Sample size: how many participants are needed in a trial?

Researchers investigated the effectiveness of a home based early intervention on children’s body mass index (BMI) at age 2 years. A randomised controlled superiority trial was used. The intervention consisted of eight home visits from specially trained community nurses in the first 24 months after birth; this was in addition to the usual childhood nursing service from community health service nurses. The control group received the usual childhood nursing service alone. Participants were first time mothers and their infants. The primary outcome was children’s BMI at age 2.1

The sample size calculation was based on having 80% power to detect a difference in mean BMI of 0.25 units between treatment groups at age 2, using a two sided hypothesis test and critical level of significance of 0.05. It was assumed that the standard deviation of observations in each group was the same and equal to 1.5 BMI units. A total sample size of 504 participants (252 in each treatment arm) was required. To allow for an estimated 20% dropout rate it would be necessary to recruit 630 first time mothers. In total, 667 first time mothers and their infants were recruited to the trial.

At age 2 years, mean BMI was significantly lower in the intervention group compared with the control group (16.53 v 16.82; difference 0.29, 95% confidence interval −0.55 to −0.02; P=0.04). The researchers concluded that a home based early intervention delivered by trained community nurses was effective in reducing mean BMI in children at age 2 years.

Which of the following statements, if any, are true?

• a) A difference in mean BMI of 0.25 between treatments was the smallest effect of clinical interest

• b) If power was increased to …