What is sample size calculation and why is it relevant?

Sample size calculation determines the optimal number of participants that need to be included in a clinical trial. When designing a new trial, sample size calculations are essential to ensure sufficient power to evaluate the effect of a treatment.

What have we done?

To help researchers calculate the appropriate sample size, we have developed the ART (Analysis of Resources for Trials) suite of commands for Stata. This piece of software allows users to compute sample size or power for randomised trials of various designs. It also allows users to project accrual and power over time, based on a range of assumptions.

Over the years, we have improved the ART suite, which now accommodates features such as cross-over between treatments, loss to follow-up, staggered entry, and flexible patient accrual patterns. The software also supports non-inferiority designs, multiple treatment groups with joint tests, trend tests overdose levels of a covariate, time-to-event outcomes under non-proportional hazards, variants of the log-rank test and binary and ordered-categorical outcomes.

These commands have been extensively tested and have been shown to compare well both with Stata’s built-in power calculators (which are limited to parallel-group superiority trials only) and with other commercially available products such as Cytel’s EAST and the Sealed Envelope calculators.

In today’s world, where complex clinical trial designs are becoming more common, it is essential that sample size and accrual are accurately estimated. This ensures that trials get the right amount of resources and are of optimal clinical relevance.

The figure above represents some of the basic concepts in statistical sample size calculations. The null hypothesis is shown in red (with mean 0), and the alternative hypothesis in blue (with mean Δ). The type I error rate α is the probability of falsely declaring a difference between groups (“false positive”), whilst the type II error rate β is the probability of falsely declaring no difference (“false negative”). Typically, α is fixed at the conventional level of 0.05 (“5% significance”), and sample size is calculated for the desired power 1-β (usually 80%–90%). The vertical black line represents the critical value at which statistical significance would be declared.



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