A new approach for joint modelling of longitudinal measurements and survival times with a cure fraction

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.

BILITE: A Bayesian randomized phase II design for immunotherapy by jointly modeling the longitudinal immune response and time-to-event efficacy

Immunotherapy-treatments that target a patient's immune system-has attracted considerable attention in cancer research. Its recent success has led to generation of novel immunotherapeutic agents that need to be evaluated in clinical trials. Two unique features of immunotherapy are the immune response and the fact that some patients may achieve long-term durable response. In this article, we propose a two-arm Bayesian adaptive randomized phase II clinical trial design for immunotherapy that jointly models the longitudinal immune response and time-to-event efficacy (BILITE), with a fraction of patients assumed to be cured by the treatment. The longitudinal immune response is modeled using hierarchical nonlinear mixed-effects models with possibly different trajectory patterns for the cured and susceptible groups. Conditional on the immune response trajectory, the time-to-event efficacy data for patients in the susceptible group is modeled via a time-dependent Cox-type regression model. We quantify the desirability of the treatment using a utility function and propose a two-stage design to adaptively randomize patients to treatments and make treatment recommendations at the end of the trial. Simulation studies show that compared with a conventional design that ignores the immune response, BILITE yields superior operating characteristics in terms of the ability to identify promising agents and terminate the trial early for futility.

Joint analysis of longitudinal measurements and survival times with a cure fraction based on partly linear mixed and semiparametric cure models

In a joint analysis of longitudinal quality of life (QoL) scores and relapse-free survival (RFS) times from a clinical trial on early breast cancer conducted by the Canadian Cancer Trials Group, we observed a complicated trajectory of QoL scores and existence of long-term survivors. Motivated by this observation, we proposed in this paper a flexible joint model for the longitudinal measurements and survival times. A partly linear mixed effect model is used to capture the complicated but smooth trajectory of longitudinal measurements and approximated by B-splines and a semiparametric mixture cure model with the B-spline baseline hazard to model survival times with a cure fraction. These two models are linked by shared random effects to explore the dependence between longitudinal measurements and survival times. A semiparametric inference procedure with an EM algorithm is proposed to estimate the parameters in the joint model. The performance of proposed procedures are evaluated by simulation studies and through the application to the analysis of data from the clinical trial which motivated this research.

Jointly modeling longitudinal proportional data and survival times with an application to the quality of life data in a breast cancer trial

Motivated by the joint analysis of longitudinal quality of life data and recurrence free survival times from a cancer clinical trial, we present in this paper two approaches to jointly model the longitudinal proportional measurements, which are confined in a finite interval, and survival data. Both approaches assume a proportional hazards model for the survival times. For the longitudinal component, the first approach applies the classical linear mixed model to logit transformed responses, while the second approach directly models the responses using a simplex distribution. A semiparametric method based on a penalized joint likelihood generated by the Laplace approximation is derived to fit the joint model defined by the second approach. The proposed procedures are evaluated in a simulation study and applied to the analysis of breast cancer data motivated this research.

A generalized partially linear mean-covariance regression model for longitudinal proportional data, with applications to the analysis of quality of life data from cancer clinical trials

Motivated by the analysis of quality of life data from a clinical trial on early breast cancer, we propose in this paper a generalized partially linear mean-covariance regression model for longitudinal proportional data, which are bounded in a closed interval. Cholesky decomposition of the covariance matrix for within-subject responses and generalized estimation equations are used to estimate unknown parameters and the nonlinear function in the model. Simulation studies are performed to evaluate the performance of the proposed estimation procedures. Our new model is also applied to analyze the data from the cancer clinical trial that motivated this research. In comparison with available models in the literature, the proposed model does not require specific parametric assumptions on the density function of the longitudinal responses and the probability function of the boundary values and can capture dynamic changes of time or other interested variables on both mean and covariance of the correlated proportional responses. Copyright © 2017 John Wiley & Sons, Ltd.