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

Abstract

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.