Calculating 95% Confidence Intervals

• Rule of 3's
  • Used when the numerator is zero or 1 and there are at least 30 patients in the sample

    100 x 3/number of patients = upper limit of the 95% CI

  • Example: 50/50 patients die; the upper limit of the 95% CI for survival = 100 x 3/50 = 6%

    Given a sample size of 50, the survival rate could still be as high as 6%.

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• Calculating the 95% CI from the Standard Error of a Proportion
  • Used when 2 or more patients have the outcome of interest.

    p = proportion = number of patients with the outcome/total number of patients

    sep = standard error of the proportion = square root of: [p x (1-p)]/n.

    95% CI = 100 x (p - (1.96 x sep)), 100 x (p + (1.96 x sep))

  • Example: 8/36 die, p = 0.22, sep = square root of (0.22 x 0.78)/36 = 0.069 1.96 x sep = 1.96 x 0.069 = 0.135

    95% CI = 100 x (0.22 - 0.135), 100 x (0.22 + 0.135) = 8.5% to 35.5%

    If the study meets validity criteria, the true death rate probably lies between 8.5% to 35.5%.

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