For a continuous normally distributed outcome, in a superiority trial, the sample size per treatment arm, n, to ensure adequate power (1–β) where β is the Type II error rate whilst controlling the Type I error rate, α, for a specified/required treatment difference, d, and standard deviation, σ, is given by
where r is the allocation ratio of participants between the two treatment arms, experimental to control.6 Subjective clinical expertise can be used to specify the required treatment difference and there are agreed values used for the Type I and II error levels. However, a difficulty arises when trying to quantify the standard deviation.7 (link) Estimating the standard deviation at an inappropriate level can have a serious effect on the power of the study.8 (link) If the anticipated standard deviation is estimated to be too high, the trial will contain more participants than necessary. If the anticipated value is estimated to be too low, the trial will not contain enough participants to find the required effect, leading to the problems outlined in Section 1.
One of the methods investigators might use to try to get an accurate prediction of the true standard deviation (or variance) of the outcome measure is to conduct an external pilot trial prior to the main trial. Pilot trials are often small; therefore, they tend to imprecisely predict the true variance. The anticipated distribution of the pilot variance is a chi-squared distribution.9 As a consequence, the accuracy of the variance prediction will depend on the pilot sample size and, hence, the degrees of freedom for the variance. Estimating the main trial sample size fromequation (1) can result in a loss of power when the variance is imprecisely estimated. Using previous trial results to estimate the variance introduces a type of imprecision that should be allowed for when estimating the sample size for the main trial.9
where r is the allocation ratio of participants between the two treatment arms, experimental to control.6 Subjective clinical expertise can be used to specify the required treatment difference and there are agreed values used for the Type I and II error levels. However, a difficulty arises when trying to quantify the standard deviation.7 (link) Estimating the standard deviation at an inappropriate level can have a serious effect on the power of the study.8 (link) If the anticipated standard deviation is estimated to be too high, the trial will contain more participants than necessary. If the anticipated value is estimated to be too low, the trial will not contain enough participants to find the required effect, leading to the problems outlined in Section 1.
One of the methods investigators might use to try to get an accurate prediction of the true standard deviation (or variance) of the outcome measure is to conduct an external pilot trial prior to the main trial. Pilot trials are often small; therefore, they tend to imprecisely predict the true variance. The anticipated distribution of the pilot variance is a chi-squared distribution.9 As a consequence, the accuracy of the variance prediction will depend on the pilot sample size and, hence, the degrees of freedom for the variance. Estimating the main trial sample size from