Daniel L. Terrago, Jr.
Jachelle Anne D. Terrago
How to Cite:
Terrago, D. L., Jr., & Terrago, J. A. D. (2024). Predicting length of hospital stay of COVID-19 patients using accelerated failure time model. NEU Likha Journal: A Refereed Journal of the New Era University School of Graduate Studies, 1(1), 49-70. https://doi.org/10.64303/n3u-Lailj24Hk0un2o-rpL0hs09oCpuAf-mT
Abstract
The objective of the study was to predict the length of hospital stay (LOS) of COVID-19 patients using accelerated failure time model (AFT). Estimates of LOS can be used to project demands and to allocate resources efficiently. Retrospective data of 131 recovered patients who were admitted at a secondary hospital in Quezon City, Philippines was used for model development while another set of 131 patients’ records was used for model validation. An AFT model using log-logistic distribution showed that age (TR = 0.996, 95% CI [0.992, 0.999], p = .010), temperature (TR = 0.909, 95% CI [0.832, 0.992], p = .033), and the interaction of gender and vaccination status (TR = 1.810, 95% CI [1.269, 2.582], p = .001) are significant predictors of LOS at .05 level of significance, with Adjusted R2 of 12.11%.
Keywords: COVID-19, length of hospital stay, survival analysis, accelerated failure time model
The Philippines had its first confirmed COVID-19 case on January 30, 2020 [Department of Health (DOH), 2020]. Since then, until December 2021, Philippines experienced four waves of COVID-19 infections—first wave in April 2020, which was considered modest with a peak of 316 seven-day rolling case average; second wave in August 2020 which peaked at 4,300 daily cases; third wave in April 2021, peaking at 11,000 average cases; and forth wave in September 2021 with the highest number of reported daily infection of more than 26,000 cases on September 11 (Pazzibugan & Cinco, 2021). The surge in September 2021 was fueled by the Delta variant which was highly transmittable. Hospitals reported full utilization of intensive care units (ICU) and COVID wards. The number of deaths during this time was also higher than previous waves, with some patients dying looking for hospitals (Pazzibugan & Cinco, 2021). In November 2021, Philippines experienced decreasing number of cases. However, in December 2021, another variant, named Omicron which first reported in South Africa, had also reached the country (DOH, 2021) and by January 2022, there was again a surge in number of cases again due to Omicron variant. The number of cases started to decrease in February 2022. WHO Philippines warns that pandemic is still not over and urges to prepare for the next possible COVID-19 surge (Yadav & Moon, 2022).
Hospital preparedness is crucial to maintain operations, manage resources, and mitigate shortages in staff and beds in order to lessen the burden in the healthcare system and save more lives during surge of cases. One important element of planning is the prediction of length of hospital stay (LOS). Several studies investigated the LOS of COVID-19 patients and the factors associated with it. One study in China found that a prolonged LOS in COVID-19 patients was associated with female sex, fever, chronic kidney or liver disease before admission and increasing creatinine levels. The median LOS of 75 patients involved in the study was 17 days (IQR 13-22 days) (Guo et al., 2021). In Vietnam, the median LOS of 251 COVID-19 patients was 16 days while age, residence and sources of contamination were significantly associated with longer LOS (Thai et al., 2020). In a systematic review of 52 studies about COVID-19 LOS, majority of which (46 out of 52) came from China, China registered longer median LOS (4 to 53 days) as compared to 4 to 21 days outside China (Rees et al., 2020). The authors explained that such difference could be due to different admission and discharge criteria among countries and different timing within the pandemic. Thus, a localized study of COVID-19 situation is crucial to better understand its dynamics. Estimates of LOS are more often not the primary outcomes of various studies which report LOS (Rees et al., 2020). This study aimed to contribute to the existing literature by exploring how data that were collected in a secondary hospital in Quezon City, Philippines can be used to model length of hospital stay of COVID-19 patients.
Moreover, during the pandemic, the main Researcher, along with his colleagues in a secondary hospital in Quezon City, Philippines, had struggled in efficiently allocating resources. The oversupply of some materials and shortage of others had affected the financial resources of the hospital. The surge of the number of cases had stretched the hospital capacity in terms of manpower. These circumstances have motivated the Researchers to explore the accumulated data during the pandemic and predict the COVID-19 patients’ length of hospital stay which could be used in resource allocation and planning. The study aimed to answer the research question and test the hypothesis that follows:
How does a function of the following variables predict the length of stay in the hospital of a COVID-19 patient—gender, age, vaccination status, blood pressure category (normal, elevated to stage 1, and stage 2), heart rate, respiratory rate, temperature, weight, having comorbidities, and use of oxygen support upon admission?
Hypotheses
Ho: All independent variables are not predictors of LOS, βi = 0, i = 1, 2, …, 11.
Ha: At least one of the β’s is not 0.
Method
Research Design
The study is a retrospective cohort study in which secondary data of confirmed COVID-19 patients were analyzed in order to determine whether there are significant relationships among variables that could help in modeling the patients’ length of hospital stay. This type of study was utilized so that the complete information on the patients’ length of hospital stay was used, which might not be the case for prospective approach in which some patients might still be in the hospital during the duration of a prospective study.
The explanatory variables used in model building were gender, age, vaccination (vaccinated or not vaccinated), blood pressure category (normal, elevated to stage 1, and stage 2), heart rate, respiratory rate, temperature, weight, comorbidity (with or without comorbidities), and oxygen support (with or without oxygen support upon admission). The outcome variable is the length of hospital stay (LOS) which is the number of days from date of admission to date of discharge.
Population and Sample
The study population consisted of recovered or discharged COVID-19 patients who were admitted at a secondary hospital in Quezon City from March 1, 2021 to December 31, 2021. The bed capacity of the said hospital is 100 which was extended to 200 during the pandemic with permission granted by the Department of Health. The hospital is situated in Quezon City which is the largest among the cities of the National Capital Region (NCR) (Quezon City Government, n.d.) and is also considered as one of the most populous cities in the region (Department of Environment and Natural Resources, n.d.).
Out of 2,941 admissions within the time frame of the study, 16 patients were readmitted to the same hospital due to COVID-19. In order to satisfy the assumption of independence of observations, only the first admission of these patients was considered. Thus, the sampling frame used in the study is the list of distinct patients with the data of their first or only admission to the hospital due to COVID-19.
The obtained sample size for multiple regression analysis with 11 predictors based on .05 level of significance, and medium effect size (f2 = .15) was computed at 131 using G*Power version 3.1.9.7 with obtained power of .84. The sample was selected using simple random sampling. Each patient in the sampling frame was assigned with a number. Random numbers were generated using Excel and the patient with the corresponding number became part of the sample.
Studied Patients
Most of the studied patients are male (67.2%); majority are unvaccinated (88.5%); and many do not have comorbidity (67.2%). The mean age is 46 (SD = 17.8). Also, most of the studied patients do not have fever (91.6%); and many do not need oxygen support upon admission (80.9%). The mean heart rate (HR) is normal (M = 92.63, SD = 16.19) while the respiratory rate (RR) is slightly above normal range (M = 22.05, SD = 3.89). Other clinical and nonclinical characteristics are found in Table 1.
Source of Data
The data were extracted from patient’s medical records, including non-clinical and clinical data. Non-clinical data includes age and gender. Clinical data includes vaccination status, vital signs (temperature, blood pressure, respiratory rate, heart rate), weight, comorbidities, use of oxygen support upon admission, and the length of hospital stay (LOS).
Data Analysis
Accelerated failure time model (AFT), a parametric survival regression model, was used to predict LOS using the explanatory variables at .05 level of significance. The event of interest in the study is discharge from the hospital while LOS is considered as the survival time. There were no censored observations in the study as all participants had already been discharged. An AFT model assumes that error term follows a parametric distribution in survival models such as exponential, Weibull, generalized gamma, log-normal, and log-logistic. The following steps were performed in building the parametric regression model for LOS. All statistical analyses were performed using SPSS v21 and Stata v17.
Step 1. Model Development
The first model, Model 1, expressed the logarithm of LOS as linear combination of all main effects:
ln (LOS) = β0 + β1age + β2male + β3vaccination + β4oxygen +
β5 commorbidity + β6stage1BP + β7stage2BP+ β8temperature + β9weight + β10HR+ β11RR + ln (ε), where male, vaccination, oxygen, comorbidity, stage1BP and stage2BP are dichotomous variables with value equals to 1 when the specified characteristic is present (e.g., being male). HR or heart rate, RR or respiratory rate, along with temperature, and weight are continuous variables. The random error term ε is assumed to follow a particular distribution. Akaike’s information criteria (AIC) and Bayesian information criteria (BIC) were computed to determine the distribution for Model 1 (Table 2). The distribution with lowest AIC and BIC is log-normal distribution which was fit into Model 1 and backward elimination was used to select significant predictors. The only significant predictor is age (p = .012).
Another model, Model 2, which consists of all main effects and pairwise interaction effect of categorical variables, was fit using log-logistic distribution based on AIC and BIC (Table 3). Using backward elimination, the final model, Model 3, is left with four significant predictors: age (z = -2.72, p = .007), temperature (z = -2.13, p = .033), vaccination (z = -3.15, p = .002), and the interaction of gender and vaccination (z = 3.59, p <.001).
Step 2. Diagnostic Checking
Diagnostic checking was performed to check if the assumptions are satisfied. For linearity, based on correlation analysis, there is a significant but weak linear relationship between ln(LOS) and age, r(129) = -.216, p = .013. On the other hand, temperature had no significant linear relationship with ln(LOS) based on the scatter plots of the variables (Figure 2). Nevertheless, temperature was retained in the model since its plot showed no pattern of nonlinear relationship. Moreover, the nonsignificant and weak relationship between age and temperature indicates absence of multicollinearity.
For homoscedasticity, the plot of residuals (res) and fitted values (predicted median _t) showed that most of the points are concentrated and randomly distributed at point 0 (Figure 3). This is an indication that homoscedasticity is satisfied and the residuals are unrelated (independence).
For the goodness-of-fit of the final model, the plot of Cox-Snell showed small departure from a 45-degree line which indicates that the model fits the data well (Figure 4). Another criterion used for goodness-of-fit is AIC. Table 4 shows that the lowest AIC is computed for log-logistic distribution. Hence, the log-logistic distribution is considered the best fitted model.
Step 3. Cross-Validation
To determine the level of generalizability of the model, the final model was used to predict the LOS of a new set of randomly selected sample. Pearson r was calculated between the actual and predicted logarithm of LOS of the new dataset.
Results and Discussion
The overall mean and median LOS of sampled patients are 16.73 days (SD = 6.56) and 14.75 days (IQR: 12.87–19.73), respectively. On the average, male patients had longer LOS than female patients by 2.4 days (Table 5). Among the age groups, patients who are 11 to 20 years old had the longest LOS (Md = 26.5, IQR: 14.96–27.73). Based on clinical characteristics, patients who registered longer LOS were those who were vaccinated (Md = 16.04, IQR: 12.11–20.94); those without comorbidity (Md = 14.86, IQR: 13.09–19.71); those who did not need oxygen support upon admission (Md = 14.89, IQR: 12.85–19.78); and those who had no fever (Md = 14.85, IQR: 12.88–19.76). Result of survival analysis using AFT model showed that age, temperature and interaction of gender and vaccination status were significant predictors of LOS at .05 level of significance (Table 6).
The final model is significant, χ2 (5) = 19.95, p = .001, with Adjusted R2 of 12.11%. This indicates that 12.11% variability in logarithm of LOS is explained by the linear combination of the significant predictors. Among the significant predictors, age and temperature have negative coefficients which means that these factors tend to accelerate the recovery time and shorten LOS (Table 6).
The time ratio (TR) of 0.996 for age indicates that a year increase in age shortens LOS by 0.4%, while holding other factors constant. In other words, the recovery of younger patients is slower than older patients. This is supported by the result of Kaplan-Meier survival analysis which shows that the patients in age group 0-39 had higher probability of longer LOS than that of older age groups (Figure 5). One possible explanation for this is the low vaccination rate among young adults during the time on the study. According to a study of researchers from University of California, young adults may be vulnerable to have long COVID symptoms due to high infection rates and low vaccination rates in that group (Leigh, 2021). In the case of the Philippines, the vaccination roll-out for adolescents aged 12-17 started on November 2021, compared to older age group who received their first dose as early as March 2021, with priority given to senior citizens. Among the sampled patients, none of those aged 12-17 were vaccinated.
The TR of 0.909 for temperature indicates that a degree Celsius increase in temperature shortens LOS by 9.1%, while holding other factors constant. This indicates that the recovery of patients with lower temperature upon admission is slower than patients with higher temperature. Among the studied patients, majority or 91.6% of the total sample had no fever (≤ 37.7ºC) and their mean LOS is 17 days (SD = 6.7) while patients with fever had mean LOS of 13 days (SD = 2.7). As a general guideline in the studied hospital, patients will only be discharged if they have no more symptoms and test negative in an antigen test. Some studied patients who had no fever upon admission tested positive in antigen longer which prevented them from being discharged. Two studied patients, for instance, had LOS of 42 and 39 days. According to reports, some people are testing positive for COVID-19 longer which means that they “may be shedding viral particles for a longer period or that the tests are picking up leftover viral debris as their infection fades” (Times as cited by Crist, 2022).
The only significant predictor with positive coefficient (TR > 1) is the interaction of gender and vaccination. Being a male patient with vaccination decelerate the recovery time and increase LOS by 81%, while holding other factors constant. The plot of survival curves showed that the probability of staying at the hospital, say for more than 20 days, is higher for male vaccinated group than other gender*vaccination groups (Figure 6). Among the studied patients, mean LOS of female vaccinated patients (M = 10.47, SD = 1.31) is almost half of that of male vaccinated patients (M = 20.51, SD = 8.65). A systematic review of studies revealed that “adult females develop higher antibody responses to vaccines than males” (Klein et al., 2010, as cited by Ciarambino et al., 2021). The doctors explained that the difference between male and female could be due to the presence of two X chromosomes in women while men only have one.
In terms of the relative importance of each significant independent variable, the interaction of gender and vaccination status (β = 0.458) contributed the most in predicting LOS, followed by age (β = -0.197), and temperature (β = -0.167) (Table 6).
For the cross-validation of the model, result of correlation analysis using Pearson r showed that there is a weak nonsignificant relationship between the actual and predicted logarithm of LOS, r(129) = .143, p = .103. The actual and predicted values only share 2% common variance. This result showed weak evidence for the generalizability of the final model to the study population.
Conclusion
The study was able to identify an AFT model that significantly predicts the length of hospital stay of COVID-19 patients. Despite the low generalizability of the model, the study was able to demonstrate how predictive analytics such as survival analysis can be used in analyzing data that were generated during the pandemic. Results of the study can help understand the dynamics of length of stay of COVID-19 patients which are crucial in making data-driven decisions and hospital management.
Limitations and Recommendation
This study is a single-site study and the generalization to other settings is limited and must be done with caution. The study was not able to test the significance of interaction of continuous and categorical variables due to the sample size. Inclusion of this interaction could have increased the prediction accuracy of the model. Sample size had to be reduced by considering lower power due unavailability of some of the patients’ information in electronic format. The study was also limited by the use of simple random sampling due to unavailability of some of the patient’s clinical and nonclinical characteristics in the sampling frame. Other sampling techniques with lower sampling error could have been performed if needed information are available. The study was only able to demonstrate single time-to-event modelling of LOS of patients’ first admission due to COVID-19.
Based on these limitations, the study recommends the inclusion of interaction of continuous and categorical variables to increase the prediction accuracy and achieve higher level of generalizability. Moreover, it is recommended to analyze the data using other predictive modelling techniques and compare the prediction accuracy of the generated models. Lastly, study recommends modelling recurrent events to analyze data from multiple hospital admissions that could provide more information about patients’ length of hospital stay.
References
Ciarambino, T., Barbagelata, E., Corbi, G., Ambrosino, I., Politi, C., Lavalle, F., Ruggieri, A., Moretti, A. M. (2020). Gender differences in vaccine therapy: where are we in Covid-19 pandemic?. Monaldi Archives for Chest Disease, 91(4). http:dx.doi.org/10.4081/monaldi.2021.1669
Crist, C. (2022, July 1). Some Test Positive for COVID for 10 Days or Longer. WebMD. https://www.webmd.com/lung/news/20220601/testing-positive-covid-10-days-or-longer
Department of Health. (2020, January 30). DOH Confirms First 2019-Ncov Case in the Country; Assures Public of Intensified Containment Measures. Retrieved from https://doh.gov.ph/doh-press-release/doh-confirms-first-2019-nCoV-case-in-the-country
Department of Health. (2021, December 15). DOH Confirms 2 Omicron Cases Among International Travelers. Retrieved from https://doh.gov.ph/press-release/DOH-CONFIRMS-2-OMICRON-CASES-AMONG-INTERNATIONAL-TRAVELERS
Department of Environment and Natural Resources. (n.d.). Regional Profile. https://ncr.emb.gov.ph/regionalprofile/
Guo, A., Lu, J., Tan, H., Kuang, Z., Luo, Y., Yang, T., Xu, J., Yu, J., Wen, C., & Shen, A. (2021a). Risk factors on admission associated with hospital length of stay in patients with COVID-19: A retrospective cohort study. Scientific Reports, 11(1), 7310. https://doi.org/10.1038/s41598-021-86853-4
