Estimating the ratio of multivariate recurrent event rates with application to a blood transfusion study

In comparative effectiveness studies of multicomponent, sequential interventions like blood product transfusion (plasma, platelets, red blood cells) for trauma and critical care patients, the timing and dynamics of treatment relative to the fragility of a patient's condition is often overlooked and underappreciated. While many hospitals have established massive transfusion protocols to ensure that physiologically optimal combinations of blood products are rapidly available, the period of time required to achieve a specified massive transfusion standard (e.g. a 1:1 or 1:2 ratio of plasma or platelets:red blood cells) has been ignored. To account for the time-varying characteristics of transfusions, we use semiparametric rate models for multivariate recurrent events to estimate blood product ratios. We use latent variables to account for multiple sources of informative censoring (early surgical or endovascular hemorrhage control procedures or death). The major advantage is that the distributions of latent variables and the dependence structure between the multivariate recurrent events and informative censoring need not be specified. Thus, our approach is robust to complex model assumptions. We establish asymptotic properties and evaluate finite sample performance through simulations, and apply the method to data from the PRospective Observational Multicenter Major Trauma Transfusion study.