Testing is one of the most effective lever in managing pandemics. The recent experience of Coronavirus disease 2019 (COVID-19) is a case in point where the disease was first reported in December 2019 in Wuhan, China and since then it had spread across the world. As a measure to address this pandemic, testing helped with keeping track of the status of the disease and in planning for other measures such as stay-at-home orders. The need for accelerated testing along with social distancing was soon felt to control the outbreak of infections. "Americans need access to rapid diagnostic testing. The sooner clinicians, patients, and public health officials know whether someone is infected with the novel coronavirus, the sooner they can take action to mitigate the spread of COVID-19," said the Director of Biomedical Advanced Research and Development Authority, Department of Health and Human Services' Office. Hence, both building testing capacity via augmenting capacity at public and private laboratories (labs), and improving speed of obtaining test results are critical for early testing, diagnosis, and patient's path to recovery. In our research we examine how to manage testing strategies by accounting both human-behavior and testing-site specific factors. In particular, human-behavior related factors include social interactions vs isolation during the waiting times. Healthcare policy makers can leverage our research insights in developing testing guidelines, which would enable rapid response to swab processing. We consider testing site factors such as type of swab analysis site (public vs. private), relative analysis capacity, distance between collection and testing sites. In addition, the results of this study are instrumental to control the spread of infections during pandemics.
As the cases grew, state governors responded with multiple mechanisms to enhance testing capacity such as augmenting capacity at public and private labs. Private labs typically possess greater testing capacity due to high degree of process automation. Hence, demand allocation decision between private and public labs could be an lever for effectively managing testing capacity, speedy testing and containing the disease spread, which results in maximizing the number of people recoveries.
Typically, treatment for a pandemic is not immediately available to all patients; hence, early diagnosis and then quarantine is the best known strategy to control the spread of diseases. This approach was followed globally during the recent COVID-19 pandemic. Early diagnosis necessitates the efficient management of the limited testing availability. In an effort to address the testing requirements, the United States has authorized their public labs (operated by local government) and private labs (operated by private companies including pharmacies and medical practices or not-for-profit organizations) to undertake manual, semi-automated and automated testing for COVID-19. In addition, drive-through sampling facilities and mobile testing units are also put in place that prioritize sampling for symptomatic individuals that are part of the highest risk population, such as those who have been in close contact with a positive case, health care workers, nursing home employees, and first responders on the front lines. These drive-through testing sites help reduce density and the potential for spread by keeping people who are sick or at risk of having contracted Coronavirus out of healthcare facilities. This system of labs creates a diagnosis network that has similarities to early infant diagnosis (EID)/network (EIN) that has received some research attention.
Considering the case of COVID-19, we note that the testing process forms an important part of patient flow. A typical flow of patients that begins from the onset of COVID-19 symptoms until the post-hospitalization stage (in the event of getting infected) is shown in the figure below. In the event of suspicion of COVID-19, the patients consult with primary care physicians. Based on the patient symptoms and the Centers for Disease Control and Prevention (CDC) guidelines, physicians recommend to perform a COVID-19 test on the patient. The physicians can also categorize the potential state of the disease (mild, moderate and severe) by combining the patient's symptoms and medical history. After the swabs from the patients are collected, the swabs become the flow unit through the remainder of the process. Depending on the stage of disease, the patients' swabs are directed to either public or private analysis sites for further investigation. The transit time involved in collecting the test swab, batch preparation, and transporting the swab varies depending on the type of lab. Typically, it may take more than 48 hours for the swab to reach the large private analysis sites. Depending on the backlogs and capacity at the swab analysis site (lab), the test batch samples may wait for analysis. Testing delays can be significantly high, especially when the pandemic is in the initial phase and testing capacities are low. For example, in Arizona, patients report a delay of 6-8 days to receive the test analysis results. The delays in testing could be attributed to several factors such as swab analyzer capacity constraints, shortage of supplies to perform the testing etc. Once the test results are obtained, the patients are recommended to either stay at home or undergo hospitalization.
Within the outlined testing system, it is important to be cognizant of the turnaround times (TAT), which can include the time it takes for a person to reach the testing center as well as the delays from the time when the sample is drawn and the time when the results are reported. The shortening of TAT is an important metric in mitigating the spread of the virus. It helps in identifying individuals who need to be administered the necessary care to manage their disease condition. It also helps in determining individuals who need to self-quarantine to limit the spread of the virus.
The high demand on healthcare resources during the COVID-19 pandemic created a situation of scarcity. Overcrowding and associated delays resulting from the scarcity relates to the literature stream on delays in primary care. Similar to the adverse patient outcomes such as sub-optimal quality of care and increased mortality rates due to delays in the primary care context, within the testing context for the COVID-19 pandemic delays can result in higher infections, mortality rates, and low quality of care for high risk patients. Additionally, these delays also create adverse social outcome since it limits the ability to appropriately structure mechanisms to reduce the spread of the disease within communities.
In the event of pandemic, reducing infection rates ought to be prioritized. Testing delays can extend the time an infected person begins quarantine, thereby increasing the chances of infecting others. Considering the complex and stochastic nature of the influence of testing delays on infection rates, in this study, we aim to capture the marginal effect of delay in obtaining testing results on the expected number of infected patients.
One of the possible approaches to manage testing is to employ a preferential testing policy. The CDC in the US developed prioritization guidelines for testing, so that individuals likely of developing a quick infection receive early testing and diagnosis. Studies report that about 20% cases of COVID-19 are severe or critical. This characteristic of COVID-19 underscores the need for a priority-based testing to diagnose infection in the early phase of progression. The priority-based testing enables early initiation of the treatment and lowering the spread of the disease. Hence, we analyze the effect of patient priority on the volume of secondary infections.
Severe cases can experience rapid progression and exhibit the onset of acute respiratory distress syndrome. Several studies had shown the mortality rate for severe cases is higher than the mortality rate for benign cases. The need of effective testing policy is more profound for COVID-19 because undiagnosed patients could potentially infect others during the time elapsed due to delay. While it is known that an early diagnosis can help patients isolate and reduce secondary infections, how to manage segmented patients (high and low priority) to effectively control secondary infections is unclear. There are several operational strategies that control the spread of infections, such as assignment of the test swab to a public vs a private lab. Private testing labs that are typically larger may be located farther from the test swab collection site as compared to relatively smaller public labs. Further, CDC has mandated certain categories of patients be given a high priority for testing. High priority could be based on patient age, profession, or the degree of symptoms. While prioritizing certain high risk symptomatic patients seems natural, the effect of priority on the secondary infections induced by low risk symptomatic patients is unclear. We argue that delaying test results for low risk symptomatic patients (younger patients) can affect large masses through social interactions than high risk patients (older). Hence, developing an understanding of the testing priority dynamics on the overall infection volumes is crucial. This delay could be a result of prioritization policy as well as the site assignment decision.
To address the issues raised above, we attempt to answer the following research questions related to testing strategies: (i) How should the patient population be prioritized after accounting for social interactions during waiting time for testing results? (ii) Under what conditions should we prioritize the older high-risk patients over younger low-risk patients? (iii) How do different patient segments affect the site assignment decision in light of social interactions?
We develop a stylized queuing model to analyze the two-phase testing process which includes the 1) swab collection, batching, and transport to the test analysis, and 2) waiting and processing swab analysis at the test site. We characterize the testing process parameters using evidence from the testing data obtained from public health CDC repository. A patient may exhibit different social behavior during the waiting time to obtain the test results i.e., interaction followed by isolation. We account for this social behavior using a two-phase waiting time model. We develop a closed-form expression for estimating the expected number of infected patients. Then, we leverage this model as a building block to analyze the effect of testing delays on two patient types, where one possess a testing priority over the other. As discussed earlier, prioritizing a patient class may have negative effects as patients can socialize and infect others. To analyze scenarios with social interactions between two patient types, we develop Markov chain models to estimate the testing delay distributions at the sites. As a final step, we obtain the optimal test assignment probabilities between two sites.
Our study provides implications for considering priority testing policy on expected number of secondary infections. If the patient's state of health deteriorates due to the faster progression of the disease, the time delay in testing can make a significant difference in the recovery of the patients. During the waiting time to obtain the test results, patients may continue to interact socially before getting into isolation phase. Further, different patient types exhibit difference in their social interaction pattern i.e., older patients may have a short social interaction phase compared to younger patients. Due to a highly contagious nature of COVID-19, the number of infections increase due to social interactions during testing delays. There exists an interaction heterogeneity among the young and the old patients. Since, the young patients are at low-risk, they tend to socialize and show low compliance to quarantine.
We show the impact of delayed testing of low-risk patients in the overall spread of the disease. When we consider a state-dependent arrival policy, we find that more social interactions by the low priority patients results in more testing requirements. Hence, we observe that irrespective of the proportion of high-priority patients, the FCFS testing policy is superior when compared to a threshold-based priority for the high-risk patients. Hence, it is critical to stratify patients for the preferential testing depending on the class of the patients. This is more true for coronavirus, where studies had shown that patients with underlying conditions are at a higher risk of the severe outcome.
From experimental results, we find that delaying tests for low priority patients can increase the number of secondary infections. This presents implications for policy makers to consider the likelihood of social interactions among low priority patients when a testing service is delayed. Evidence of such secondary infections were reported in popular media. CDC reported that infections among young adults may have eventually spread to older, more vulnerable high priority population. A high priority testing policy needs to account for the higher propensity of social interactions among low priority patients. In fact, a recent study published in Science uses aggregated, age-specific mobility trends from more than 10 million individuals in the United States and notes that 70% of the spread of COVID-19 can be attributed to American's aged between 20 and 49 years. Similar points are echoed by news media. For instance, Dr. John Brownstein, an epidemiologist at Boston Children's Hospital and ABC News contributor notes that, "This addresses this underlying false narrative ... that if you guard the most vulnerable, you can let the virus run rampant. If you let it run rampant in the younger age groups it will still affect the elderly and vulnerable groups." Our results indicate that a priority testing policy may not necessarily be the best approach given the nature of this disease and human tendency to interact socially.
In a scenario when an exposed person does not require testing, the preferential testing is, in fact, a better testing strategy. However, the magnitude of advantage depends of the mix of low and high priority testing proportion. If a testing site is majorly serving either low priority patients or high priority patients, the advantages of preferential testing are not significant. In this scenario (a fixed arrival rate), we also investigate to find optimal proportion of testing swab sent to public and private labs. As noted earlier, private labs are relatively larger than public labs, but they are typically located farther. The transportation time and resulting longer turnaround times have important policy implications in how high and low priority cases should be assigned to these labs. When one considers preferential testing of high priority cases, transportation times associated with shipping swabs to private labs, and social interactions among low priority patients while waiting for their test results, our findings offer some counter-intuitive insights regarding the assignment of high and low priority swabs to labs. Provided two types of lab have different capacity and transportation time, it is critical to understand the distribution of the proportion of swab batches sent to each lab. In case of preferential testing and a significant difference in transportation time, the low priority cases should be sent to the lab that is closer, contrary to our initial belief of sending low priority samples to the lab that is far. The primary reason is that the advantages of preferential testing are overshadowed by the newly generated infections due to the high mobility of low-priority patients. In case of preferential testing and a insignificant difference in transportation time, the low-priority cases should be sent to the lab with high capacity.
The proposed model also helps policy makers to jointly consider the role of transportation times and the proportion of swabs to be sent to public labs. As the ratio of transportation times to public labs versus to private labs increase, we find that the number of secondary infections (by a person while waiting for test results) increases. If policy makers plan assignment of swabs to private and public labs, greater benefits in terms of reduced infections can be attained by reducing the transportation time to public labs relative to the transportation time to private labs.
In the U.S., public and private labs contributed to a great extent in easing the need for testing potential COVID-19 cases. Initially, public labs were the primary testing sites but this severely constrained their capacity. Given the unprecedented backlogs in public labs, after a long-drawn approval process during the initial phase (January 2020 to early March 2020) of the pandemic in U.S., private labs were authorized to perform COVID-19 testing. However, by the peak of the first wave in early April 2020, private labs were processing most of the testing requirements within U.S. With more than 85% of the testing being done by these private labs, amounting to more than 35,000 tests per day, their capacity also started to get constrained. The situation faced with regards to testing calls attention to a more systematic approach to assigning private and public labs in the event of pandemic. Our study provides some important insights into this issue.
We consider some important parameters that should play a role in assigning testing demand to available public and private lab capacities. Private labs in the U.S. have higher capacity than public labs, but they are located far from the collection sites. Hence, it is important to simultaneously account for lab capacities and transportation time. In addition to these aspects, testing cases need to consider the level of risk faced by the person seeking testing. As the testing demand rose during the initial phase of the pandemic, guidelines mandated that patients who are at high-risk and hospitalized should be given priority at the public lab. The public labs were expected to provide fast turnaround, primarily because they were located either in the hospital or a nearby location. However, over time, the decision to send samples to the public labs resulted in the demand for high-risk testing exceeding beyond their capacity. At this point in time private labs also started testing for high risk patients. However, as more private labs began to test, delays were observed partly due to a failure to prioritize patients and partly because of the transportation times needed to reach private labs given that they are typically located farther away. Our study accounts for these site-specific factors to offer directions for optimally assigning private and public labs in a region.
Given the high demand and quick need for actions such as quarantine, our results suggest that the allocation of testing should be done in view of both transportation time and the available capacity at the lab. While urgent testing can be done at a nearby public lab, lack of capacity in these labs can increase the delays and secondary infection volumes. By considering the trade-off between transportation time and relative capacity available in private and public labs, we provide directions for optimal assignment of samples to two labs located in Michigan to minimize the spread of infection.
Source: Roy, D., Gupta, A., Nair, A., van Ommeren, J.C.W. Managing Testing during Pandemics: Considerations of Site-specific and Human-behavior Related Factors. Working paper.
