Sample Size Calculations for Indirect Standardization

Indirect standardization, and its associated parameter the Standardized Incidence Ratio, is a commonly-used tool in hospital profiling for comparing the incidence of negative outcomes between an index hospital and a larger population of reference hospitals, while adjusting for confounding factors. For hypothesis testing and statistical inference, the denominator of the Standardized Incidence Ratio, whose computation requires the distribution of confounding covariates in the index hospital, is assumed to be known, and is thus fixed. This assumption severely compromises one's ability to compute required sample sizes for high-powered indirect standardization, as in the contexts where sample size calculation is desired, it's difficult to even estimate such a covariate distribution, much less know it outright. This paper presents novel statistical methodology to perform hypothesis testing and sample size calculation for the Standardized Incidence Ratio while not knowing the covariate distribution of the index hospital, accounting for the mathematical uncertainty this lack of knowledge induces. We apply our methods to example data, as well as to simulation studies, to assess both its capabilities in a vacuum and in comparison to traditional methods of indirect standardization.