Three new methodologies for calculating the effective sample size when performing population adjustment

Background: The concept of the population is of fundamental importance in epidemiology and statistics. In some instances, it is not possible to sample directly from the population of interest. Weighting is an established statistical approach for making inferences when the sample is not representative of this population. Methods: The effective sample size (ESS) is a descriptive statistic that can be used to accompany this type of weighted statistical analysis. The ESS is an estimate of the sample size required by an unweighted sample that achieves the same level of precision as the weighted sample. The ESS therefore reflects the amount of information retained after weighting the data and is an intuitively appealing quantity to interpret, for example by those with little or no statistical training. Results: The conventional formula for calculating ESS is derived under strong assumptions, for example that outcome data are homoscedastic. This is not always true in practice, for example for survival data. We propose three new approaches to compute the ESS, that are valid for any type of data and weighted statistical analysis, and so can be applied more generally. Conclusion: We illustrate all methods using an example and conclude that our proposals should accompany, and potentially replace, the existing approach for computing the ESS.<p></p>