Table 1.

The minimum mixture size required to give precision of ±0.05 around a prevalence of 0.1 with increasing AUC.

Method/AUC	0.6	0.65	0.7	0.75	0.8	0.85	0.9
Excess	–	–	–	–	3200	3100	3100
	Q25: –	Q25: –	Q25: –	Q25: –	Q25:3000	Q25:2900	Q25:3000
	Q75: –	Q75: –	Q75: –	Q75: –	Q75:3400	Q75:3300	Q75:3200
	87/100	62/100	42/100	19/100	13/100	2/100	3/100
Means	26,500	11,500	6200	3700	2500	1700	1100
	Q25:25,850	Q25:11,100	Q25:6000	Q25:3600	Q25:2400	Q25:1600	Q25:1100
	Q75:27,300	Q75:11,700	Q75:6375	Q75:3900	Q75:2525	Q75:1700	Q75:1200
	4/100	1/100	1/100	0/100	3/100	4/100	1/100
EMD	25,500	10,800	5700	3400	2200	1500	1000
	Q25:24,600	Q25:10,400	Q25:5550	Q25:3300	Q25:2100	Q25:1400	Q25:1000
	Q75:26,300	Q75:11,200	Q75:6000	Q75:3600	Q75:2300	Q75:1500	Q75:1000
	0/100	0/100	0/100	1/100	0/100	2/100	0/100
KDE	38,250	17,000	9000	5500	3400	2100	1300
	Q25:37,000	Q25:16,000	Q25:8500	Q25:5300	Q25:3300	Q25:2100	Q25:1300
	Q75:39,500	Q75:18,000	Q75:9125	Q75:5700	Q75:3500	Q75:2200	Q75:1400
	54/100	17/100	15/100	4/100	3/100	0/100	0/100

The table shows the median minimum mixture size, 25% quantile, 75% quantile, and the number of misses (coverage probability)—when the confidence interval at the minimum mixture size did not contain the true prevalence value ($p_{\mathrm{C}}=0.1$); the minimum mixture size is based on 100 estimation runs (see Methods—Varying mixture size). The estimates based on the Excess method do not converge to $p_{\mathrm{C}}=0.1$ with increasing sample size for AUC = {0.6, 0.65, 0.7, 0.75}. The number of misses quickly increases to 100, showing that the estimates converge to a value much smaller than 0.1. The estimates based on the KDE method converge to $p_{\mathrm{C}}=0.1$ for AUC = 0.6. For further details of the computations see “Methods”.