Mean Residual Life Regression with Functional Principal Component Analysis on Longitudinal Data for Dynamic Prediction

Abstract

Predicting patient life expectancy is of great importance for clinicians in making treatment decisions. This prediction needs to be conducted in a dynamic manner, based on longitudinal biomarkers repeatedly measured during the patient's post-treatment follow-up period. The prediction is updated any time a new biomarker measurement is obtained. The heterogeneity across patients of biomarker trajectories over time requires flexible and powerful approaches to model noisy and irregularly measured longitudinal data. In this article, we use functional principal component analysis (FPCA) to extract the dominant features of the biomarker trajectory of each individual, and use these features as time-dependent predictors (covariates) in a transformed mean residual life (MRL) regression model to conduct dynamic prediction. Simulation studies demonstrate the improved performance of the transformed MRL model that includes longitudinal biomarker information in the prediction. We apply the proposed method to predict the remaining time expectancy until disease progression for patients with chronic myeloid leukemia, using the transcript levels of an oncogene, BCR-ABL.

A comparison of two approaches to dynamic prediction: Joint modeling and landmark modeling

“…A variety of landmark modeling approaches are available 2,3,16,17 and the ideas are similar. In this paper, we use the LM method studied by Li et al 16 Unlike the JM, which estimates the joint distribution of all data and derives the prediction from that distribution, the LM directly estimates the association between predictor variables at the prediction time and the outcome variable at that prediction time, that is, the residual survival time.…”

“…However, it is more difficult to incorporate the longitudinal history prior to $$$ t $$$ into the prediction (in contrast, this is done automatically in JM without extra work). Predictive features of the history usually need to be pre‐specified, such as slope of a longitudinal predictor, 16 functional principal component analysis scores, 17 or volatility in a period prior to $$$ t $$$ 18 . The calculation of these features can be affected by irregularly spaced clinical encounters, sparse data, and measurement errors 19 .…”

“…However, it is more difficult to incorporate the longitudinal history prior to t into the prediction (in contrast, this is done automatically in JM without extra work). Predictive features of the history usually need to be pre-specified, such as slope of a longitudinal predictor, 16 functional principal component analysis scores, 17 or volatility in a period prior to t. 18 The calculation of these features can be affected by irregularly spaced clinical encounters, sparse data, and measurement errors. 19 Since the model fitting is not based on the likelihood of all the data, the LM is widely considered as working model 8,20 that does not satisfy the consistency condition of Jewell et al, 21 and it is unclear whether optimal prediction accuracy is achieved with this approach.…”

Dynamic prediction of disease processes based on recurrent history and functional principal component analysis of longitudinal biomarkers: Application for ovarian epithelial cancer

“…In Yan et al, 3,4 FPCA was proven to be an efficient method to capture the changing pattern of biomarkers for dynamic prediction. Then, Lin et al 5,6 explored moving time windows, which could capture changing patterns when the right boundary of the interim observation time interval was changing, and applied a regression model to predict the residual lifetime. The simulation study in these studies showed that the method was superior compared with other methods that only used part of the information from longitudinal measurements.…”

Analysis of Dynamic Restricted Mean Survival Time Based on Pseudo-Observations

“…These models are limited, however, because they do not account for the changes in these covariates (Thomas and Reyes, 2014), or they only consider the dichotomous time-varying covariate with, at most, one change from untreated to treated (Zhang et al, 2022). To overcome this challenge, Lin et al (2018) extended the traditional regression model by using functional principal component analysis to extract the dominant features of the biomarker trajectory of each individual as time-dependent covariates to conduct dynamic predictions. But as pointed out by the authors, the proposed model focuses on prediction rather than coefficient interpretation.…”