Recurrent events modelling of haemophilia bleeding events

A pharmacokinetic–pharmacodynamic (PK‐PD) approach is developed for modelling the recurrent bleeding events in patients with severe haemophilia to investigate the relationship between factor VIII plasma activity level and the instantaneous risk of a bleed. The model incorporates patient‐level pharmacokinetic (PK) information obtained through measurements taken prior to the study which are used to fit a non‐linear mixed‐effects two‐compartment PK model. Dosing times within the study are combined with the PK model to provide the estimated factor VIII plasma level for all patients, which is used as a time‐dependent covariate within the recurrent events model. Methods are developed to correct the attenuation in covariate effects that would otherwise arise due to the discrepancy between estimated and true factor VIII. In contrast to existing methods proposed for such data, such as count data regression or time‐to‐event analysis, the new method allows all the bleeding times to be used to investigate the relationship between current factor VIII and risk of a bleed. The performance of the proposed estimators are assessed via simulation and found to outperform the naive estimator, which treats the estimated factor VIII levels as if they were measured without error, both in terms of bias and mean squared error.