If you’re using propensity score weighting (e.g., inverse probability weighting), one question that will arise is how big a sample you need.
Solutions have been proposed that rely on a variance inflation factor (VIF). You calculate the sample size for a simple design and then multiply that by the VIF to take account of weighting.
But the problem is that it is difficult to choose a VIF in advance.
Austin (2021) has developed a simple method (R code in the paper) to estimate VIFs from c-statistics (area under the curve; AOC) of the propensity score models. These c-statistics are often published.
A larger c-statistic means a greater separation between treatment and control, which in turn leads to a larger VIF and requirement for a larger sample.
Picture illustrating different c-statistics.
The magnitude of the VIF also depends on the estimand of interest, e.g., whether average treatment effect (ATE), average treatment effect on the treated (ATET/ATT), or average treatment effect where treat and control overlap (ATO).
References
Austin, P. C. (2021). Informing power and sample size calculations when using inverse probability of treatment weighting using the propensity score. Statistics in Medicine.