Estimating epidemiologic dynamics from cross-sectional viral load distributions

Abstract

Estimating an epidemic's trajectory is crucial for developing public health responses to infectious diseases, but incidence data used for such estimation are confounded by variable testing practices. We show instead that the population distribution of viral loads observed under random or symptom-based surveillance, in the form of cycle threshold (Ct) values, changes during an epidemic and that Ct values from even limited numbers of random samples can provide improved estimates of an epidemic's trajectory. Combining multiple such samples and the fraction positive improves the precision and robustness of such estimation. We apply our methods to Ct values from surveillance conducted during the SARS-CoV-2 pandemic in a variety of settings and demonstrate new approaches for real-time estimates of epidemic trajectories for outbreak management and response.

Fig. 1.. The cycle threshold (Ct) value distribution reflects epidemiological dynamics over the course of an outbreak.

(A) Per capita daily incidence (histogram) and daily growth rate (blue line) of new infections in a simulated epidemic using a susceptible-exposed-infectious-recovered (SEIR) model. (B) Median days since infection vs. daily growth rate of new infections by epidemic day. Labeled points here and in (E–G) show five time points in the simulated epidemic. (C) Observed Ct value by day for 500 randomly sampled infected individuals. (D) Viral kinetics model (increasing Ct value following peak and subsequent plateau near the limit of detection), demonstrating the time course of Ct values (x-axis, line shows mean and ribbon shows 95% quantile range) against days since infection (y-axis). Note that the y-axis is arranged to align with (E). (E) Distribution of days since infection (violin plots and histograms) for randomly selected individuals over the course of the epidemic. Median and first and third quartiles are shown as green lines and points. (F) Skewness of observed Ct value distribution vs. daily growth rate of new infections by epidemic day. (G) Distribution of observed Ct values (violin plots and histograms) among sampled infected individuals by epidemic day. Median and first and third quartile are shown as purple lines and points. (H) Time-varying effective reproductive number, R_t, derived from the SEIR simulation, plotted against median and skewness of observed Ct value distribution.

Fig. 2.. Single cross-sectional distributions of observed cycle threshold (Ct) values can be used to reconstruct epidemic trajectories in a Massachusetts nursing home.

(A) Estimated prevalence (faint teal lines show posterior samples, solid teal line shows posterior median, teal ribbon shows 95% CrI) and incidence (red line shows posterior median, red ribbon shows 95% CrI) from the standard compartmental (SEEIRR) model fit to point prevalence at three sampling times (error bars show 95% binomial confidence intervals). (B) Model-predicted Ct distributions (blue) fitted to the observed Ct values (grey bars) from each of three cross-sectional samples. Shown are the posterior median (black line) and 95% CrI for the expected Ct distribution (dark blue ribbon), and 95% prediction intervals based on simulated observations (light blue ribbon). Note that prediction intervals are much wider than credible intervals, as they result from simulating observations with a small sample size. (C) Each panel shows results from fitting the Ct-based SEIR model separately to three cross-sections of virologic data. Shown are random posterior samples (red lines) and the maximum posterior probability trajectory (purple line) for the incidence curve. (D) Ct model-predicted median (blue point) and 95% CrI (blue error bars) for the proportion of samples testing positive compared to the observed proportion tested positive (grey cross). (E) 35-day (green) and 1-day (magenta) average growth rates from the Ct model estimates in part (C) at three time points (violin plots) compared to growth rate estimates from the SEEIRR model in part (A) (lines and shaded ribbons).

Fig. 3.. Inferring epidemic trajectory from cross-sectional surveillance samples with observed cycle threshold (Ct) values yields nearly unbiased estimates of the time-varying effective reproductive number, R_t, whereas changing testing rates lead to biased estimation using reported case counts.

(A) Number of positive tests per day by sampling time in epidemic and testing scheme for reported case counts (top row) and surveillance Ct sampling (bottom row), from a simulated susceptible-exposed-infectious-recovered (SEIR) epidemic. Observation times are shown by vertical lines. (B) R_t estimates from 100 simulations for each epidemic sampling time, testing scheme, and estimation method. Each point is the posterior median from a single simulation. R_t estimates for reported case counts use EpiNow2 estimation and for surveillance Ct samples use the Ct-based likelihood for one or multiple cross-sections fitted to an SEIR model. True model-based R_t on the sampling day is indicated by the black star and dashed horizontal line, while an R_t of 1, indicating a flat outbreak, is indicated by the solid horizontal line.

Fig. 4.. Single cross-sectional distributions of observed cycle threshold (Ct) values can estimate growth rate and multiple cross-sectional distributions can estimate the complex statewide epidemic trajectory from hospital-based surveillance at Brigham & Women’s Hospital in Massachusetts.

(A) Daily confirmed new cases in Massachusetts (gray bars) and estimated time-varying effective reproductive number, R_t. (B) Estimated R_t from the case counts vs. median and skewness of observed Ct value distribution by weekly sampling times. (C) Distribution (violin plots and points) and smoothed median (blue line) of observed Ct values by sampling week. (D) Posterior median (yellow arrow) and distribution (blue shaded area) of estimated daily growth rate of incident infections from a susceptible-exposed-infectious-recovered (SEIR) model fit to a single cross-section of observed Ct value data from the week commencing 2020-05-24. Shading density is proportional to posterior density. (E) Posterior medians (yellow arrow) and full distributions (blue shaded area) of estimated daily growth rate of incident infections from SEIR models each fit to a single cross-section by sampling week used. Red box denotes the panel from (D). (F) Posterior distribution of relative probability of infection by date from a Gaussian Process (GP) model fit to all observed Ct values (ribbons show 95% and 50% credible intervals, line shows posterior median). (G) Comparison of estimated daily growth rate of incident infections from GP model (blue line and shaded ribbons show posterior median and 95% CrI) to that from R_t estimation using observed case counts (red and green line and shaded ribbons show posterior median and 95% CrI) by date. Note that the x-axis is truncated at 2020-04-01, but estimates stretch back to 202-03-01 (Fig. S13).