A copula-based mixed Poisson model for bivariate recurrent events under event-dependent censoring

Regression analysis of multivariate recurrent event data allowing time-varying dependence with application to stroke registry data

In multivariate recurrent event data, each patient may repeatedly experience more than one type of event. Analysis of such data gets further complicated by the time-varying dependence structure among different types of recurrent events. The available literature regarding the joint modeling of multivariate recurrent events assumes a constant dependency over time, which is strict and often violated in practice. To close the knowledge gap, we propose a class of flexible shared random effects models for multivariate recurrent event data that allow for time-varying dependence to adequately capture complex correlation structures among different types of recurrent events. We developed an expectation-maximization algorithm for stable and efficient model fitting. Extensive simulation studies demonstrated that the estimators of the proposed approach have satisfactory finite sample performance. We applied the proposed model and the estimating method to data from a cohort of stroke patients identified in the University of Texas Houston Stroke Registry and evaluated the effects of risk factors and the dependence structure of different types of post-stroke readmission events.

Efficacy of GV1001 with gemcitabine/capecitabine in previously untreated patients with advanced pancreatic ductal adenocarcinoma having high serum eotaxin levels (KG4/2015): an open-label, randomised, Phase 3 trial

BACKGROUND

The TeloVac study indicated GV1001 did not improve the survival of advanced pancreatic ductal adenocarcinoma (PDAC). However, the cytokine examinations suggested that high serum eotaxin levels may predict responses to GV1001. This Phase III trial assessed the efficacy of GV1001 with gemcitabine/capecitabine for eotaxin-high patients with untreated advanced PDAC.

METHODS

Patients recruited from 16 hospitals received gemcitabine (1000 mg/m2, D 1, 8, and 15)/capecitabine (830 mg/m2 BID for 21 days) per month either with (GV1001 group) or without (control group) GV1001 (0.56 mg; D 1, 3, and 5, once on week 2-4, 6, then monthly thereafter) at random in a 1:1 ratio. The primary endpoint was overall survival (OS) and secondary end points included time to progression (TTP), objective response rate, and safety.

RESULTS

Total 148 patients were randomly assigned to the GV1001 (n = 75) and control groups (n = 73). The GV1001 group showed improved median OS (11.3 vs. 7.5 months, P = 0.021) and TTP (7.3 vs. 4.5 months, P = 0.021) compared to the control group. Grade >3 adverse events were reported in 77.3% and 73.1% in the GV1001 and control groups (P = 0.562), respectively.

CONCLUSIONS

GV1001 plus gemcitabine/capecitabine improved OS and TTP compared to gemcitabine/capecitabine alone in eotaxin-high patients with advanced PDAC.

CLINICAL TRIAL REGISTRATION

NCT02854072.

Semiparametric recurrent event vs time-to-first-event analyses in randomized trials: Estimands and model misspecification

Insights regarding the merits of recurrent event and time-to-first-event analyses are needed to provide guidance on strategies for analyzing intervention effects in randomized trials involving recurrent event responses. Using established asymptotic results we introduce a framework for studying the large sample properties of estimators arising from semiparametric proportional rate function models and Cox regression under model misspecification. The asymptotic biases and power implications are investigated for different data generating models, and we study the impact of dependent censoring on these findings. Illustrative applications are given involving data from a cystic fibrosis trial and a carcinogenicity experiment, following which we summarize findings and discuss implications for clinical trial design.

Semiparametric modelling and estimation of covariate-adjusted dependence between bivariate recurrent events

A time-dependent measure, termed the rate ratio, was proposed to assess the local dependence between two types of recurrent event processes in one-sample settings. However, the one-sample work does not consider modeling the dependence by covariates such as subject characteristics and treatments received. The focus of this paper is to understand how and in what magnitude the covariates influence the dependence strength for bivariate recurrent events. We propose the covariate-adjusted rate ratio, a measure of covariate-adjusted dependence. We propose a semiparametric regression model for jointly modeling the frequency and dependence of bivariate recurrent events: the first level is a proportional rates model for the marginal rates and the second level is a proportional rate ratio model for the dependence structure. We develop a pseudo-partial likelihood to estimate the parameters in the proportional rate ratio model. We establish the asymptotic properties of the estimators and evaluate the finite sample performance via simulation studies. We illustrate the proposed models and methods using a soft tissue sarcoma study that examines the effects of initial treatments on the marginal frequencies of local/distant sarcoma recurrence and the dependence structure between the two types of cancer recurrence.

Joint analysis of recurrence and termination: A Bayesian latent class approach

Like many other clinical and economic studies, each subject of our motivating transplant study is at risk of recurrent events of non-fatal tissue rejections as well as the terminating event of death due to total graft rejection. For such studies, our model and associated Bayesian analysis aim for some practical advantages over competing methods. Our semiparametric latent-class-based joint model has coherent interpretation of the covariate (including race and gender) effects on all functions and model quantities that are relevant for understanding the effects of covariates on future event trajectories. Our fully Bayesian method for estimation and prediction uses a complete specification of the prior process of the baseline functions. We also derive a practical and theoretically justifiable partial likelihood-based semiparametric Bayesian approach to deal with the analysis when there is a lack of prior information about baseline functions. Our model and method can accommodate fixed as well as time-varying covariates. Our Markov Chain Monte Carlo tools for both Bayesian methods are implementable via publicly available software. Our Bayesian analysis of transplant study and simulation study demonstrate practical advantages and improved performance of our approach.

Dependence modeling for multi-type recurrent events via copulas

When several types of recurrent events may arise, interest often lies in marginal modeling and studying the nature of the dependence structure. In this paper, we propose a multivariate mixed-Poisson model with the dependence between events accommodated by type-specific random effects which are associated through use of a Gaussian copula. Such models retain marginal features with a simple interpretation, reflect the heterogeneity in risk for each type of event, and provide insight into the dependence between the different types of events. Semiparametric inference is proposed based on composite likelihood to avoid high dimensional integration. An application to a study of nutritional supplements in malnourished children is given in which the goal is to evaluate the reduction in the rate of several different kinds of infection.

Power and sample size calculation for paired recurrent events data based on robust nonparametric tests

The purpose of this paper is to develop a formula for calculating the required sample size for paired recurrent events data. The developed formula is based on robust non-parametric tests for comparing the marginal mean function of events between paired samples. This calculation can accommodate the associations among a sequence of paired recurrent event times with a specification of correlated gamma frailty variables for a proportional intensity model. We evaluate the performance of the proposed method with comprehensive simulations including the impacts of paired correlations, homogeneous or nonhomogeneous processes, marginal hazard rates, censoring rate, accrual and follow-up times, as well as the sensitivity analysis for the assumption of the frailty distribution. The use of the formula is also demonstrated using a premature infant study from the neonatal intensive care unit of a tertiary center in southern Taiwan. Copyright © 2017 John Wiley & Sons, Ltd.

A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution

The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world high-dimensional count-valued data found in word counts, genomics, and crime statistics, for example, exhibit rich dependencies, and motivate the need for multivariate distributions that can appropriately model this data. We review multivariate distributions derived from the univariate Poisson, categorizing these models into three main classes: 1) where the marginal distributions are Poisson, 2) where the joint distribution is a mixture of independent multivariate Poisson distributions, and 3) where the node-conditional distributions are derived from the Poisson. We discuss the development of multiple instances of these classes and compare the models in terms of interpretability and theory. Then, we empirically compare multiple models from each class on three real-world datasets that have varying data characteristics from different domains, namely traffic accident data, biological next generation sequencing data, and text data. These empirical experiments develop intuition about the comparative advantages and disadvantages of each class of multivariate distribution that was derived from the Poisson. Finally, we suggest new research directions as explored in the subsequent discussion section.