Fig. 5: Association between household cluster size and the per-person infection risk.

Owing to the sampling procedure, study participants were clustered within households. a Estimated per-person infection risk by household cluster size (black dots; 95% CIs: gray lines). Estimates and CI limits were determined by fitting a logistic GEE model with the infection status as response variable and household cluster size as a factor covariable. No association between household cluster size and the per-person infection risk was found (p = 0.933). b Per-person infection risk in household clusters in which at least one person was found infected (black curve based on 86 household clusters, with 213 persons). The gray line below the black curve shows the expected per-person infection risk under the assumption that infection statuses of the household cluster members are independent. Estimates and CI limits were determined by fitting a logistic GEE model with the infection status as response variable and household cluster size as a factor covariable (excluding 13 household clusters of size 1 each). An association between household cluster size and the per-person infection risk was found (p < 0.001). The excess per-person infection risks are given by the deviations of the black curve from the gray reference curve (71.79% – 54.21%  = 17.59%, 57.14% – 39.09% = 18.05%, and 38.75% – 31.64% = 7.11%, respectively, for 2-, 3-, and 4-person household clusters). Under the assumption that transmissions to household members occurred independently and were due to only one infected person in each household, the black curve further allows for an estimation of the secondary infection risk: Assigning a 100% risk to the already infected household member, these risk estimates are given by (71.79% × 2 – 100%) = 43.59%, (57.14% × 3 – 100%)/2 = 35.71%, and (38.75% × 4 –  100%)/3 = 18.33%, respectively, for 2-, 3-, and 4-person household clusters (compared to an unconditional estimated infection risk of 15.53%). All statistical tests were two-sided. No adjustments for multiple comparisons were made. Source data are provided as a Source Data file.