Conceptual approach
This analysis is based on an analytical model (i.e., a mathematical model with a closed form solution) that can capture the binary outcomes of interest as described below. The model uses secondary data. All methods were carried out in accordance with the relevant guidelines and regulations.
In the base case, I assumed contacts at average risk of infection with the Delta variant and an average disease course in the event of an infection. The probability of transmission and outcomes of COVID-19 consider the proportion of the population that is fully vaccinated and the vaccine effectiveness. The likelihood of infections in contacts also depends on the regional SARS-CoV-2 incidence including the number of unreported cases, the viral strain underlying the infection, the number of contacts, and general COVID-19 containment measures. The harm of an infection depends on the risk factors of contacts (e.g., age).
The benefits of self-tests are measured by the number of SARS-CoV-2 infections avoided in contacts. In addition, the study goes beyond determining contagiousness by capturing severe clinical events following an infection (death, intensive care unit (ICU) admission, and long COVID syndrome). To avoid double counting of severe clinical events, only non-fatal ICU stays were taken into account. A combined endpoint consisting of death, ICU admission, and long COVID syndrome was defined, and the components were weighted according to their incidence.
The study does not take non-severe symptoms of COVID-19 into consideration assuming that testing is not motivated by the desire to avoid non-severe symptoms in contacts (otherwise influenza testing for the purpose of avoiding non-severe infections would be much more prevalent). In addition, the study computes the cost of testing per avoided event and per quality-adjusted life year (QALY) gained. The time horizon was set to less than 1 year, which is sufficiently long to capture all clinical events (especially long COVID syndrome) and transmissions following the index case infection.
The comparator of self-testing is the next effective intervention, which is the absence of self-testing but the maintenance of personal protective measures. In the counterfactual scenario without self-testing, infected contacts infect their contacts and so on, resulting in a chain of infection that spreads in this manner. To calculate the number of infections avoided by self-tests over the entire chain of infection, the convergence of a geometric series with quotient q of two adjacent elements of the sequence is considered: \(\sum_{k=0}^{\infty }{q}^k=\frac{1}{1-q}\). In this analysis, variable q corresponds to the effective reproduction number R, i.e., the number of people infected by the index case.
In a sensitivity analysis, an additional lowering of the R value caused by an increase in utilization of rapid tests in the population was calculated using a mathematical formula. According to equation 13 in Kuniya and Inaba [
8], there is a linear relationship between the R value and the reciprocal of the product of the population test rate and the sensitivity. Given that the testing rate does not equal the testing frequency, a logarithmic relationship of the following form was assumed: testing rate = −ln(1 - testing frequency) [
9].
By multiplying the 7-day incidence per 100,000 population, test sensitivity, and R value and dividing the product by the number of infections avoided over the entire infection chain, the number of self-tests that need to be conducted to prevent exactly one infection is calculated. By dividing the number by the probability of a combined endpoint, the number of self-tests that need to be conducted to prevent one severe clinical event is determined.
The advantages of self-testing are traded off against the disadvantages, i.e., false negative and false positive results. To determine false positive results, the number of tests required to prevent one severe event was multiplied by 1 minus specificity. Furthermore, the case is considered in which the consumer neglects personal protective measures such as the so-called AHA + L rule (social distancing, hand hygiene, wearing face masks, and ventilation) after a negative self-test. In this case of a false negative test result the number of infections and clinical events increases. The increase in infections is calculated by multiplying the 7-day incidence, 1 minus test sensitivity, the increase in the effective R value without protective measures (considering its linear dependence on the fraction of immunized individuals [
10]), and the number of infections avoided along the entire chain of infection.
Moreover, from a consumer perspective, the cost of testing per avoided clinical event and per QALY gained is determined. The gain in QALYs reflects the health gain from avoiding death, ICU admission, and long COVID syndrome. To compute the number of QALYs from preventing death, the analysis multiplied the remaining life expectancy at the average age of death from COVID-19 with the preference weight over the same period. To calculate QALYs gained from avoiding ICU admission, the remaining life expectancy of ICU patients was deducted from the remaining life expectancy in the general population. In addition, the loss of quality of life in ICU patients was considered.
Furthermore, I analyzed the relationship of testing years to avoid one clinical event and costs per QALY gained with respect to the age of contacts. To this end, I applied age-specific infection fatality rates (IFRs) and probabilities of ICU admission. To determine probabilities of ICU admission, I applied the age-gradient of the IFR assuming that ICU case fatality is independent of age (as a younger age of ICU patients has not been associated with a change in ICU fatality [
11]). For the age group 80+ years this approach leads an overestimation of the ICU admission rate, however, because of the significant share of deaths occurring in nursing homes (approximately 25% [
12]). For this age group I therefore applied the age-specific hospital admission rate as a proxy. Of note, for age groups below 80 years, data on hospital admission rates [
13] did not match the age groups for IFR and hence was not used.
The base-case analysis does not consider downstream costs associated with clinical events and the costs of false positive tests because they are largely borne by social health insurance and employers. In a sensitivity analysis, the maximum co-payment, which is 2% of the gross household income [
14], was applied.