Developing prediction models to estimate the risk of two survival outcomes both occurring: A comparison of techniques

Introduction
This study considers the prediction of the time until two survival outcomes have both occurred. We compared a variety of analytical methods motivated by a typical clinical problem of multimorbidity prognosis.

Methods
We considered five methods: product (multiply marginal risks), dual-outcome (directly model the time until both events occur), multistate models (msm), and a range of copula and frailty models. We assessed calibration and discrimination under a variety of simulated data scenarios, varying outcome prevalence, and the amount of residual correlation. The simulation focused on model misspecification and statistical power. Using data from the Clinical Practice Research Datalink, we compared model performance when predicting the risk of cardiovascular disease and type 2 diabetes both occurring.

Results
Discrimination was similar for all methods. The product method was poorly calibrated in the presence of residual correlation. The msm and dual-outcome models were the most robust to model misspecification but suffered a drop in performance at small sample sizes due to overfitting, which the copula and frailty model were less susceptible to. The copula and frailty model's performance were highly dependent on the underlying data structure. In the clinical example, the product method was poorly calibrated when adjusting for 8 major cardiovascular risk factors.

Discussion
We recommend the dual-outcome method for predicting the risk of two survival outcomes both occurring. It was the most robust to model misspecification, although was also the most prone to overfitting. The clinical example motivates the use of the methods considered in this study.