Cross-site imputation for recovering variables without individual pooled data

In multi-site studies, it is common for some sites not to have recorded key variables. Although it is theoretically possible to use data from sites with recorded observations to impute the missing values, this process becomes challenging when data pooling is not feasible due to logistic or legal constraints. We therefore propose a multiple imputation approach — cross-site imputation — to recover any variables across sites without the need to pool individual-level data. The solution involves transporting predicted regression coefficients and variances from studies with observed data to impute missing variables at sites without data. The approach is illustrated in an applied example of recovering confounders across Swedish hospitals, and theoretical considerations are outlined. Given the increasing importance of multi-site studies in observational research, cross-site imputation could offer a practical approach for imputing variables that have not been recorded in some study sites.