This was a retrospective study design. Hospital admission and occupancy data for isolation beds was collected from Tan Tock Seng hospital for the period 14th March 2003 to 31st May 2003. The main outcome measure was daily number of isolation beds occupied by SARS patients, including those fulfilling WHO criteria for suspect and probable SARS[16 ], as well as those admitted not fulfilling WHO case definitions but admitted to isolation rooms for observation. Among the covariates considered were daily number of people screened, daily number of people admitted (including observation, suspect and probable cases) and days from the most recent significant event discovery. Key events considered were as follows:
1. 14th Mar: discovery of the TTSH outbreak
2. 22nd Mar: press release that TTSH would dedicated to SARS management
3. 4th Apr: discovery of an outbreak at Singapore General Hospital (SGH)
4. 11th Apr: discovery of an outbreak at National University Hospital (NUH)
5. 20th Apr: discovery and press release on an outbreak at Pasir Panjang Wholesale Market (PPWM)
6. 13th May: discovery of a cluster of febrile staff and patients at the Institute of Mental Health (IMH)
Details on the above can be found in the chronology of press releases on SARS events in Singapore[17 ]. Events 1–5 all involved probable SARS cases, whereas event 6 proved to be a false alarm[18 (link)].
We utilized the following strategy for the analysis. Firstly, we split the outbreak data into two. Data from 14th March to 21st April 2003 was used for model development. We used structural ARIMA models in an attempt to model the number of beds occupied[19 ]. Estimation is via the maximum likelihood method using the Kalman filter[20 ]. For the ARIMA model parameters, we considered the simplest parsimonious lowest order model.
We computed various permutations of the order of correlation (AR), order of integration (I) and order of moving average (MA), and chose the optimal combination of parameters using the mean square error. The correlogram and partial correlogram graphs were also used to help in deciding the order of moving average (MA) and auto-regressive (AR) terms to include in the model. To ensure the model was robust to symmetric nonnormality in the disturbances, including heteroskedasticity, we computed Huber/White/sandwich estimator of variance for the coefficient estimates[21 ]. Before modeling the bed occupancy, we examined whether the series was stationary. In the event of non-stationarity, we opted to set an a-prior value of 1 for starting the Kalman recursions[22 ].
We used the likelihood ratio test to determine if inclusion of other covariates helped improve the fit of the model. Based on the final model selected, we assessed the out-sample validity of the model, by applying the model to predict the number of beds occupied for the remaining period of the outbreak (i.e. 22nd April 2003 to 31st May 2003). In addition, we also made three-day forecasts for selected periods during the outbreak, starting from day 4 of the outbreak. We used the mean absolute percentage error (MAPE) to measure and quantify the quality of fit. A lower MAPE value will indicate a better fit of the data. All tests were conducted at the 5% level of significance, and data analysis was performed in Stata V7.0 (Stata Corporation, College Station, TX, USA).
1. 14th Mar: discovery of the TTSH outbreak
2. 22nd Mar: press release that TTSH would dedicated to SARS management
3. 4th Apr: discovery of an outbreak at Singapore General Hospital (SGH)
4. 11th Apr: discovery of an outbreak at National University Hospital (NUH)
5. 20th Apr: discovery and press release on an outbreak at Pasir Panjang Wholesale Market (PPWM)
6. 13th May: discovery of a cluster of febrile staff and patients at the Institute of Mental Health (IMH)
Details on the above can be found in the chronology of press releases on SARS events in Singapore[17 ]. Events 1–5 all involved probable SARS cases, whereas event 6 proved to be a false alarm[18 (link)].
We utilized the following strategy for the analysis. Firstly, we split the outbreak data into two. Data from 14th March to 21st April 2003 was used for model development. We used structural ARIMA models in an attempt to model the number of beds occupied[19 ]. Estimation is via the maximum likelihood method using the Kalman filter[20 ]. For the ARIMA model parameters, we considered the simplest parsimonious lowest order model.
We computed various permutations of the order of correlation (AR), order of integration (I) and order of moving average (MA), and chose the optimal combination of parameters using the mean square error. The correlogram and partial correlogram graphs were also used to help in deciding the order of moving average (MA) and auto-regressive (AR) terms to include in the model. To ensure the model was robust to symmetric nonnormality in the disturbances, including heteroskedasticity, we computed Huber/White/sandwich estimator of variance for the coefficient estimates[21 ]. Before modeling the bed occupancy, we examined whether the series was stationary. In the event of non-stationarity, we opted to set an a-prior value of 1 for starting the Kalman recursions[22 ].
We used the likelihood ratio test to determine if inclusion of other covariates helped improve the fit of the model. Based on the final model selected, we assessed the out-sample validity of the model, by applying the model to predict the number of beds occupied for the remaining period of the outbreak (i.e. 22nd April 2003 to 31st May 2003). In addition, we also made three-day forecasts for selected periods during the outbreak, starting from day 4 of the outbreak. We used the mean absolute percentage error (MAPE) to measure and quantify the quality of fit. A lower MAPE value will indicate a better fit of the data. All tests were conducted at the 5% level of significance, and data analysis was performed in Stata V7.0 (Stata Corporation, College Station, TX, USA).
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