Using the entire history in the analysis of nested case cohort samples

Re-calibrating pure risk integrating individual data from two-phase studies with external summary statistics

Accurate risk assessment is critical in clinical decision-making. It entails the projected risk based on a risk prediction model agreeing with the observed risk in the target cohort. However, the model often over- or under-estimates the risk. Building a new model for the target cohort would be ideal but costly. It is therefore of great interest to recalibrate an existing model for the target cohort. Existing methods have been proposed to recalibrate the model by leveraging the disease incidence rates from the target cohort. However, they assume the same covariate distribution across cohorts and when the assumption is violated, the recalibrated model can be substantially biased. Further, recalibration is also complicated by the two-phase sampling design that is commonly used for developing risk prediction models. In this paper, we develop a weighted estimating-equation approach accounting for the two-phase design and combine it with a weighted empirical likelihood that leverages the summary information on both disease incidence rates and covariates from the target cohort. We provide a resampling-based inference procedure. Our extensive simulation results show that using the summary information from the target population, the proposed recalibration method yields nearly unbiased risk estimates under a wide range of scenarios. An application to a colorectal cancer study also illustrates that the proposed method yields a well-calibrated model in the target cohort.

Bootstrapping complex time-to-event data without individual patient data, with a view toward time-dependent exposures

We consider nonparametric and semiparametric resampling of multistate event histories by simulating multistate trajectories from an empirical multivariate hazard measure. One advantage of our approach is that it does not necessarily require individual patient data, but may be based on published information. This is also attractive for both study planning and simulating realistic real-world event history data in general. The concept extends to left-truncation and right-censoring mechanisms, nondegenerate initial distributions, and nonproportional as well as non-Markov settings. A special focus is on its connection to simulating survival data with time-dependent covariates. For the case of qualitative time-dependent exposures, we demonstrate that our proposal gives a more natural interpretation of how such data evolve over the course of time than many of the competing approaches. The multistate perspective avoids any latent failure time structure and sampling spaces impossible in real life, whereas its parsimony follows the principle of Occam's razor. We also suggest empirical simulation as a novel bootstrap procedure to assess estimation uncertainty in the absence of individual patient data. This is not possible for established procedures such as Efron's bootstrap. A simulation study investigating the effect of liver functionality on survival in patients with liver cirrhosis serves as a proof of concept. Example code is provided.