LitCovid-sentences  

PMC:7449695 / 24377-40081 JSONTXT 10 Projects

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Id Subject Object Predicate Lexical cue
T168 0-21 Sentence denotes Materials and methods
T169 23-80 Sentence denotes Estimating the time-varying effective reproduction number
T170 82-90 Sentence denotes Overview
T171 91-221 Sentence denotes The method used to estimate R𝑒𝑓𝑓 is described in Cori et al., 2013, as implemented in the R package, EpiNow (Abbott et al., 2020).
T172 222-502 Sentence denotes This method is currently in development by the Centre for the Mathematical Modelling of Infectious Diseases at the London School of Hygiene and Tropical Medicine (London School of Hygiene & Tropical Medicine Mathematical Modelling of Infectious Diseases nCoV working group, 2020).
T173 503-624 Sentence denotes Full details of their statistical analysis and code base is available via their website (https://epiforecasts.io/covid/).
T174 625-944 Sentence denotes The uncertainty in the R𝑒𝑓𝑓 estimates (shown in Figure 2; Figure 2β€”figure supplements 1, 2 and 3) represents variability in a population-level average as a result of imperfect data, rather than individual-level heterogeneity in transmission (i.e., the variation in the number of secondary cases generated by each case).
T175 945-1157 Sentence denotes This is akin to the variation represented by a confidence interval (i.e., variation in the estimate resulting from a finite sample), rather than a prediction interval (i.e., variation in individual observations).
T176 1158-1304 Sentence denotes We provide a brief overview of the method and sources of imperfect data below, focusing on how the analysis was adapted to the Australian context.
T177 1306-1310 Sentence denotes Data
T178 1311-1430 Sentence denotes We used line-lists of reported cases for each Australian state/territory extracted from the national COVID-19 database.
T179 1431-1659 Sentence denotes The line-lists contain the date when the individual first exhibited symptoms, date when the case notification was received by the jurisdictional health department and where the infection was acquired (i.e., overseas or locally).
T180 1661-1697 Sentence denotes Reporting delays and under-reporting
T181 1698-1981 Sentence denotes A pre-hoc statistical analysis was conducted in order to estimate a distribution of the reporting delays from the line-lists of cases, using the code base provided by London School of Hygiene & Tropical Medicine Mathematical Modelling of Infectious Diseases nCoV working group, 2020.
T182 1982-2052 Sentence denotes The estimated reporting delay is assumed to remain constant over time.
T183 2053-2230 Sentence denotes These reporting delays are used to: (i) infer the time of symptom onset for those without this information, and; (ii) infer how many cases in recent days are yet to be recorded.
T184 2231-2348 Sentence denotes Adjusting for reporting delays is critical for inferring when a drop in observed cases reflects a true drop in cases.
T185 2349-2447 Sentence denotes Trends identified using this approach are robust to under-reporting, assuming that it is constant.
T186 2448-2514 Sentence denotes However, absolute values of R𝑒𝑓𝑓 may be biased by reporting rates.
T187 2515-2591 Sentence denotes Pronounced changes in reporting rates may also impact the trends identified.
T188 2592-2732 Sentence denotes The delay from symptom onset to reporting is likely to decrease over the course of the epidemic, due to improved surveillance and reporting.
T189 2733-2961 Sentence denotes We used a delay distribution estimated from observed reporting delays from the analysis period, which is therefore likely to underestimate reporting delays early in the epidemic, and overestimate them as the epidemic progressed.
T190 2962-3254 Sentence denotes Underestimating the delay would result in an overestimate of R𝑒𝑓𝑓, as the inferred onset dates (for those that were unknown) and adjustment for right-truncation, would result in more concentrated inferred daily cases (i.e., the inferred cases would be more clustered in time than in reality).
T191 3255-3312 Sentence denotes The converse would be true when overestimating the delay.
T192 3313-3499 Sentence denotes The impact of this misspecified distribution will be greatest on the most recent estimates of R𝑒𝑓𝑓, where inference for both right-truncation and missing symptom onset dates is required.
T193 3501-3555 Sentence denotes Estimating the effective reproduction number over time
T194 3556-3739 Sentence denotes Briefly, the R𝑒𝑓𝑓 was estimated for each day from 24 February 2020 up to 5 April 2020 using line list data – date of symptom onset, date of report, and import status – for each state.
T195 3740-3898 Sentence denotes The method assumes that the serial interval (i.e., time between symptom onset for an index and secondary case) is uncertain, with a mean of 4.7 days (95% CrI:
T196 3899-3955 Sentence denotes 3.7, 6.0) and a standard deviation of 2.9 days (95% CrI:
T197 3956-4045 Sentence denotes 1.9, 4.9), as estimated from early outbreak data in Wuhan, China (Nishiura et al., 2020).
T198 4046-4169 Sentence denotes Combining the incidence over time with the uncertain distribution of serial intervals allows us to estimate R𝑒𝑓𝑓 over time.
T199 4170-4266 Sentence denotes A different choice of serial interval distribution would affect the estimated time varying R𝑒𝑓𝑓.
T200 4267-4388 Sentence denotes This sensitivity is explored in detail in Flaxman et al., 2020, though we provide a brief description of the impact here.
T201 4389-4552 Sentence denotes For the same daily case data, a longer average serial interval would correspond to an increased estimate of R𝑒𝑓𝑓 when R𝑒𝑓𝑓>1, and a decreased estimate when R𝑒𝑓𝑓<1.
T202 4553-4656 Sentence denotes This effect can be understood intuitively by considering the epidemic dynamics in these two situations.
T203 4657-4715 Sentence denotes When R𝑒𝑓𝑓>1 , daily case counts are increasing on average.
T204 4716-4916 Sentence denotes The weighted average case counts (weighted by the serial interval distribution), decrease as the mean of the serial interval increases (i.e., as the support is shifted to older/lower daily case data).
T205 4917-5007 Sentence denotes In order to generate the same number of observed cases in the present, R𝑒𝑓𝑓 must increase.
T206 5008-5053 Sentence denotes A similar observation can be made for R𝑒𝑓𝑓<1.
T207 5054-5396 Sentence denotes In the context of our analyses (Figure 2), when the estimated R𝑒𝑓𝑓 is above 1, assuming a longer mean serial interval would further increase the R𝑒𝑓𝑓 estimates in each jurisdiction (i.e., the upper 75% of the Victorian posterior distribution for approximately the first 7–10 days, while stretching the upper tails in the other jurisdictions).
T208 5397-5502 Sentence denotes When the estimated R𝑒𝑓𝑓 is below 1, a higher mean serial interval would further decrease those estimates.
T209 5503-5598 Sentence denotes Qualitatively, this does not impact on the time series of R𝑒𝑓𝑓 in each Australian jurisdiction.
T210 5599-5768 Sentence denotes AΒ prior distribution was specified for R𝑒𝑓𝑓, with mean 2.6 (informed by Imai et al., 2020) and a broad standard deviation of 2 so as to allow for a range of R𝑒𝑓𝑓 values.
T211 5769-6016 Sentence denotes Finally, R𝑒𝑓𝑓 is estimated with a moving average window, selected to optimise the continuous ranked probability score, in order to smooth the curve and reduce the impact of localised events (i.e., cases clustered in time) causing large variations.
T212 6017-6152 Sentence denotes Note that up to 20% of reported cases in the Australian national COVID-19 database do not have a reported import status (see Figure 1).
T213 6153-6270 Sentence denotes Conservatively, we assumed that all cases with an unknown or unconfirmed source of acquisition were locally acquired.
T214 6272-6301 Sentence denotes Accounting for imported cases
T215 6302-6403 Sentence denotes A large proportion of cases reported in Australia from January until now were imported from overseas.
T216 6404-6612 Sentence denotes It is critical to account for two distinct populations in the case notification data – imported and locally acquired – in order to perform robust analyses of transmission in the early stages of this outbreak.
T217 6613-6809 Sentence denotes The estimated time-varying R𝑒𝑓𝑓 value is based on cases that have been identified as a result of local transmission, whereas imported cases contribute to transmission only (Thompson et al., 2019).
T218 6810-6908 Sentence denotes Specifically, the method assumes that local and imported cases contribute equally to transmission.
T219 6909-6969 Sentence denotes The results under this assumption are presented in Figure 2.
T220 6970-7201 Sentence denotes However, it is likely that imported cases contributed relatively less to transmission than locally acquired cases, as a result of quarantine and other border measures which targeted these individuals (Figure 1β€”figure supplement 2).
T221 7202-7441 Sentence denotes In the absence of data on whether the infector of local cases was themselves an imported or local case (from which we could robustly estimate the contribution of imported cases to transmission), we explored this via a sensitivity analysis.
T222 7442-7630 Sentence denotes We aimed to explore the impact of a number of plausible scenarios, based on our knowledge of the timing, extent and level of enforcement of different quarantine policies enacted over time.
T223 7631-7769 Sentence denotes Prior to 15 March, returning Australian residents and citizens (and their dependents) from mainland China were advised to self-quarantine.
T224 7770-8011 Sentence denotes Note that further border measures were implemented during this period, including enhanced testing and provision of advice on arrivals from selected countries based on a risk assessment tool developed in early February (Shearer et al., 2020).
T225 8012-8206 Sentence denotes On 15 March, Australian authorities imposed a self-quarantine requirement on all international arrivals, and from 27 March, moved to a mandatory quarantine policy for all international arrivals.
T226 8207-8648 Sentence denotes Hence for the sensitivity analysis, we assumed two step changes in the effectiveness of quarantine of overseas arrivals (timed to coincide with the two key policy changes), resulting in three intervention phases: prior to 15 March (self-quarantine of arrivals from selected countries); 15–27 March inclusive (self-quarantine of arrivals from all countries); and 27 March onward (mandatory quarantine of overseas arrivals from all countries).
T227 8649-8758 Sentence denotes We further assumed that the relative infectiousness of imported cases decreased with each intervention phase.
T228 8759-9062 Sentence denotes The first two intervention phases correspond to self-quarantine policies, so we assume that they resulted in a relatively small reduction in the relative infectiousness of imported cases (the first smaller than the second, since the pre-15 March policy only applied to arrivals from selected countries).
T229 9063-9297 Sentence denotes The third intervention phase corresponds to mandatory quarantine of overseas arrivals in hotels which we assume is highly effective at reducing onward transmission from imported cases, but allows for the occasional transmission event.
T230 9298-9434 Sentence denotes We then varied the percentage of imported cases contributing to transmission over the three intervention phases, as detailed in Table 2.
T231 9435-9443 Sentence denotes Table 2.
T232 9445-9578 Sentence denotes Percentage of imported cases assumed to be contributing to transmission over three intervention phases for each sensitivity analysis.
T233 9579-9931 Sentence denotes We assume two step changes in the effectiveness of quarantine of overseas arrivals, resulting in three intervention phases: prior to 15 March (self-quarantine of arrivals from selected countries); 15–27 March inclusive (self-quarantine of arrivals from all countries); and 27 March onward (mandatory quarantine of overseas arrivals from all countries).
T234 9932-9975 Sentence denotes Imported cases contributing to transmission
T235 9976-10039 Sentence denotes Sensitivity analysis Prior to 15 March 15–27 March 27 March–
T236 10040-10055 Sentence denotes 1 90% 50% 1%
T237 10056-10071 Sentence denotes 2 80% 50% 1%
T238 10072-10087 Sentence denotes 3 50% 20% 1%
T239 10088-10190 Sentence denotes The results of these three analyses are shown in Figure 2β€”figure supplements 1, 2 and 3, respectively.
T240 10192-10241 Sentence denotes Forecasting short-term ward and ICU bed occupancy
T241 10242-10365 Sentence denotes We used the estimates of time-varying R𝑒𝑓𝑓 to forecast the national short-term ward/ICU occupancy due to COVID-19 patients.
T242 10367-10390 Sentence denotes Forecasting case counts
T243 10391-10626 Sentence denotes The forecasting method combines an SEEIIR (susceptible-exposed-infectious-recovered) population model of infection with daily COVID-19 case notification counts, through the use of a bootstrap particle filter (Arulampalam et al., 2002).
T244 10627-10792 Sentence denotes This approach is similar to that implemented and described in Moss et al., 2019b, in the context of seasonal influenza forecasts for several major Australian cities.
T245 10793-10932 Sentence denotes Briefly, the particle filter method uses post-regularisation (Doucet et al., 2001), with a deterministic resampling stage (Kitagawa, 1996).
T246 10933-11013 Sentence denotes Code and documentation are available at https://epifx.readthedocs.io/en/latest/.
T247 11014-11332 Sentence denotes The daily case counts by date of diagnosis were modelled using a negative binomial distribution with a fixed dispersion parameter k, and the expected number of cases was proportional to the daily incidence of symptomatic infections in the SEEIIR model; this proportion was characterised by the observation probability.
T248 11333-11667 Sentence denotes Natural disease history parameters were sampled from narrow uniform priors, based on values reported in the literature for COVID-19 (Table 3), and each particle was associated with an R𝑒𝑓𝑓 trajectory that was drawn from the state/territory R𝑒𝑓𝑓 trajectories in Figure 2 up to 5 April, from which point they are assumed to be constant.
T249 11668-11822 Sentence denotes The model was subsequently projected forward from April 14 to April 28, to forecast the number of reported cases, assuming a detection probability of 80%.
T250 11823-11831 Sentence denotes Table 3.
T251 11833-11869 Sentence denotes SEEIIR forecasting model parameters.
T252 11870-11917 Sentence denotes Parameter Definition Value/Prior distribution
T253 11918-11985 Sentence denotes Οƒ Inverse of the mean incubation period U ⁒ ( 4 - 1 , 3 - 1 )
T254 11986-12054 Sentence denotes γ Inverse of the mean infectious period U ⁒ ( 10 - 1 , 9 - 1 )
T255 12055-12120 Sentence denotes Ο„ Time of first exposure (days since 2020-01-01) U ⁒ ( 0 , 28 )
T256 12121-12164 Sentence denotes p π‘œπ‘π‘  Probability of observing a case 0.8
T257 12165-12214 Sentence denotes k Dispersion parameter on Negative-Binomial 100
T258 12215-12573 Sentence denotes observation model In order to account for imported cases, we used daily counts of imported cases to construct a time-series of the expected daily importation rate and, assuming that such cases were identified one week after initial exposure, introduced exposure events into each particle trajectory by adding an extra term to the force of infection equation.
T259 12574-12786 Sentence denotes Model equations below describe the flow of individuals in the population from the susceptible class (S), through two exposed classes (E1, E2), two infectious classes (I1, I2) and finally into a removed class (R).
T260 12787-12917 Sentence denotes The state variables S,E1,E2,I1,I2,R correspond to the proportion of individuals in the population (of size N) in each compartment.
T261 12918-13176 Sentence denotes Given the closed population and unidirectional flow of individuals through the compartments, we evaluate the daily incidence of symptomatic individuals (at time t) as the change in cumulative incidence (the bracketed term in the expression for 𝔼⁒[yt] below).
T262 13177-13317 Sentence denotes Two exposed and infectious classes are chosen such that the duration of time in the exposed or infectious period has an Erlang distribution.
T263 13318-13368 Sentence denotes The corresponding parameters are given in Table 2.
T264 13369-13482 Sentence denotes Model equations:dSdt=βˆ’Ξ²(t)β‹…S(I1+I2)dE1dt=Ξ²(t)β‹…S(I1+I2)βˆ’2ΟƒE1dE2dt=2ΟƒE1βˆ’2ΟƒE2dI1dt=2ΟƒE2βˆ’2Ξ³I1dI2dt=2Ξ³I1βˆ’2Ξ³I2dRdt=2Ξ³I2
T265 13483-13550 Sentence denotes With initial conditions:S(0)=Nβˆ’10NE1(0)=10NE2(0)=I1(0)=I2(0)=R(0)=0
T266 13551-13685 Sentence denotes Observation model:E[yt]=Nβ‹…pobsβ‹…[I2(t)+R(t)βˆ’(I2(tβˆ’1)+R(tβˆ’1))]xt=[S(t),E1(t),E2(t),I1(t),I2(t),R(t),Ξ²i(t),Οƒ,Ξ³,Ο„]β„’(yt∣xt)∼NegBin(E[yt],k)
T267 13686-13806 Sentence denotes With time-varying transmission rate corresponding to R𝑒𝑓𝑓 trajectory i:Ξ²i(t)={0,ift<Ο„Reffi(t)β‹…Ξ³,iftβ‰₯Ο„,forΒ i∈{1,2,...,10}
T268 13808-13886 Sentence denotes Forecasting ward and ICU bed occupancy from observed and projected case counts
T269 13887-14015 Sentence denotes The number of new daily hospitalisations and ICU admissions were estimated from recently observed and forecasted case counts by:
T270 14016-14170 Sentence denotes Estimating the age distribution of projected case counts using data from the national COVID-19 database on the age-specific proportion of confirmed cases;
T271 14171-14286 Sentence denotes Estimating the age-specific hospitalisation and ICU admission rates using data from the national COVID-19 database.
T272 14287-14491 Sentence denotes We assumed that all hospitalisations and ICU admissions were either recorded or were missing at random (31% and 58% of cases had no information recorded under hospitalisation or ICU status, respectively);
T273 14492-14846 Sentence denotes Randomly drawing the number of hospitalisations/ICU admissions in each age-group (for both the observed and projected case counts) from a binomial distribution with number of trials given by the expected number of cases in each age group (from 1), and probability given by the observed proportion of hospitalisations/ICU admissions by age group (from 2).
T274 14847-15069 Sentence denotes Finally, in order to calculate the number of occupied ward/ICU beds per day, length-of-stay in a ward bed and ICU bed were assumed to be Gamma distributed with means (SD) of 11 (3.42) days and 14 (5.22) days, respectively.
T275 15070-15205 Sentence denotes We assumed ICU admissions required a ward bed prior to, and following, ICU stay for a Poisson distributed number of days with mean 2.5.
T276 15206-15359 Sentence denotes Relevant Australian data were not available to parameterise a model that captures the dynamics of patient flow within the hospital system in more detail.
T277 15360-15503 Sentence denotes Instead, these distributions were informed by a large study of clinical characteristics of 1099 COVID-19 patients in China (Guan et al., 2020).
T278 15504-15704 Sentence denotes This model provides a useful indication of hospital bed occupancy based on limited available data and may be updated as more specific data (e.g., on COVID-19 patient length-of-stay) becomes available.