Sample size {14}
RECRUITMENT
Assuming 150 births in the opioid treatment program over an 18-month recruitment period, > 90% rate of maternal legal guardianship at birth, 80% study participation rate, and equivalent group allocation (50%), we expect to enroll 108 participants (n = 54 per study arm) during the project period. A sample size of 54 per study arm will produce a two-sided 95% CI with a distance from the standardized difference in means between two arms to the limits that are equal to 0.38. Additionally, with a sample size of 54 per study arm, a two-sided test for the time-averaged difference between two means in a repeated measures design with a significance level of 0.05 will have 80% power to detect a standardized difference in means of 0.43 in a design with 4 repeated-measurements taken over the 18-month period and with between level correlations of 0.5. A sample size of 54 per study arm will give us 80% power to detect a standardized difference in means of 0.54 (effect size) between two arms using a two-sided two-sample t-test with a significance level of 0.05. Of note, we were unable to find reported data about the cluster effect of different birth months. However, we expect only a negligible cluster effect for birth-month, and so assumed no to negligible intra-cluster correlation coefficient (ICC; 0 to 0.05) to perform the power calculations, which is almost equivalent to performing simple random sampling. However, we preferred the design of cluster random sampling to simple random sampling to account for the effect of birth-month if there is any.