Using quadratic programming to reconstruct data from published survival and competing risks analyses

The ability to retrieve pseudo-individual patient data (IPD) from published survival study results is important to facilitate meta-analysis, evidence synthesis or secondary data analyses for the purpose of decision modelling for cost effectiveness analysis. While established methods exist for retrieving pseudo-IPD from Kaplan--Meier plots, these algorithms are not easily extendable to other types of survival data, nor do they allow all available information to be incorporated. An optimization-based approach is proposed where the task of reconstructing the IPD is formulated as a quadratic program (QP) with linear constraints. The method easily allows auxiliary information such as marked censoring times. Moreover, the same approach can be used to reconstruct patient-level competing risks survival data from published cumulative incidence functions. In simulation, the QP-based method is shown to outperform existing algorithms particularly when data on numbers at risk and marked censoring times are available. The methods are illustrated through reconstruction of data from a published study on patients with advanced stage follicular lymphoma.