The Design of Intervention Trials Involving Recurrent and Terminal Events

Simulation-based sample size calculations of marginal proportional means models for recurrent events with competing risks

In randomised controlled trials, the outcome of interest could be recurrent events, such as hospitalisations for heart failure. If mortality rates are non-negligible, both recurrent events and competing terminal events need to be addressed when formulating the estimand and statistical analysis is no longer trivial. In order to design future trials with primary recurrent event endpoints with competing risks, it is necessary to be able to perform power calculations to determine sample sizes. This paper introduces a simulation-based approach for power estimation based on a proportional means model for recurrent events and a proportional hazards model for terminal events. The simulation procedure is presented along with a discussion of what the user needs to specify to use the approach. The method is flexible and based on marginal quantities which are easy to specify. However, the method introduces a lack of a certain type of dependence. This is explored in a sensitivity analysis which suggests that the power is robust in spite of that. Data from a randomised controlled trial, LEADER, is used as the basis for generating data for a future trial. Finally, potential power gains of recurrent event methods as opposed to first event methods are discussed.

The incidence and predictors of new brain metastases in patients with non-small cell lung cancer following discontinuation of systemic therapy

OBJECTIVE

Patients with non-small cell lung cancer (NSCLC) metastatic to the brain are living longer. The risk of new brain metastases when these patients stop systemic therapy is unknown. The authors hypothesized that the risk of new brain metastases remains constant for as long as patients are off systemic therapy.

METHODS

A prospectively collected registry of patients undergoing radiosurgery for brain metastases was analyzed. Of 606 patients with NSCLC, 63 met the inclusion criteria of discontinuing systemic therapy for at least 90 days and undergoing active surveillance. The risk factors for the development of new tumors were determined using Cox proportional hazards and recurrent events models.

RESULTS

The median duration to new brain metastases off systemic therapy was 16.0 months. The probability of developing an additional new tumor at 6, 12, and 18 months was 26%, 40%, and 53%, respectively. There were no additional new tumors 22 months after stopping therapy. Patients who discontinued therapy due to intolerance or progression of the disease and those with mutations in RAS or receptor tyrosine kinase (RTK) pathways (e.g., KRAS, EGFR) were more likely to develop new tumors (hazard ratio [HR] 2.25, 95% confidence interval [CI] 1.33-3.81, p = 2.5 × 10-3; HR 2.51, 95% CI 1.45-4.34, p = 9.8 × 10-4, respectively).

CONCLUSIONS

The rate of new brain metastases from NSCLC in patients off systemic therapy decreases over time and is uncommon 2 years after cessation of cancer therapy. Patients who stop therapy due to toxicity or who have RAS or RTK pathway mutations have a higher rate of new metastases and should be followed more closely.

Evaluating response-adaptive randomization procedures for recurrent events and terminal event data using a composite endpoint

Recurrent event and terminal event data commonly arise in clinical and observational studies. To evaluate the efficacy of a treatment effect for both types of events, a composite endpoint has been used as a possible assessment, particularly when faced with high costs and a longer follow-up study. To model recurrent event processes complicated by the existence of a terminal event, joint frailty modeling has been typically employed. In this study, the objective was to develop some target-driven response adaptive randomization strategies using a composite endpoint based on joint frailty modeling. We first implemented a balanced randomized design and then investigated the response adaptive randomization. The former is intuitively first adopted while the latter is expected to be desirable and ethical in terms of allocating more subjects to the more effective treatment. The results show that the proposed procedures using a composite endpoint are capable of reducing the number of trial participants who receive inferior treatment while simultaneously reaching a desired optimal target as compared to a balanced randomized design. The R shiny application for calculating the sample size and allocation probabilities is also available. Finally, two clinical trials were used as pilot datasets to introduce the proposed procedures.

Response-adaptive treatment allocation for clinical studies with recurrent event and terminal event data

In long-term clinical studies, recurrent event data are frequently collected to contrast the efficacy of two different treatments. However, the recurrent event process can be stopped by a terminal event, such as death. For analyzing recurrent event and terminal event data, joint frailty modeling has recently received considerable attention because it makes it possible to study the joint evolution over time of both recurrent and terminal event processes and gives consistent and efficient parameters. For a two-arm clinical trial design based on these data sets, there has been limited research on investigating the balanced design, let alone adaptive treatment allocation. Although equal sample size allocation obtained for both treatments is intuitively first adopted in a trial design, if one treatment is expected to be superior, it may be desirable to allocate more subjects to the effective treatment. In this article, we calculate the required sample size based on restricted randomization and then propose a target response-adaptive randomization procedure for recurrent and terminal event outcomes based on the joint frailty model. A randomization procedure, the doubly adaptive biased coin design that targets some optimal allocations, is implemented. The proposed adaptive treatment allocation schemes have been shown to be capable of reducing the number of trial participants who receive inferior treatment while simultaneously reaching an optimal target, as well as retaining a comparable test power as compared to a restricted randomization design. Finally, two clinical studies, the COAPT trial and the A-HeFT trial, are used to illustrate the advantages of adopting the proposed procedure.