Statistical issues in survival analysis (Wavelet survival models)
March 12, 2025 The authors used a novel method based on wavelet filtering and landmarking to obtain the prognostic role of a biomarker in patient death. Wavelet filters have been common in time series data to extract features and reduce noise. They also utilized landmark last observation carried forward model (LOCF) and the landmark mixed survival model along with the novel landmark wavelet model. In their methods they described different landmark methods to consider for obtaining dynamic predictions of survival. Their landmark LOCF used a grid of time points, called landmarks, in which information on their main predictor, potassium, can be updated. At each landmark point, they studied the association between potassium and time of death by estimating a Cox proportional hazard model using as a covariate the last potassium measurement collected before the landmark point. They also delineated a mixed landmark model where they modeled individual potassium trajectories using a linear mixed effect model. For both methods they were able to derive dynamic predictions. Finally, they described their mixed-wavelet landmark models, which used linear mixed effect models along with wavelets. They focused on the wavelet Morlet (WM) filter, which are continuous, complex valued functions used to smooth nonstationary time-series data and can distinguish frequencies at which oscillations occur. This transform is characterized by a mother wavelet. They used it to extract from the repeated measures data by applying it to the residuals of the linear mixed effect model. In incorporating the wavelet filter into their model, they defined a landmark wavelet Cox model which has covariates terms with one being a vector of predicted slope at each landmark time from the linear mixed effect model and now the second being a vector of local changes in the biomarker at different duration intervals of interest for the ith subject, each with a non-linear transform like a spline basis.