Combining estimates of interest in prognostic modelling studies after multiple imputation: current practice and guidelines

Guidelines for combining the estimates of interest when analysing prognostic modelling studies are provided. A literature review is performed to identify current practice for combining such estimates in prognostic modelling studies.Methods for combining all reported estimates after MI were not well reported in the current literature. Rubin's rules without applying any transformations were the standard approach used, when any method was stated.The proposed simple guidelines for combining estimates after MI may lead to a wider and more appropriate use of MI in future prognostic modelling studies.Prognostic models play an important role in the clinical decision making process as they help clinicians to determine the most appropriate management of patients. A good prognostic model can provide an insight into the relationship between the outcome of patients and known patient and disease characteristics [1,2].Missing covariate data and censored outcomes are unfortunately common occurrences in prognostic modelling studies [3], which can complicate the modelling process. Multiple imputation (MI) is one approach to handle the missing covariate data that can properly account for the missing data uncertainty [4]. Missing values are replaced with m (>1) values to give m imputed datasets. Previously, three to five imputations were considered sufficient to give reasonable efficiency provided that the fraction of missing information is not excessive [4]. However, with increased computer capabilities, the limitations on m have diminished and therefore it may be more sensible to use 20 [5] or more [6] imputations. The imputation model, used to generate plausible values for the missing data, should contain all variables to be subsequently analysed including the outcome and any variables that help to explain the missing data [7]. Outcome tends to be incorporated into the imputation model by including both the event status, indicating whether the event, i.e. death, has occurred or not,