Figure 1 presents the estimator’s performance across all epidemic scenarios considered.

Bias decreased as the analysis time window expanded, achieving near-zero levels once the group had reached its epidemic peak (ε=1), with no substantial further improvements at later epidemic stages (ε>1, Figure 1A).

Coverage performance was contingent upon the significance (α) level and the stage of the group’s epidemic (ε) (Figure 1B). Halfway before the epidemic peak (peak coefficient ε=0.5), coverage at α levels up to 25% was too low, with average errors of 0.22, 0.18 and 0.07 for α levels of 5, 10, and 25%, respectively. In contrast, the 50% coverage was too high with an average error of -0.10. Around the epidemic peak (ε 0.7-1.3), coverage for α = 5-10% was good, whilst coverage for α = 25-50% was too high (average error -0.14). At later epidemic stages (ε 1.5-5), coverage was good across most significance levels, although the 50% coverage remained high across all epidemic stages.

Sensitivity and specificity were contingent upon the CI significance level α and the stage of the group’s epidemic (ε) (Figure 1C). Larger α values enhanced sensitivity at the expense of specificity, irrespective of the epidemic stage. And, regardless of α, analysing transmission chains later in the epidemic (i.e. increasing ε) also enhanced sensitivity, although this improvement was marginal past a peak coefficient of 1.5. However, the gain in sensitivity relative to the loss in specificity induced by delaying the analysis varied with α, with more pronounced tradeoffs for larger α values.

Figure 2 presents the relationship between various epidemic characteristics (columns) and the estimator’s performance metrics (rows), for a peak coefficient of 1 and a significance level of 0.05. Additional configurations are shown in supplementary materials (Figure S6).

Our estimator maintained consistent unbiased performance across the entire assortativity range (δ from -1 to 1) (Figure 2 column A row 1). Coverage consistently met the 95% target for δ < 0.5, with a slight decrease in coverage performance for δ > 0.5, although coverage remained close to the target, averaging at 0.91 (sd = 0.10) (Figure 2A2). This decrease in coverage in highly assortative scenarios could be due to a saturation effect: high assortativity will accelerate the depletion of susceptibles in the group, eventually resulting in lower observed assortativity compared to the true value (Figure S4). Although the assortativity coefficient δ only had a small effect on bias or coverage, it had a substantial impact on sensitivity, which was higher for larger absolute values of δ. However, sensitivity rose more gradually as |δ| increased on the disassortative scale compared to the assortative scale (Figure 2A3, Table S1.1), reaching an average of 82% for δ ≥ 0.5 compared to 55% for δ ≤ -0.5, suggesting a better ability to detect assortative than disassortative transmission. Indeed, assortative transmission implies that transmissions propagate within the same group across multiple generations, consequently increasing the sample size (τ.←a in equation 5) compared to disassortative transmission, and thus narrowing the CI, thereby enhancing sensitivity. Our linear regression suggested that the assortativity coefficient explained nearly 60% of the variance observed in sensitivity (Table S1.1).

Increasing the number of cases substantially reduced bias (Figure 2C1, Table S2), and increased sensitivity (Figure 2C3, Table S1.2) but had little effect on specificity or coverage (Figure 2C4 and 2C2). Bias was negligible (mean: 0.04, sd: 0.07) once the group reached 30 to 40 cases. Sensitivity was positively correlated with the number of cases: controlling for δ, the odds of detecting an assortative or disassortative pattern increased by 4% with each additional case (Table S1.2).

The relative size of the group had a substantial effect on bias (Figure 2B1, Table S2) and sensitivity (Figure 2 B3, Table S1.2) but no effect on specificity (Figure 2B4) nor coverage (Figure 2B2). When groups comprised 10% or more of the total population size, bias was close to 0 (Figure 2B1), and the odds of detecting an assortative pattern increased fourfold, compared to smaller groups (odds ratios (OR) = 4.15, 95% CI = 4.07 – 4.24) (Figure 2B3, Table S.1.2). Relative size and the number of cases jointly accounted for 72% of the variation in bias (Table S2), and contributed to a 42% increase in the pseudo R-squared for the linear regression on sensitivity (from 0.566 in Table S1.1 to 0.805 in Table S1.2).

Diverse transmission dynamics emerge from numerous groups, varying group sizes, reproduction numbers, and/or assortativity coefficients (Figure S5). This diversity results in varying saturation levels between groups over time, affecting transmission patterns within and between groups. Peak asynchronicity, a measure of heterogeneity in epidemic peak timing across groups was negatively associated with coverage (OR = 0.78, 95% CI = 0.78-0.78) and specificity (OR = 0.76, 95% CI = 0.76-0.76), explaining 18% and 24% of the variance, respectively (Table S3 and S4, Figure 2D2 and 2D4). These results suggest a decrease in our estimator’s performance with increasing heterogeneity between groups. However, our estimates remained unbiased (Figure 2D1) and with consistent sensitivity (Figure 2D3) irrespective of that heterogeneity.

In summary, analysing transmission chains at least up to the group’s epidemic peak generally improved all performance metrics. Near the group’s epidemic peak, coverage with significance levels of 5 or 10% yielded good performance, while levels of 25 and 50% were a bit too high, improving after the peak. Specificity was higher at lower significance levels, while sensitivity was higher at larger significance levels. Increased cases and relative group size contributed to improved estimator accuracy, reduced bias, and heightened sensitivity, with no significant impact on coverage nor specificity. Complex epidemic settings, measured through peak asynchronicity, did not significantly affect sensitivity or bias but were associated with a reduction in coverage and specificity.