Quantifying the Risk and Cost of Active Monitoring for Infectious Diseases

During outbreaks of deadly emerging pathogens (e.g., Ebola, MERS-CoV) and bioterror threats (e.g., smallpox), actively monitoring potentially infected individuals aims to limit disease transmission and morbidity. Guidance issued by CDC on active monitoring was a cornerstone of its response to the West Africa Ebola outbreak. There are limited data on how to balance the costs and performance of this important public health activity. We present a framework that estimates the risks and costs of specific durations of active monitoring for pathogens of significant public health concern. We analyze data from New York City’s Ebola active monitoring program over a 16-month period in 2014–2016. For monitored individuals, we identified unique durations of active monitoring that minimize expected costs for those at “low (but not zero) risk” and “some or high risk”: 21 and 31 days, respectively. Extending our analysis to smallpox and MERS-CoV, we found that the optimal length of active monitoring relative to the median incubation period was reduced compared to Ebola due to less variable incubation periods. Active monitoring can save lives but is expensive. Resources can be most effectively allocated by using exposure-risk categories to modify the duration or intensity of active monitoring.

For Ebola, the data structure was different. Rather than having a unique single interval censored observation for every case, we had 300 draws from the posterior distribtion of incubation periods for each individual in the transmission tree. We ran a single parallel MCMC chain for each of the 300 posterior samples. Each chain had 110,000 samples, we discarded the first 100,000 as burn-in and did not thin. This procedure yielded 3 million samples from the posterior distribution. We chose to retain more samples for this analysis to account for the greater number of chains being run.
Two-dimensional credible regions were estimated using kernel density estimation on the joint posterior distribution of gamma parameters with flexible bandwidth matrices estimated by multivariate smooth cross-validation. (4,5) Missing data had limited impact on our analysis because reported cases typically have known possible times of infection. There were no missing data for either MERS or smallpox. Seven index cases out of 152 total cases from the Ebola outbreak in Guinea did not have known possible times of infection. Incubation periods were not estimated for these individuals in the original manuscript describing this outbreak (6), and these seven observations were excluded from our analysis, leaving 145 observations of the incubation period for Ebola. We note that there may be biased sampling of incubation periods as typically only more severe cases may be reported or observed, and these cases may have different incubation periods than cases with less severe symptoms.

Estimates of probabilities of infection
To provide first approximations of the probabilities of infection associated with each exposure risk category, we used available data on cases diagnosed in the United States (as the numerator) and number of individuals monitored in the United States (as the denominator). Because no cases were diagnosed in the United States after monitoring programs were implemented, we extrapolated the number of monitored individuals to cover the entire duration of the outbreak.
We used public data on the four cases diagnosed in the United States to classify these cases into appropriate exposure-risk categories. (7,8) Although some news reports have indicated that the Dallas index case may have had direct exposure to infected individuals, reports of initial statements made by the index case do not cite this known exposure, therefore he would have likely been classified as being at low (but not zero) risk.
The two Dallas healthcare workers, per CDC exposure risk definitions, would also have been considered low (but not zero) risk. (9) The New York City case would have been classified as some risk, due to his recent work in an Ebola treatment center abroad.(10)

Supplemental
By plugging in S(21) = 1-0.0056, we solve for λ, the constant per-day hazard, and obtain the estimateλ = 0.27/1000. This translates into one hospitalized case per every 3755 person-days of active monitoring.
Therefore, for the model below we estimate the probability of a monitored individual developing Ebola-like symptoms during a d day monitoring period as r d = 1 − (1 −λ) d .

Probabilistic model
We The model-based probabilities for the disease of concern (see Figure 1, main text) are shown in Table 3.
Supplemental Table 3: Outcomes and associated probabilities for model outcome probability does not develop disease of concern p 1 = 1 − φ does not develop disease of concern & not hospitalized for other symptoms does not develop disease of concern & hospitalized for other symptoms p 1 r d develops disease of concern during active monitoring develops disease of concern after active monitoring We quantified the uncertainty about the probability for each outcome scenario attributable to parameter uncertainty (in our estimates of the incubation period distribution) and to uncertainty associated with not

Sensitivity analyses: model assumptions about risk
We conducted sensitivity analyses to calculate the duration of active monitoring that minimized the maximum expected cost for a range of different probabilities of developing symptomatic disease. Assuming the same cost structure for active monitoring, we used our model to estimate a cost range of monitoring for each pathogen.

Sensitivity analysis: outlying Ebola incubation periods
We ran a sensitivity analysis on our incubation period estimation. We left out the two observations that had   Figure 4 in the main text, but uses different parameters, specifically, it assumes that a case gives rise to at most one secondary infection, that the cost is a fixed $4 million per case, and that the cost per monitored-person day is $20 The second plot for Ebola shows the posterior distribution leaving out the two observations that had incubation periods above 25 days. The shaded elliptical areas represent regions that contain 95% of the estimated posterior distributions for each of the three diseases. The disease-specific curves plotted on the right show the estimated distribution for the incubation period for each disease (dark line). To show some of the uncertainty associated with these estimates, a random selection of density functions sampled from the joint posterior are represented by colored transparent lines around the heavy lines. Shaded vertical bands indicate the marginal credible regions for the median and 95th percentile. decreased by 1 day (Figure 1).