# Using Quadratic Programming to Reconstruct Data From Published Survival and Competing Risks Analyses

## TL;DR

This paper introduces a new method using quadratic programming to reconstruct patient data from survival studies, improving on existing techniques and allowing for more detailed analysis.

## Contribution

The paper proposes a novel quadratic programming approach for reconstructing pseudo-IPD from survival and competing risks data.

## Key findings

- The QP-based method outperforms existing algorithms when additional data like numbers at risk are available.
- The method successfully reconstructs data from a published follicular lymphoma study.
- The approach is extendable to competing risks survival data from cumulative incidence functions.

## Abstract

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 modeling 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.