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Table 1 Expected number of observed cases; probability and expected precision of observing a treatment in practice

From: Methods of sample size calculation in descriptive retrospective burden of illness studies

  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