Mean residual life regression with functional principal component analysis on longitudinal data for dynamic prediction

Analysis of dynamic restricted mean survival time based on pseudo-observations

In clinical follow-up studies with a time-to-event end point, the difference in the restricted mean survival time (RMST) is a suitable substitute for the hazard ratio (HR). However, the RMST only measures the survival of patients over a period of time from the baseline and cannot reflect changes in life expectancy over time. Based on the RMST, we study the conditional restricted mean survival time (cRMST) by estimating life expectancy in the future according to the time that patients have survived, reflecting the dynamic survival status of patients during follow-up. In this paper, we introduce the estimation method of cRMST based on pseudo-observations, the statistical inference concerning the difference between two cRMSTs (cRMSTd), and the establishment of the robust dynamic prediction model using the landmark method. Simulation studies are conducted to evaluate the statistical properties of these methods. The results indicate that the estimation of the cRMST is accurate, and the dynamic RMST model has high accuracy in coefficient estimation and good predictive performance. In addition, an example of patients with chronic kidney disease who received renal transplantations is employed to illustrate that the dynamic RMST model can predict patients' expected survival times from any prediction time, considering the time-dependent covariates and time-varying effects of covariates.

DYNAMIC PREDICTION OF RESIDUAL LIFE WITH LONGITUDINAL COVARIATES USING LONG SHORT-TERM MEMORY NETWORKS

Sepsis, a complex medical condition that involves severe infections with life-threatening organ dysfunction, is a leading cause of death worldwide. Treatment of sepsis is highly challenging. When making treatment decisions, clinicians and patients desire accurate predictions of mean residual life (MRL) that leverage all available patient information, including longitudinal biomarker data. Biomarkers are biological, clinical, and other variables reflecting disease progression that are often measured repeatedly on patients in the clinical setting. Dynamic prediction methods leverage accruing biomarker measurements to improve performance, providing updated predictions as new measurements become available. We introduce two methods for dynamic prediction of MRL using longitudinal biomarkers. in both methods, we begin by using long short-term memory networks (LSTMs) to construct encoded representations of the biomarker trajectories, referred to as "context vectors." In our first method, the LSTM-GLM, we dynamically predict MRL via a transformed MRL model that includes the context vectors as covariates. In our second method, the LSTM-NN, we dynamically predict MRL from the context vectors using a feed-forward neural network. We demonstrate the improved performance of both proposed methods relative to competing methods in simulation studies. We apply the proposed methods to dynamically predict the restricted mean residual life (RMRL) of septic patients in the intensive care unit using electronic medical record data. We demonstrate that the LSTM-GLM and the LSTM-NN are useful tools for producing individualized, real-time predictions of RMRL that can help inform the treatment decisions of septic patients.

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

Joint modeling and landmark modeling are two mainstream approaches to dynamic prediction in longitudinal studies, that is, the prediction of a clinical event using longitudinally measured predictor variables available up to the time of prediction. It is an important research question to the methodological research field and also to practical users to understand which approach can produce more accurate prediction. There were few previous studies on this topic, and the majority of results seemed to favor joint modeling. However, these studies were conducted in scenarios where the data were simulated from the joint models, partly due to the widely recognized methodological difficulty on whether there exists a general joint distribution of longitudinal and survival data so that the landmark models, which consists of infinitely many working regression models for survival, hold simultaneously. As a result, the landmark models always worked under misspecification, which caused difficulty in interpreting the comparison. In this paper, we solve this problem by using a novel algorithm to generate longitudinal and survival data that satisfies the working assumptions of the landmark models. This innovation makes it possible for a "fair" comparison of joint modeling and landmark modeling in terms of model specification. Our simulation results demonstrate that the relative performance of these two modeling approaches depends on the data settings and one does not always dominate the other in terms of prediction accuracy. These findings stress the importance of methodological development for both approaches. The related methodology is illustrated with a kidney transplantation dataset.

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

Ovarian epithelial cancer is a gynecological tumor with a high risk of recurrence and death. In the clinical diagnosis of ovarian epithelial cancer, CA125 has become an important indicator of disease burden. To account for patient recurrence and death, a proper method is needed to integrate information from biomarkers and recurrence simultaneously. In the past 10 years, many methods have been proposed for joint modeling of longitudinal biomarkers and survival data, but few of them are applicable to longitudinal data and disease processes, including recurrence and death. In this article, we proposed a new joint frailty model based on functional principal component analysis for dynamic prediction of survival probabilities on the total time scale, which took recurrent history and longitudinal data into account simultaneously. The estimation of the joint frailty model is achieved by maximizing the penalized log-likelihood function. The simulation results demonstrated the advantages of our method in both discrimination and accuracy under different scenarios. To indicate the method's practicality, it is applied to an actual dataset of patients with ovarian epithelial cancer to predict survival dynamically using longitudinal data of biomarker CA125 and recurrent history data.