Joint models for longitudinal and time‐to‐event data in a case‐cohort design

Abstract

Studies with longitudinal measurements are common in clinical research. Particular interest lies in studies where the repeated measurements are used to predict a time‐to‐event outcome, such as mortality, in a dynamic manner. If event rates in a study are low, however, and most information is to be expected from the patients experiencing the study endpoint, it may be more cost efficient to only use a subset of the data. One way of achieving this is by applying a case‐cohort design, which selects all cases and only a random samples of the noncases. In the standard way of analyzing data in a case‐cohort design, the noncases who were not selected are completely excluded from analysis; however, the overrepresentation of the cases will lead to bias. We propose to include survival information of all patients from the cohort in the analysis. We approach the fact that we do not have longitudinal information for a subset of the patients as a missing data problem and argue that the missingness mechanism is missing at random. Hence, results obtained from an appropriate model, such as a joint model, should remain valid. Simulations indicate that our method performs similar to fitting the model on a full cohort, both in terms of parameters estimates and predictions of survival probabilities. Estimating the model on the classical version of the case‐cohort design shows clear bias and worse performance of the predictions. The procedure is further illustrated in data from a biomarker study on acute coronary syndrome patients, BIOMArCS.

Longitudinal Analysis of Continuous Pulse Oximetry as Prognostic Factor in Neonatal Respiratory Distress

“…Joint models are emerging as a useful tool to model both longitudinal and survival data. The models from Rizopoulos 14 have been applied before to studies modeling repeated measures of cardiovascular biomarkers, [23][24][25] and have also been used for risk stratification of patients in prostate cancer. 26 One study described the use of this models for renal grafts failure, 27 including a Bayesian approach with multiple longitudinal outcomes similar to the model we have proposed in this study.…”

Longitudinal Tumor Size and Neutrophil‐to‐Lymphocyte Ratio Are Prognostic Biomarkers for Overall Survival in Patients With Advanced Non‐Small Cell Lung Cancer Treated With Durvalumab

“…The prognostic value of SLD and NLR/NEU suggests that their combination in a multivariate longitudinal JM may improve predictions of individual patient survival. To address this question, we developed JMs [13,26,27,28,29], to evaluate the prognostic potential of longitudinal SLD and NLR for survival, in advanced NSCLC patients treated with durvalumab, a human immunoglobulin G1 kappa monoclonal antibody that blocks the interaction of PD-L1 with the Programmed cell Death protein 1 (PD-1). We considered a common clinical development scenario, whereby a new study is initiated, and early SLD and NLR responses in patients as well as OS, were evaluated in a 0-3 month interval after start of treatment, when a RECIST 1.1 framework for tumor response assessment may be used.…”

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

“…A two‐stage design is proposed to assign new patients to desirable treatment through adaptive randomization. Joint modeling of longitudinal measurements and survival outcome has been considered in the literature 28‐37 . In this article, we adapt these methods to accommodate the unique features of immunotherapy.…”

“…Joint modeling of longitudinal measurements and survival outcome has been considered in the literature. [28][29][30][31][32][33][34][35][36][37] In this article, we adapt these methods to accommodate the unique features of immunotherapy. To the best of our knowledge, this article provides the first phase II design for immunotherapy that jointly accounts for longitudinal immune response and time-to-event efficacy.…”