Conditional copula models for correlated survival endpoints: Individual patient data meta-analysis of randomized controlled trials

End Point Surrogacy in First-Line Chronic Lymphocytic Leukemia

PURPOSE

Surrogate end points are commonly used to estimate treatment efficacy in clinical studies of chronic lymphocytic leukemia (CLL). This patient- and trial-level analysis describes the correlation between progression-free survival (PFS) and minimal residual disease (MRD) with overall survival (OS) in first-line trials for CLL.

PATIENTS AND METHODS

First, patient-level correlation was confirmed using source data from 12 frontline German CLL Study Group (GCLLSG)-trials. Additionally, a joint-frailty copula model was fitted to validate correlation in the setting of targeted therapies (TT). Second, a meta-analysis of first-line phase III trials in CLL from 2008 to 2024 was performed. Treatment effect correlation was quantified from seven GCLLSG and nine published trials, using hazard ratios (HRs) for time-to-event and odds ratios for binary end points.

RESULTS

The GCLLSG analysis set comprised 4,237 patients. Patient-level correlation for PFS/OS was strong with Spearman Rho >0.9. The joint-frailty copula indicated a weak correlation for chemotherapy/chemoimmunotherapy (C/CIT) with a tau of 0.52 (95% CI, 0.49 to 0.55) while the correlation was strong for TT (tau, 0.91 [95% CI, 0.89 to 0.93). The meta-analysis set contained a total of 8,065 patients including 5,198 (64%) patients treated with C/CIT and 2,867 (36%) treated with TT. Treatment-effect correlation of the HRs for PFS and OS was R = 0.75 (95% CI, 0.74 to 0.76, R2 = 0.56) while correlation of end-of-treatment MRD with PFS and OS was R = 0.88 (95% CI, -0.87 to 0.89; R2 = 0.78) and 0.71 (95% CI, 0.69 to 0.73; R2 = 0.5), respectively.

CONCLUSION

Patient-level correlation was confirmed in the setting of TTs while treatment-effect correlation between PFS and OS remains uncertain. MRD response status showed a high treatment-effect correlation with PFS but not OS, with the caveat of a limited number of randomized trials with available MRD data.

Quantifying the Impact of Co-Housing on Murine Aging Studies

Analysis of preclinical lifespan studies often assume that outcome data from co-housed animals are independent. In practice, treatments, such as controlled feeding or putative life-extending compounds, are applied to whole housing units, and as a result the outcomes are potentially correlated within housing units. We consider intra-class (here, intra-cage) correlation in three published and two unpublished lifespan studies of aged mice encompassing more than 20 thousand observations. We show that the independence assumption underlying common analytic techniques does not hold in these data, particularly for traits associated with frailty. We describe and demonstrate various analytical tools available to accommodate this study design and highlight a limitation of standard variance components models (i.e., linear mixed models) which are the usual statistical tool for handling correlated errors. Through simulations, we examine the statistical biases resulting from intra-cage correlations with similar magnitudes as observed in these case studies and discuss implications for power and reproducibility.

Effectiveness comparison of third-generation EGFR-TKI as initial and sequential therapy in adjuvant treatment for EGFR mutation-sensitive stage IIIA non-small cell lung cancer after surgery

Introduction

Although third-generation epidermal growth factor receptor tyrosine kinase inhibitors (EGFR-TKIs) Osimertinib has been approved as adjuvant therapy for resected stage IIIA non-small cell lung cancer (NSCLC) with EGFR-sensitive mutations, the optimal treatment sequencing of EGFR-TKIs, particularly whether Osimertinib should be the initial or sequential therapy following the first-generation EGFR-TKIs remains uncertain.

Methods

A retrospective analysis was conducted on a cohort of patients with EGFR-mutated stage IIIA NSCLC who received treatment with either first-generation EGFR-TKIs or Osimertinib (third-generation) alone, or in sequential combination, at a single institution. The data analysis involved using the Kaplan-Meier method, log-rank test, and Cox regression.

Results

Out of the total 148 patients with stage IIIA NSCLC included in the study, 76 individuals underwent treatment with either first-generation EGFR-TKIs (referred to as subgroup "1″) or exclusively Osimertinib (subgroup "0 + 3″), or a sequential combination of the two (subgroup "1 + 3″) following surgery. Both univariate and multivariate analyses demonstrated that there were no discernible disparities in terms of disease-free survival and overall survival between subgroup " 1″ and " 1 + 3," nor between subgroup " 0 + 3″ and "1 + 3".

Conclusion

The findings from this study indicate that the introduction of third-generation EGFR-TKI Osimertinib did not yield enhanced survival benefits when compared to the first-generation drug in patients with stage IIIA completely resected NSCLC who were administered EGFR-TKIs as part of their postoperative adjuvant treatment. Additionally, within the observed sample size of this cohort, the sequential use of Osimertinib alongside first-generation EGFR-TKI did not demonstrate superiority over using either the first-generation EGFR-TKI or Osimertinib alone in terms of postoperative survival.

Semiparametric copula method for semi-competing risks data subject to interval censoring and left truncation: Application to disability in elderly

We aim to evaluate the marginal effects of covariates on time-to-disability in the elderly under the semi-competing risks framework, as death dependently censors disability, not vice versa. It becomes particularly challenging when time-to-disability is subject to interval censoring due to intermittent assessments. A left truncation issue arises when the age time scale is applied. We develop a flexible two-parameter copula-based semiparametric transformation model for semi-competing risks data subject to interval censoring and left truncation. The two-parameter copula quantifies both upper and lower tail dependence between two margins. The semiparametric transformation models incorporate proportional hazards and proportional odds models in both margins. We propose a two-step sieve maximum likelihood estimation procedure and study the sieve estimators' asymptotic properties. Simulations show that the proposed method corrects biases in the marginal method. We demonstrate the proposed method in a large-scale Chinese Longitudinal Healthy Longevity Study and provide new insights into preventing disability in the elderly. The proposed method could be applied to the general semi-competing risks data with intermittently assessed disease status.

A two‐level copula joint model for joint analysis of longitudinal and competing risks data

In this article, we propose a two-level copula joint model to analyze clinical data with multiple disparate continuous longitudinal outcomes and multiple event-times in the presence of competing risks. At the first level, we use a copula to model the dependence between competing latent event-times, in the process constructing the submodel for the observed event-time, and employ the Gaussian copula to construct the submodel for the longitudinal outcomes that accounts for their conditional dependence; these submodels are glued together at the second level via the Gaussian copula to construct a joint model that incorporates conditional dependence between the observed event-time and the longitudinal outcomes. To have the flexibility to accommodate skewed data and examine possibly different covariate effects on quantiles of a non-Gaussian outcome, we propose linear quantile mixed models for the continuous longitudinal data. We adopt a Bayesian framework for model estimation and inference via Markov Chain Monte Carlo sampling. We examine the performance of the copula joint model through a simulation study and show that our proposed method outperforms the conventional approach assuming conditional independence with smaller biases and better coverage probabilities of the Bayesian credible intervals. Finally, we carry out an analysis of clinical data on renal transplantation for illustration.

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.

The effect of obesity on chronic diseases in USA: a flexible copula approach

We analyze the effect of obesity on the incidence of hypertension, hyperlipidemia and diabetes in USA using a health production theoretical framework along with a bivariate flexible semi-parametric recursive copula model that account for endogeneity. In this approach, the effects of control variables are flexibly determined using additive predictors that allow for a variety of effects. Our findings suggest that there exist a positive and significant effect of obesity on the prevalence of all chronic diseases examined. In particular, after endogeneity is accounted for, the probability of having hypertension, hyperlipidemia and diabetes for obese individuals are, respectively, 35%, 28% and 11% higher than those under the obesity threshold. These findings suggest that lowering obesity rates could lead to significant reductions in the morbidity and mortality associated with these diseases.

Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies

Survival and reliability analyses deal with incomplete failure time data, such as censored and truncated data. Recently, the classical left-truncation scheme was generalized to analyze “field data”, defined as samples collected within a fixed period. However, existing competing risks models dealing with left-truncated field data are not flexible enough. We propose copula-based competing risks models for latent failure times, permitting a flexible parametric form. We formulate maximum likelihood estimation methods under the Weibull, lognormal, and gamma distributions for the latent failure times. We conduct simulations to check the performance of the proposed methods. We finally give a real data example. We provide the R code to reproduce the simulations and data analysis results.

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.

Optimal Constant-Stress Accelerated Life Test Plans for One-Shot Devices with Components Having Exponential Lifetimes under Gamma Frailty Models

Optimal designs of constant-stress accelerated life test plans is one of the important topics in reliability studies. Many devices produced have very high reliability under normal operating conditions. The question then arises of how to make the optimal decisions on life test plans to collect sufficient information about the corresponding lifetime distributions. Accelerated life testing has become a popular approach to tackling this problem in reliability studies, which attempts to extrapolate from the information obtained from accelerated testing conditions to normal operating conditions. In this paper, we develop a general framework to obtain optimal constant-stress accelerated life test plans for one-shot devices with dependent components, subject to time and budget constraints. The optimal accelerated test plan considers an economical approach to determine the inspection time and the sample size of each accelerating testing condition so that the asymptotic variance of the maximum likelihood estimator for the mean lifetime under normal operating conditions is minimized. This study also investigates the impact of the dependence between components on the optimal designs and provides practical recommendations on constant-stress accelerated life test plans for one-shot devices with dependent components.

Copula-Based Estimation Methods for a Common Mean Vector for Bivariate Meta-Analyses

Traditional bivariate meta-analyses adopt the bivariate normal model. As the bivariate normal distribution produces symmetric dependence, it is not flexible enough to describe the true dependence structure of real meta-analyses. As an alternative to the bivariate normal model, recent papers have adopted “copula” models for bivariate meta-analyses. Copulas consist of both symmetric copulas (e.g., the normal copula) and asymmetric copulas (e.g., the Clayton copula). While copula models are promising, there are only a few studies on copula-based bivariate meta-analysis. Therefore, the goal of this article is to fully develop the methodologies and theories of the copula-based bivariate meta-analysis, specifically for estimating the common mean vector. This work is regarded as a generalization of our previous methodological/theoretical studies under the FGM copula to a broad class of copulas. In addition, we develop a new R package, “CommonMean.Copula”, to implement the proposed methods. Simulations are performed to check the proposed methods. Two real dataset are analyzed for illustration, demonstrating the insufficiency of the bivariate normal model.

meta.shrinkage: An R Package for Meta-Analyses for Simultaneously Estimating Individual Means

Meta-analysis is an indispensable tool for synthesizing statistical results obtained from individual studies. Recently, non-Bayesian estimators for individual means were proposed by applying three methods: the James–Stein (JS) shrinkage estimator, isotonic regression estimator, and pretest (PT) estimator. In order to make these methods available to users, we develop a new R package meta.shrinkage. Our package can compute seven estimators (named JS, JS+, RML, RJS, RJS+, PT, and GPT). We introduce this R package along with the usage of the R functions and the “average-min-max” steps for the pool-adjacent violators algorithm. We conduct Monte Carlo simulations to validate the proposed R package to ensure that the package can work properly in a variety of scenarios. We also analyze a data example to show the ability of the R package.

A Meta-Analysis for Simultaneously Estimating Individual Means with Shrinkage, Isotonic Regression and Pretests

Meta-analyses combine the estimators of individual means to estimate the common mean of a population. However, the common mean could be undefined or uninformative in some scenarios where individual means are “ordered” or “sparse”. Hence, assessments of individual means become relevant, rather than the common mean. In this article, we propose simultaneous estimation of individual means using the James–Stein shrinkage estimators, which improve upon individual studies’ estimators. We also propose isotonic regression estimators for ordered means, and pretest estimators for sparse means. We provide theoretical explanations and simulation results demonstrating the superiority of the proposed estimators over the individual studies’ estimators. The proposed methods are illustrated by two datasets: one comes from gastric cancer patients and the other from COVID-19 patients.