The required size of cluster randomized trials of non-pharmaceutical interventions in epidemic settings

To control the SARS-CoV-2 pandemic and future pathogen outbreaks requires an understanding of which non-pharmaceutical interventions are effective at reducing transmission. Observational studies, however, are subject to biases, even when there is no true effect. Cluster randomized trials provide a means to conduct valid hypothesis tests of the effect of interventions on community transmission. While they may only require a short duration, they often require large sample sizes to achieve adequate power. However, the sample sizes required for such tests in an outbreak setting are largely undeveloped and the question of whether these designs are practical remains unanswered. We develop approximate sample size formulae and simulation-based sample size methods for cluster randomized trials in infectious disease outbreaks. We highlight key relationships between characteristics of transmission and the enrolled communities and the required sample sizes, describe settings where cluster randomized trials powered to detect a meaningful true effect size may be feasible, and provide recommendations for investigators in planning such trials. The approximate formulae and simulation banks may be used by investigators to quickly assess the feasibility of a trial, and then more detailed methods may be used to more precisely size the trial. For example, we show that community-scale trials requiring 220 clusters with 100 tested individuals per cluster are powered to identify interventions that reduce transmission by 40% in one generation interval, using parameters identified for SARS-CoV-2 transmission. For more modest treatment effects, or settings with extreme overdispersion of transmission, however, much larger sample sizes are required.

Comparative performance of between-population allocation strategies for SARS-CoV-2 vaccines.

2Vaccine allocation decisions during emerging pandemics have proven to be challenging due to competing ethical, practical, and political considerations. Complicating decision making, policy makers need to consider vaccine allocation strategies that balance needs both within and between populations. Due to limited vaccine stockpiles, vaccine doses should be allocated in locations where their impact will be maximized. Using a susceptible-exposed-infectious-recovered (SEIR) model we examine optimal vaccine allocation decisions across two populations considering the impact of population size, underlying immunity, continuous vaccine roll-out, heterogeneous population risk structure, and differences in disease transmissibility. We find that in the context of an emerging pathogen where many epidemiologic characteristics might not be known, equal vaccine allocation between populations performs optimally in most scenarios. In the specific case considering heterogeneous population risk structure, first targeting individuals at higher risk of transmission or death due to infection leads to equal resource allocation across populations.

Estimating vaccine efficacy against transmission via effect on viral load

Determining policies to end the SARS-CoV-2 pandemic will require an understanding of the efficacy and effectiveness (hereafter, efficacy) of vaccines. Beyond the efficacy against severe disease and symptomatic and asymptomatic infection, understanding vaccine efficacy against transmission will help model epidemic trajectory and determine appropriate control measures. Recent studies have proposed using random virologic testing in individual randomized controlled trials to improve estimation of vaccine efficacy against infection. We propose to further use the viral load measures from these tests to estimate efficacy against transmission. This estimation requires a model of the relationship between viral load and transmissibility and assumptions about the vaccine effect on transmission and the progress of the epidemic. We describe these key assumptions, potential violations of them, and solutions that can be implemented to mitigate these violations. Assessing these assumptions and implementing this random sampling, with viral load measures, will enable better estimation of the crucial measure of vaccine efficacy against transmission.

Estimating epidemiologic dynamics from single cross-sectional viral load distributions

Virologic testing for SARS-CoV-2 has been central to the COVID-19 pandemic response, but interpreting changes in incidence and fraction of positive tests towards understanding the epidemic trajectory is confounded by changes in testing practices. Here, we show that the distribution of viral loads, in the form of Cycle thresholds (Ct), from positive surveillance samples at a single point in time can provide accurate estimation of an epidemics trajectory, subverting the need for repeated case count measurements which are frequently obscured by changes in testing capacity. We identify a relationship between the population-level cross-sectional distribution of Ct values and the growth rate of the epidemic, demonstrating how the skewness and median of detectable Ct values change purely as a mathematical epidemiologic rule without any change in individual level viral load kinetics or testing. Although at the individual level measurement variation can complicate interpretation of Ct values for clinical use, we show that population-level properties reflect underlying epidemic dynamics. In support of these theoretical findings, we observe a strong relationship between the time-varying effective reproductive number, R(t), and the distribution of Cts among positive surveillance specimens, including median and skewness, measured in Massachusetts over time. We use the observed relationships to derive a novel method that allows accurate inference of epidemic growth rate using the distribution of Ct values observed at a single cross-section in time, which, unlike estimates based on case counts, is less susceptible to biases from delays in test results and from changing testing practices. Our findings suggest that instead of discarding individual Ct values from positive specimens, incorporation of viral loads into public health data streams offers a new approach for real-time resource allocation and assessment of outbreak mitigation strategies, even where repeat incidence data is not available. Ct values or similar viral load data should be regularly reported to public health officials by testing centers and incorporated into monitoring programs.

Potential biases arising from epidemic dynamics in observational seroprotection studies

The extent and duration of immunity following SARS-CoV-2 infection are critical outstanding questions about the epidemiology of this novel virus, and studies are needed to evaluate the effects of serostatus on reinfection. Understanding the potential sources of bias and methods to alleviate biases in these studies is important for informing their design and analysis. Confounding by individual-level risk factors in observational studies like these is relatively well appreciated. Here, we show how geographic structure and the underlying, natural dynamics of epidemics can also induce noncausal associations. We take the approach of simulating serologic studies in the context of an uncontrolled or a controlled epidemic, under different assumptions about whether prior infection does or does not protect an individual against subsequent infection, and using various designs and analytic approaches to analyze the simulated data. We find that in studies assessing the efficacy of serostatus on future infection, comparing seropositive individuals to seronegative individuals with similar time-dependent patterns of exposure to infection, by stratifying or matching on geographic location and time of enrollment, is essential to prevent bias.

Statistical Properties of Stepped Wedge Cluster-Randomized Trials in Infectious Disease Outbreaks

Randomized controlled trials are crucial for the evaluation of interventions such as vaccinations, but the design and analysis of these studies during infectious disease outbreaks is complicated by statistical, ethical, and logistical factors. Attempts to resolve these complexities have led to the proposal of a variety of trial designs, including individual randomization and several types of cluster randomization designs: parallel-arm, ring vaccination, and stepped wedge designs. Because of the strong time trends present in infectious disease incidence, however, methods generally used to analyze stepped wedge trials may not perform well in these settings. Using simulated outbreaks, we evaluate various designs and analysis methods, including recently proposed methods for analyzing stepped wedge trials, to determine the statistical properties of these methods. While new methods for analyzing stepped wedge trials can provide some improvement over previous methods, we find that they still lag behind parallel-arm cluster-randomized trials and individually-randomized trials in achieving adequate power to detect intervention effects. We also find that these methods are highly sensitive to the weighting of effect estimates across time periods. Despite the value of new methods, stepped wedge trials still have statistical disadvantages compared to other trial designs in epidemic settings.