Table 1 Precision/power of pilot trial size to address study aims

Estimation of recruitment rate

Recruiting 80 individuals allows an estimation of recruitment rate from our primary recruitment source of 30% with a margin of error of ± 5.80%, of 20% with a margin of error of ± 5.07%, and of 40% with ± 6.20% (according to the 95% confidence interval). Assuming a 30% recruitment rate, this will require contacting approximately 270 clients. Assuming a 20% recruitment rate, this will require contacting 400 clients. Assuming a 40% recruitment rate, this will require approaching 200 clients.

Estimation of retention rate

Recruiting 80 participants will enable estimation of retention rate (as a percentage of patients randomised) of 80% with a margin of error of ± 8.77%, of 70% with a margin of error of ± 10.04%, and of 90% with a margin of error of ± 6.57 (according to the 95% confidence interval).

Estimation of rate outcomes

Sixty-four individuals being retained allows estimation of a sutained recovery rate of 60% with a margin of error of ± 12.00%, of 70% with a margin of error of ± 11.23%, and of 50% with a margin of error of ± 12.25% (according to the 95% confidence interval).

Effect size estimates in ADepT arm

According to Cohen’s rules of thumb, at 80% power in a paired sample t test, a sample size of at least 13 is required to detect a large effect size (d ≥ .8), a sample size of at least 32 is required to detect a medium effect size (d ≥ .5), and a sample size of at least 197 is required to detect a small effect size (d ≥ .2). Therefore, assuming expected levels of recruitment and attrition, these analyses are powered to detect a medium or large pre- to post-treatment change in the ADepT arm for candidate outcome and mechanism measures to inferentially test proof of concept.