anaesthesiologists and intensivists, in- cluding nurses. Understanding the evolution of hospital- isations and ability to make short term forecasts can im- prove strategy and preparedness. Projection models are dependent on known disease prevalence, partially reflect- ing results of PCR tests. However new testing strategies, especially introduction of mass use of antigen rapid tests, changed the relationship between PCR-confirmed infec- tions and hospitalizations. Slovakia has attempted various non-traditional strate- gies to contain the spread of the epidemic. Most notable is Figure 1: Comparison of healthcare spending among EU a mass testing of the whole adult population (10–65 years countries. Source: Eurostat old) with antigen tests. Mass testing started with a pilot phase on October 23–25, followed by a nationwide test on the weekend of October 31 to November 1, and a sub- of charge. These performed 1 702 679 tests with 96 475 sequent second round of mass testing limited to districts positive findings as of December 21, 2020 (korona.gov.sk, with high positivity in the first round (over 0.7%, cov- 2020). Most results of the rapid antigen tests were not ering slightly more than half of the country) on Novem- confirmed with PCR test. Mass testing had an instant ef- ber 7–8. Pilot testing in the four most affected districts fect on lowering the number of subsequent positive PCR covered 145 945 inhabitants with 5 594 positive findings. tests, but as of the beginning of December 2020 the epi- During the second round 3 625 332 tests were performed demic was on the rise again (Public Health Authority of with 38 359 positive findings. Third phase of testing iden- the Slovak Republic, 2020). The decline in confirmed in- tified 13 509 positive tests in 2 044 855 participants. Over- fections via PCR tests after the two rounds of mass testing all, in only three weeks 5 811 163 tests were performed shows that the series is a poor determinant of the evolu- with 57 467 positive results (Ministry of Interior of the tion of the epidemic. We find that both types of tests and Slovak Republic, 2020; Ministry of Defence of the Slo- also the positivity rates contribute to the description of the vak Republic, 2020). Subsequently, mobile test centres situation. were set up in most of 80 administrative districts of coun- In this paper, we present a model explaining COVID-19 try, where inhabitants have opportunity to get tested free hospitalizations in Slovakia. We are able to make short- _____________________ Copyright ©2021 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). Figure 2: Comparison of PCR and rapid antigen test results. Statistics form the pilot and two rounds of mass tests are not included in the figure. Source: own calculations based on korona.gov.sk. term projections of hospitalizations, giving the authorities high test volumes and developed large scale contact some advance notice to adjust social distancing measures tracing, where most of infected individuals are tested or to reorganize healthcare capacities. and detected sufficiently early. Thus, it is an impor- The data collected until December 20, 2020 were used tant factor that contributes to hospital admissions as for analysis and short-time hospital admission predictions a part of infected individuals develop symptoms, and for the time period between December 21, 2020 and Jan- with some lag, the symptoms become severe enough uary 31, 2021. to lead to hospitalization. (As discussed above, the Slovak healthcare infrastructure was severely over- whelmed with mass-testing in November, leading to 2 Model a systematic decrease in traditional PCR testing and a subsequent fall in confirmed infections.) We model admissions to hospitals and discharges sepa- rately, as they follow very different processes. The ad- • Number of positive antigen (AG) tests; this factor is missions are mostly determined by the epidemic situation commonly interpreted as the number of confirmed in- in the general population. The discharges follow the med- dividuals in the early stages of infection. Since mid- ical situations of individual patients, and partly also the November 2020 Slovakia has offered AG testing for existing procedures in hospitals. the general population. AG tests are popular among the public (there are approximately 4-times more Ag 2.1 Admissions tests than PCR administered over the recent weeks), since tested individuals do not need any test pre- As the SARS-CoV-2 infection spreads among the pop- scription or official indication, and the test results are ulation, some infected individuals develop symptoms of available in approximately 15 minutes after a sample COVID-19 severe enough to warrant hospital admissions. collection. To some degree the AG tests are a substi- It follows, therefore, that admissions should be related tute for PCR tests, albeit imperfect. Both the sensi- to the new infections in the population, and possibly the tivity and specificity of the AG tests are lower. Since severity of new infections. We have identified four signif- AG tests tend to detect individuals in early stages of icant epidemiological factors that contribute significantly the COVID-19 infection, we expect a longer lag be- to hospital admissions: tween a positive AG test and eventual hospitalization • Number of positive PCR tests; this factor is com- than between a positive PCR test and hospitalization. monly interpreted as the number of confirmed infec- tions, a globally and thus far most consistently re- • Positivity of PCR and positivity of AG test; these ported dynamical variable that allows comparison of two factors identify the fraction of administered AG the epidemic situation among countries. In general, and PCR tests with positive results. Numbers of pos- the number of positive PCR tests provides a measure itive PCR and AG tests characterize the epidemio- that represents a systematic part of all infected indi- logical situation only partially, as they are strongly viduals in the country, particularly in countries with influenced by the number of tests administered. An addition of the two test positivity factors contains in- Table 1: Model for hospital admissions formation needed to asses both the number of tests taken and the information provided by their results. Variable Coefficient Std. error t-statistic P-value ln(tests) 0.5482 0.0120 45.636 0.000 AG tests (-4) weight 0.6239 0.2997 2.081 0.040 Note that the test sample is selected by either contact PCR positive rate 4.9983 0.7164 6.977 0.000 tracing, self-selected by symptoms, or a need for a certifi- AG positive rate (-10) 1.0687 1.0789 0.991 0.324 Weekend dummy -0.4438 0.0449 -9.874 0.000 cate of non-infectiousness. Therefore, we expect that the Sample: September 1 - December 18, 2020. Included observations: 109 2 2 test positivity is systematically higher than the infection R 0.958, Adj. R 0.956, S.E. of regression 0.211 Log likelihood -17.11, Durbin-Watson stat. 1.634 incidence in the general population. As long as the selec- AG tests (−4) = −4 days lag, AG positive rate (−10) = −10 days lag tion for the tests and the number of tests are not changing rapidly, the tested sample can be thought of as a condensed sample of the population and the fraction of positive tests of the infection, with a longer lag before hospitalization. is proportionally related to the overall SARS-CoV-2 inci- Note, however, that due to the 7-day moving averages of dence. the explanatory variables, the average time between a pos- itive PCR test and hospitalization is 3 days, and the respec- tive time between AG test and hospitalization is one week, Regression estimates. We use the four time series of the which agrees with the generally accepted time course of factors described above as the explanatory variables for the the COVID-19. time series of the observed hospital admissions. We allow Both the PCR and AG positive rates have expected pos- the explanatory variables to have individual time lags that itive signs. On average the rate of positive PCR tests in are also optimized within the model. December was 20.6%, the figure for AG tests being 6.9%. Both AG and PCR tests are subject to significant fluc- This indicates that the tests are scarce—the rate of PCR tuations over the week, with much lower figures over tests is significantly above the recommended WHO stan- the weekends. Therefore, we use 7-day averages of all dard of 5%. Increasing the PCR rate by one percentage explanatory variables. MA-7 was centered to the right. point (i.e. from approximately 20% to about 21%) will A weekend dummy (alias weekend effect, which has value lead to 4.4 additional hospitalizations per day, while each 1 during weekend, and 0 during week) is included to cap- percentage point of positive AG tests will lead to about ture the lower admissions on Sundays, Saturdays, and na- 2.3 extra hospitalizations per day. The optimal lag of AG tional holidays. The data on tests are provided by the Na- test positivity is 10 days, which means the voluntary free tional Health Information Center on a dedicated website AG testing is an important early warning indicator of an (Public Health Authority of the Slovak Republic, 2020). impending worsening of the situation. Since AG testing Hospital admissions data are provided by the Ministry of is available on demand, without screening, the popula- Health in a public data repository for researchers (Bodova tion tested is likely more similar to the general popula- and Kollar, 2020). tion. High positivity of AG testing indicates 10 to 14 days The functional form of the model is a linearized version ahead, that there will be high demand for admissions to of a multiplicative power function: hospitals. Admissions = (PCR_tests + β · AG_tests)α · eγ·PCR_rate · eδ ·AG_rate · weekend_effect 2.2 Discharges A vast majority of patients is discharged from the hospital or after partial log-linearization: for two different reasons: they are either reasonably cured to be released for home treatment, or they die. On aver- ln(Admissions) = α ln(PCR_tests + β · AG_tests) + age over 20% of discharges in December were reported γ · PCR_rate + δ · AG_rate + as deaths—although this figure may include some earlier weekend_effect + ε deaths reported in December, since it takes several weeks for the pathology results to be reflected in death statistics. The estimation results are summarized in Table 1 and (Slovakia is very particular in classification of COVID-19 Figure 3. Overall, we explain 96% of the variability in related deaths. Only patients who died primarily for the the admissions. All the included variables have expected reason of the respiratory form of the disease are classified signs and are very significant, except for AG positivity rate as COVID-19 related deaths.) being not statistically significant, as relevant AG testing We considered a model for the two different processes, was present only in the second half of our sample. We and also for a longer hospital stay of patients hospitalized decide to keep the variable, as it is significant in alternative at ICU or ventilated. We were not able to distinguish sta- (linear) specifications of the model. tistically between the different treatment regimes or their The optimal time lag for the time series of PCR tests outcomes. The best fit of the hospital discharges time se- turns out to be zero, while the optimal time lag for AG ries we obtained as 9.2% of the 7-day moving average of tests is 4 days. This agrees with our hypothesis that the time series of hospitalizations without a time lag. This cor- AG tests detect individuals on average in an earlier stage responds to approximately 11 days of average hospital stay a high rate of contacts during the holiday period. An al- Table 2: Model for hospital discharges. ternative way to interpret the pessimistic scenario is ma- Variable Coefficient Std. error t-statistic P-value terialization of the risks from a recently reported more in- Hospitalizations 0.1129 0.0017 64.55 0.000 Hospitalizations fectious virus strain (Davies et al., 2021). In this scenario · weekend dummy -0.0735 0.0032 -23.20 0.000 incidence grows by 4.4% until January 10 and then con- Sample: September 1 - December 22, 2020. Included observations: 113 2 2 R 0.942, Adj. R 0.942, S.E. of regression 17.96 tinues growing at the same rate as in the main scenario. Log likelihood -485.72, Durbin-Watson stat. 1.55 Figure 3 shows the weighted sum of test incidence used for the forecasts in the three scenarios described above. Figure 4 and Figure 5 show the forecasts for hospital ad- per patient. The only other significant variable is a week- missions and discharges. Figure 6 shows the forecast of end dummy, reflecting a much lower number of patients the number of hospitalized patients. discharged on weekends. The projection interval is constructed from one standard Linear regression. The estimation results are presented in error confidence band of admissions, while using respec- Table 2 and Figure 4. Despite the simplicity of the model, tive point estimates for discharges, conditional on the dy- we are able to explain 94% of the variability of hospi- namics of hospitalizations stocks. This is given by the tal discharges. On weekdays 11% of the COVID-19 pa- larger uncertainty in the exogenous variables, notably re- tients are discharged, while on weekends and holidays this sults of AG and PCR tests, that determine admissions, falls to just 4%. Note again that the hospitalizations vari- while discharges are endogenous to the model system. able is a 7-day moving average, thus the number of dis- Based on the data available at the ond of December charges roughly corresponds to the volume of hospitaliza- 2020, our model predicted continuation of the trend of ris- tions three days prior to the discharge. Thus the equation ing hospital utilization (even in the optimistic scenario), for discharges is: which started at the very end of December 2020. The model predicted the increase from 2895 hospitalized pa- Discharges = αHospitalizations + β weekend_effect + ε tients (as of December 31) to around 3700 by the end of January 2021. Model for the pessimistic scenario pre- dicted over 5100 hospitalized COVID patients at the end of January 2021. 3 Short-term hospitalization forecasts A forecast of time series of hospitalizations requires as 4 Discussion and conclusions an input time series of the four explanatory variables de- scribed above with appropriate time lags. Thus, a predic- tion model is needed for the number of positive PCR and Different hospital admissions prediction strategies were AG tests and the overall PCR and AG positivity. In the previously published (Wesner et al., 2021; Mohimont main scenario, we assume that both PCR and AG positiv- et al., 2021; Gerlee et al., 2021). We have presented a set of ity is constant for the period of prediction (using values simple statistical models robustly explaining the hospital- as of December 27, 2020). This assumption is reasonable izations, hospital admissions and discharges in Slovakia. due to the fact that the rate of positive tests is rather sta- The model, applied to the data available at the end of De- ble in recent history and also it allows to use the observed cember 2020, predicted gradually increasing demand on trends in the number of positive tests observed in individ- hospital resources in January 2021. The model has shown ual countries. that even if there was a marked improvement in COVID- Based on the regression used in the volume of hos- 19 containment policies, the explanatory variables were on pitalizations prediction it is only necessary to forecast a a trajectory with a high degree of inertia. To the best of our weighted linear combination of the appropriately time- knowledge, this is the first work using both PCR and AG lagged time series of the number of positive PCR and AG tests as predictors of hospital admissions. tests (see Table 1). The weighted linear combination is then a measure representing the overall observed incidence of COVID-19. The trends in the overall observed inci- Acknowledgements dence were described by Bodova and Kollar (2020). For the purpose of this projection we use an ARMA model We are grateful to Brian Fabo, Martin Huba and Martin with automatically optimized lag structure. Smatana for helpful comments and assistance with data. We also add two alternative scenarios. An optimistic This work has been supported by the Slovak Research and scenario assumes the incidence declines by about 1.5% a Development Agency under the Contract Nos. APVV-18- day during the lockdown scheduled until January 10. This 0308 (RK) PP-COVID-20-0017 (RK, KB) and by the Sci- roughly corresponds to a 7-day reproduction number of entific Grant Agency of the Slovak Republic under the 0.9. After January 10 the incidence grows approximately Grants Nos. 1/0755/19 (RK, KB) and 1/0521/20 (KB, as in the main scenario. 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