Bridging the gap between two-stage and joint models: The case of tumor growth inhibition and overall survival models

Many clinical trials generate both longitudinal biomarker and time-to-event data. We might be interested in their relationship, as in the case of tumor size and overall survival in oncology drug development. Many well-established methods exist for analyzing such data either sequentially (two-stage models) or simultaneously (joint models). Two-stage modeling (2stgM) has been challenged (i) for not acknowledging that biomarkers are endogenous covariable to the survival submodel and (ii) for not propagating the uncertainty of the longitudinal biomarker submodel to the survival submodel. On the other hand, joint modeling (JM), which properly circumvents both problems, has been criticized for being time-consuming, and difficult to use in practice. In this paper, we explore a third approach, referred to as a novel two-stage modeling (N2stgM). This strategy reduces the model complexity without compromising the parameter estimate accuracy. The three approaches (2stgM, JM, and N2stgM) are formulated, and a Bayesian framework is considered for their implementation. Both real and simulated data were used to analyze the performance of such approaches. In all scenarios, our proposal estimated the parameters approximately as JM but without being computationally expensive, while 2stgM produced biased results.

Sensitivity Analysis for Survival Prognostic Prediction with Gene Selection: A Copula Method for Dependent Censoring

Prognostic analysis for patient survival often employs gene expressions obtained from high-throughput screening for tumor tissues from patients. When dealing with survival data, a dependent censoring phenomenon arises, and thus the traditional Cox model may not correctly identify the effect of each gene. A copula-based gene selection model can effectively adjust for dependent censoring, yielding a multi-gene predictor for survival prognosis. However, methods to assess the impact of various types of dependent censoring on the multi-gene predictor have not been developed. In this article, we propose a sensitivity analysis method using the copula-graphic estimator under dependent censoring, and implement relevant methods in the R package “compound.Cox”. The purpose of the proposed method is to investigate the sensitivity of the multi-gene predictor to a variety of dependent censoring mechanisms. In order to make the proposed sensitivity analysis practical, we develop a web application. We apply the proposed method and the web application to a lung cancer dataset. We provide a template file so that developers can modify the template to establish their own web applications.

Dynamic Risk Prediction via a Joint Frailty-Copula Model and IPD Meta-Analysis: Building Web Applications

Clinical risk prediction formulas for cancer patients can be improved by dynamically updating the formulas by intermediate events, such as tumor progression. The increased accessibility of individual patient data (IPD) from multiple studies has motivated the development of dynamic prediction formulas accounting for between-study heterogeneity. A joint frailty-copula model for overall survival and time to tumor progression has the potential to develop a dynamic prediction formula of death from heterogenous studies. However, the process of developing, validating, and publishing the prediction formula is complex, which has not been sufficiently described in the literature. In this article, we provide a tutorial in order to build a web-based application for dynamic risk prediction for cancer patients on the basis of the R packages joint.Cox and Shiny. We demonstrate the proposed methods using a dataset of breast cancer patients from multiple clinical studies. Following this tutorial, we demonstrate how one can publish web applications available online, which can be manipulated by any user through a smartphone or personal computer. After learning this tutorial, developers acquire the ability to build an online web application using their own datasets.

Robust joint modelling of longitudinal and survival data: Incorporating a time-varying degrees-of-freedom parameter

Monitoring of individual biomarkers has the potential of explaining the hazard of survival outcomes. In practice, these measurements are intermittently observed and are known to be subject to substantial measurement error. Joint modelling of longitudinal and survival data enables us to associate intermittently measured error-prone biomarkers with risks of survival outcomes and thus plays an important role in the analysis of medical data. Most of the joint models available in the literature have been built on the Gaussian assumption. This makes them sensitive to outliers. In this work, we study a range of robust models to address this issue. Of particular interest is the common occurrence in medical data that outliers can occur with different frequencies over time, for example, in the period when patients adjust to treatment changes. Motivated by the analysis of data gathered from patients with primary biliary cirrhosis, a new model with a time-varying robustness is introduced. Through both the motivating example and a simulation study, this research not only stresses the need to account for longitudinal outliers in the analysis of medical data and in joint modelling research but also highlights the bias and inefficiency from not properly estimating the degrees-of-freedom parameter. This work presents a number of methods in addition to the time-varying robustness, and each method can be fitted using the R package robjm.