Sample size​ ​and detectable effect size calculations were performed for a broad range of event probabilities based on ​those reported in ​​a ​systematic review which was commissioned for the TB and pregnancy consensus process. The estimates provided in the ​“​TB and pregnancy toolkit power calculations” spreadsheet should be considered examples only. Study investigators should conduct their own calculations based on target populations using local data if available. 

​​The sample sizes and detectable effect sizes were calculated using a two-sided alpha = .05 z-test (normal approximation) for a difference in proportions with an unpooled variance, for power of 0.80 and 0.90.​ ​​​​​The sample sizes for both groups were assumed to be equal (N1=N2; N=N1+N2). No adjustment for missing data or lost-to-follow-up was made.

The reference group probability is denoted as ​P2​ and was set using a range of values. ​P1​ is the event probability for the experimental group. The ​ratio (i.e. relative proportion) is denoted ​R1​ and is calculated ​P1​​/​​P2​ and ​is the alternative hypothesis (working hypothesis).

In the “Detectable effect” worksheet for a total study size, ​N​, (ranging from 100 to 2000) and ​P2 ​(from 0.00001 to 0.70), we solved for the relative proportion ​R1 ​(or ​P1​) that resulted in desired power for a range of P2 values.

For sample size calculations first set ​R1 ​(i.e., 1.25, 1.5, 2.0, 2.5, 3.0) to compute ​P1 ​and then solved for ​N ​to obtain the desired level power.

When considering power for a safety endpoint, it is important to consider that power is 1 minus type II error. If power is set to 0.80, there is a probability of 0.20 ​(i.e. 20% chance) ​to fail to reject the null hypothesis of no difference, when in fact the alternative hypothesis is true. If power is set to 0.90, there is a probability of 0.10 ​(i.e. 10% chance) ​to fail to reject the null hypothesis of no difference, when in fact the alternative hypothesis is true. Higher power is generally preferred to minimize type II error. 

Power Analysis Sample Size (PASS) V25.0.1 was used for all sample size calculations.