Skip to main content

Table 3 Sample size rationale by primary aims

From: Facilitating HIV/AIDS and HIV testing literacy for emergency department patients: a randomized, controlled, trial

Primary Aims Minimum sample by stratum Total minimum sample Rationale and assumptions for minimum sample sizes and final sample sizes for each primary aim
Aim 1. Short-term improvement in HIV/AIDS and HIV testing knowledge
 HA1: 3-way interaction
 (mode*language*literacy level)
 HA2: 2-way interaction
 (mode*language or literacy level)
 HA3: no interaction
 (difference by mode only)
 HA4: no difference
125
This minimum sample size by stratum will yield a power of 0.80, 0.97 and 0.99 for testing HA1, HA2, HA3 versus HA4 (HA4 as the NULL)
Final sample per stratum (information delivery mode, language, and health literacy level) is 150
1000
The final sample after adding 20% to account for the heterogeneity in patients among study sites is 1200 = 1000*(1 + 20%)
• Based on our prior video studies [17, 19, 21], we assume that the scores on the 25-item questionnaire is a normal distribution with a standard deviation of ~ 3
• Before information delivery, mean scores of the two arms are assumed to be the same (due to random assignment) per stratum
• Short-term within-person correlation is 0.7 or higher [21]
• The pictorial brochure will improve knowledge by an average of 2 points. The video will improve the knowledge by an average of 3.5 points. The effect size is Δ = 3.5–2 = 1.5. (HA3)
• 2-way intrxn (mode*language or literacy level) effect size is Δ = 1.5 + 0.75 = 2.25. (HA2), e.g. for those speaking English OR with high health literacy
• 3-way intrxn (mode*language*literacy level) effect size is Δ = 1.5 + 0.75 + 0.75 = 3.0, e.g. for those speaking English AND having high literacy AND watching the video
Aim 2. Retention of HIV/AIDS and HIV testing knowledge at 3, 6, 9, and 12 months
 HA1: 3-way interaction
 (mode*language*literacy level)
 HA2: 2-way interaction
 (mode*language or literacy level)
HA3: no interaction
 (difference by mode only)
 HA4: no difference
100
This minimum sample size by stratum will yield a power of 0.80, 0.97 and 0.99 for testing HA1, HA2, and HA3, versus HA4 (as the NULL)
800
After adding 25% to account for loss-to-follow-up and 20% for heterogeneity among study sites, the final sample size is 1200 = 800*(1 + 25%)*(1 + 20%)
• Long-term within-person correlation is 0.4 or higher
• The scores on the knowledge questionnaire in the pictorial brochure arm will degrade to the pre-information baseline level with an average drop of 2 points by 12 months. The score in the video information arm will degrade by an average drop of 1 point. So, compared to baseline, the difference (effect size) in long-term retention of information in the video arm as compared to the pictorial brochure arm is Δ = (3.5–1)-(2–2) = 2.5.
• We will assume a similar effect size for 2- and 3-way interactions