We generated long-tailed degree distributions using the power law with exponential cut-off described in Section 2, and found that the average distance to the empirical distributions was about 5.2 times zB. We then applied each of the rounding schemes described in Section 2. Scheme 1 (rounding all degrees up by 5) and Scheme 2 (by 10), reduced the factor from 5.2 to 2.7 and 2.3, respectively. Scheme 3 (adding 5 to every degree) increased the distance somewhat to 5.5. However, the more sophisticated FG-4592 mw Scheme 4 (rounding to the nearest 10 for k < 100 and to the nearest 100 for k > 100)

reduced the factor to 1.4; while Scheme 5, which is like Scheme 4 but also draws all degrees under 10 from the combined Bristol distributions, decreases this factor further still to 1.2, Table S3. In other words, these schemes produce distributions almost as close to the empirical ones as the two Bristol datasets are to each other. Note, however, that the level of interference involved in Schemes 4 and 5 should be seen as the minimum reporting error required to obtain realistic reported distributions from smooth underlying ones. If in fact it were the individuals with few contacts who nonetheless claimed to have hundreds while the

highly connected reported only a small number, this would not be evident in the data. The bias introduced by inaccuracies in reported degrees which we go on to analyse should therefore be regarded as a lower bound to the potential importance of this Florfenicol effect. Inaccuracy in reported degrees selleck kinase inhibitor had a large effect on the reliability of estimates of prevalence and incidence (Fig. 2). The top half of Fig. 2 shows estimates of prevalence from RDS surveys where degree was mis-reported by the 5 rounding schemes. The estimates were calculated using the Volz–Heckathorn estimator. Mis-reporting degrees caused all surveys to over-estimate prevalence (compare to the ‘Actual’ prevalence in the

whole network, top). However, if degrees were correctly reported (standard RDS) the average prevalence estimate from 100 surveys was accurate, but individual variation was large. Even with inaccurate degreees, the adjusted estimates (blue bars) were still closer to the true prevalence or incidence than the point estimate from the raw data (green bars). Two of our degree-biasing rounding schemes were based on degrees collected in Bristol, UK. Scheme 4 adjusted only those degrees larger than 10: the prevalence estimate is comparable with the estimate using correct degrees. However, the error increased when inaccuracies were added to the lower degrees (1 ≤ d ≤ 10) in Scheme 5. Those with low degree have a higher weighting in the estimator (Eq. (1)) than those with high degree; therefore mis-reporting these degrees had a larger effect on the estimate. The average prevalence for rounding Scheme 5 was 39.8% [31.1–51.4% 95% CI] compared to the actual average prevalence of 27.2% [26.1–28.4% 95% CI].