Table 1.

Expected number of observed cases; probability and expected precision of observing a treatment in practice

	Expected number of individuals receiving treatment; (Probability of observing treatment at least once) ± Expected 95% confidence interval width for proportion receiving treatment
	n = 50	n = 100	n = 200	n = 300	n = 500	n = 1000
p = 0.01	1 (0.39); ±0.03	1 (0.63); ±0.02	2 (0.87); ±0.01	3 (0.95); ±0.01	5 (0.99); ±0.01	10 (1.00); ±0.01
p = 0.05	3 (0.92) ±0.06	5 (0.99) ±0.04	10 (1.00) ±0.03	15 (1.00) ±0.02	25 (1.00) ±0.02	50 (1.00) ±0.01
p = 0.10	5 (0.99) ±0.08	10 (1.00) ±0.06	20 (1.00) ±0.04	30 (1.00) ±0.03	50 (1.00) ±0.03	100 (1.00) ±0.02
p = 0.25	13 (1.00) ±0.12	25 (1.00) ±0.08	50 (1.00) ±0.06	75 (1.00) ±0.05	125 (1.00) ±0.04	250 (1.00) ±0.03
p = 0.50	25 (1.00) ±0.14	50 (1.00) ±0.10	100 (1.00) ±0.07	150 (1.00) ±0.06	250 (1.00) ±0.04	500 (1.00) ±0.03
p = 0.75	28 (1.00) ±0.12	75 (1.00) ±0.08	150 (1.00) ±0.06	225 (1.00) ±0.05	375 (1.00) ±0.04	750 (1.00) ±0.03