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*.