When fairly assessing the quality of a hospital, it is important to account for confounding traits beyond the hospital's control, such as patient case-mix. One of the most common assessment methods is indirect standardization, which, when adjusting for multiple confounding factors, requires the acquisition of individual-level data: a process which is logistically taxing and could potentially compromise patient confidentiality.
To address this issue, we propose a novel method of performing indirect standardization when the index hospital provides only the marginal distributions of confounding variables. This method is an improvement upon existing literature by Wang et al (2018), whose methods make certain simplifying assumptions our methods address through identifying latent clusters among reference hospitals. We show the superiority of our novel methods in an application to a study on prevalence of high-radiation computed tomography scans, as well as in a simulation of the same medical context.