Wavelet-Mixed Landmark Survival Models for the Effect of Short-Term Changes of Potassium in Heart Failure Patients

Statistical methods to study the association between a longitudinal biomarker and the risk of death are very relevant for the long-term care of subjects affected by chronic illnesses, such as potassium in heart failure patients. Particularly in the presence of comorbidities or pharmacological treatments, sudden crises can cause potassium to undergo very abrupt yet transient changes. In the context of the monitoring of potassium, there is a need for a dynamic model that can be used in clinical practice to assess the risk of death related to an observed patient's potassium trajectory. We considered different landmark survival approaches, starting from the simple approach considering the most recent measurement. We then propose a novel method based on wavelet filtering and landmarking to retrieve the prognostic role of past short-term potassium shifts. We argue that while taking into account the smooth changes in the biomarker, short-term changes cannot be overlooked. State-of-the-art dynamic survival models are prone to give more importance to the smooth component of the potassium profiles. However, our findings suggest that it is essential to also take into account recent potassium instability to capture all the relevant prognostic information. The data used comes from over 2000 subjects, with a total of over 80,000 repeated potassium measurements collected through administrative health records. The proposed wavelet landmark method revealed the prognostic role of past short-term changes in potassium. We also performed a simulation study to assess how and when to apply the proposed wavelet-mixed landmark model.