Joint modeling of binary response and survival for clustered data in clinical trials

Multilevel joint frailty model for hierarchically clustered binary and survival data

Hierarchical data arise when observations are clustered into groups. Multilevel models are practically useful in these settings, but these models are elusive in the context of hierarchical data with mixed multivariate outcomes. In this article, we consider binary and survival outcomes and assume the hierarchical structure is induced by clustering of both outcomes within patients and clustering of patients within hospitals which frequently occur in multicenter studies. We introduce a multilevel joint frailty model that analyzes the outcomes simultaneously to jointly estimate their regression parameters and explicitly model within-patient correlation between the outcomes and within-hospital correlation separately for each outcome. Estimation is facilitated by a computationally efficient residual maximum likelihood method that further predicts cluster-specific frailties for both outcomes and circumvents the formidable challenges induced by multidimensional integration that complicates the underlying likelihood. The performance of the model and estimation procedure is investigated via extensive simulation studies. The practical utility of the model is illustrated through simultaneous modeling of disease-free survival and binary endpoint of platelet recovery in a multicenter allogeneic bone marrow transplantation dataset that motivates this study.

Multi-parameter regression survival modelling with random effects

We consider a parametric modelling approach for survival data where covariates are allowed to enter the model through multiple distributional parameters (i.e., scale and shape). This is in contrast with the standard convention of having a single covariate-dependent parameter, typically the scale. Taking what is referred to as a multi-parameter regression (MPR) approach to modelling has been shown to produce flexible and robust models with relatively low model complexity cost. However, it is very common to have clustered data arising from survival analysis studies, and this is something that is under developed in the MPR context. The purpose of this article is to extend MPR models to handle multivariate survival data by introducing random effects in both the scale and the shape regression components. We consider a variety of possible dependence structures for these random effects (independent, shared and correlated), and estimation proceeds using a h-likelihood approach. The performance of our estimation procedure is investigated by a way of an extensive simulation study, and the merits of our modelling approach are illustrated through applications to two real data examples, a lung cancer dataset and a bladder cancer dataset.

A class of two-sample nonparametric statistics for binary and time-to-event outcomes

We propose a class of two-sample statistics for testing the equality of proportions and the equality of survival functions. We build our proposal on a weighted combination of a score test for the difference in proportions and a weighted Kaplan–Meier statistic-based test for the difference of survival functions. The proposed statistics are fully non-parametric and do not rely on the proportional hazards assumption for the survival outcome. We present the asymptotic distribution of these statistics, propose a variance estimator, and show their asymptotic properties under fixed and local alternatives. We discuss different choices of weights including those that control the relative relevance of each outcome and emphasize the type of difference to be detected in the survival outcome. We evaluate the performance of these statistics with small sample sizes through a simulation study and illustrate their use with a randomized phase III cancer vaccine trial. We have implemented the proposed statistics in the R package SurvBin, available on GitHub (https://github.com/MartaBofillRoig/SurvBin).

Design of phase III trials with long-term survival outcomes based on short-term binary results

Pathologic complete response (pCR) is a common primary endpoint for a phase II trial or even accelerated approval of neoadjuvant cancer therapy. If granted, a two-arm confirmatory trial is often required to demonstrate the efficacy with a time-to-event outcome such as overall survival. However, the design of a subsequent phase III trial based on prior information on the pCR effect is not straightforward. Aiming at designing such phase III trials with overall survival as primary endpoint using pCR information from previous trials, we consider a mixture model that incorporates both the survival and the binary endpoints. We propose to base the comparison between arms on the difference of the restricted mean survival times, and show how the effect size and sample size for overall survival rely on the probability of the binary response and the survival distribution by response status, both for each treatment arm. Moreover, we provide the sample size calculation under different scenarios and accompany them with the R package survmixer where all the computations have been implemented. We evaluate our proposal with a simulation study, and illustrate its application through a neoadjuvant breast cancer trial.

Longitudinal-Survival Models for Case-Based Tuberculosis Progression

Introduction: Tuberculosis (TB) disease continues to be responsible for a high global burden with an estimated 10 million people falling ill each year and an estimated 1.45 million deaths. Widely carried out analyses to utilize routine data coming from this disease, and well-established in literature, have paid attention to time-to-event with sputum smear results being considered only at baseline or even ignored. Also, logistic regression models have been used to demonstrate importance of sputum smear results in patient outcomes. A feature presented by this disease, however, is that each individual patient is usually followed over a period of time with sputum smear results being documented at different points of the treatment curve. This provides both repeated measures and survival times, which may require a joint modeling approach. This study aimed to investigate the association between sputum smear results and the risk of experiencing unfavorable outcome among TB patients and dynamically predict survival probabilities.

Method: A joint model for longitudinal and time-to-event data was used to analyze longitudinally measured smear test results with time to experiencing unfavorable outcome for TB patients. A generalized linear mixed-effects model was specified for the longitudinal submodel and cox proportional hazards model for the time-to-event submodel with baseline hazard approximated using penalized B-splines. The two submodels were then assumed to be related via the current value association structure. Bayesian approach was used to approximate parameter estimates using Markov Chain Monte Carlo (MCMC) algorithm. The obtained joint model was used to predict the subject's future risk of survival based on sputum smear results trajectories. Data were sourced from routinely collected TB data stored at National TB Program database.

Results: The average baseline age was 35 (SD: 15). Female TB patients constituted 36.42%. Patients with previous history of TB treatment constituted 6.38% (event: 15.25%; no event: 5.29%). TB/HIV co-infection was at 31.23% (event: 47.87%; no event: 29.20%). The association parameter 1.03 (CI[1.03,1.04]) was found to be positive and significantly different from zero, interpreted as follows: The estimate of the association parameter α = 1.033 denoted the log hazard ratio for a unit increase in the log odds of having smear positive results. HIV status (negative) 0.47 (CI [0.46,49]) and history of TB treatment (previously treated) (2.52 CI [2.41,2.63]), sex (female) (0.82 CI [0.78,0.84]), and body mass index (BMI) categories (severe malnutrition being reference) were shown to be statistically significant.

Conclusion: Sputum smear result is important in estimating the risk to unfavorable outcome among TB patients. Men, previously treated, TB/HIV co-infected and severely malnourished TB patients are at higher risk of unfavorable outcomes.