Identification of the relative timing of infectiousness and symptom onset for outbreak control

Robert C. Cope; Joshua V. Ross

The key design points (i.e., sampling days) for optimal designs were consistently the first 197 day (Figure 2b) , followed by other days early in the outbreak (i.e., days 2-4), and the final 198 sampling day (day 14). Days 6-13 typically had little impact on model discrimination accuracy 199 (i.e., optimal Accuracy consistently levelled off as design size increased beyond 5; Figure 1d , 200 Supplemental Figure S3 ), and the optimal combination of these days varied due to stochasticity 201 in both training and test data. This is consistent with the feature importance used to develop 202 the heuristic (Figure 1b) , i.e., those days that were consistently optimal were those with highest 203 feature importance. It is remarkable that it is possible to discriminate models so accurately, given that they share 220 identical epidemic dynamics, and only differ in observation. The non-parametric nature of the 221 random forest is able to use small but clear differences between models (e.g., Figure 2c ) to 222 extract sufficient information to discriminate them. Combining the raw household data to form 223 summary statistics is critical to this: if the raw household data is used rather than the summary Figure 1 : (a) Model schematic describing: transitions between states within each household continuous-time Markov chain; the three observation models being discriminated between; and, the way that these household-level data are observed. (b) Random forest feature importance for the full 14-day design, used to construct the heuristic for smaller designs. (c) Histogram summaries of the daily household-level data under a given design, used as predictors in the random forest. (d) Resulting random forest accuracy as design size increases, for the true optimal design (solid lines) and heuristic solution (crosses with dashed line). These results correspond to households of size 5, with 10,000 training samples from each model, each with parameters drawn from the distributions displayed in Supplemental Figure S1 . 9 . CC-BY-NC 4.0 International license author/funder. It is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/571547 doi: bioRxiv preprint Figure 2 : (a) Accuracy of model discrimination in designs of size 5, as the number of households increases, and under partial observation. Note that p obs is not a fixed parameter but is sampled from a distribution; the listed value is its mean. The case with mean p obs of 0.5 was sampled from a Beta(5,5) distribution, and a mean p obs of 0.75 from a Beta(7.5,2.5) distribution. (b) Difference between heuristic designs (coloured points) and optimal designs (black boxes) as the design size increases. Note that the heuristic selects the optimal design at design sizes 4, 5, 13, and 14. (c) Distribution of training sample observations (under each model and number of households) for the most important feature under the heuristic: the proportion of households with 2 cases observed on day 1. These results correspond to households of size 5, with 10,000 training samples from each model, each with parameters drawn from the distributions that appear in Supplemental Figure S1 .