Piecewise exponential models with time-varying effects: Estimating mortality after listing for solid organ transplant

Patient mortality after listing for a solid organ transplant is a relevant, patient-centric metric, but risk factors for patient mortality after listing present severe non-proportional hazards. We propose piecewise exponential models (PEMs) with time-varying effects to account for the non-proportional hazards, and we use the LASSO to minimize the risk of overfitting. We consider two parameterizations of a PEM: The first model has an overall effect in addition to the time-varying effects (PEM-TID), whereas the second model has only time-varying effects (PEM-TD). Because the LASSO can shrink every time-varying effect to 0, risk factors in the PEM-TID model can have proportional effects during follow-up. In contrast, covariates in the PEM-TD model must have different or no effects during follow-up. These characteristics were illustrated for patients listed for liver transplant. The PEM-TID model had similar or better predictive performance than the PEM-TD model, and both were better than the Cox proportional hazards model. Thus, PEMs with time-varying effects can improve predictive performance for patient mortality after listing for a solid organ transplant.