Bivariate pseudo-observations for recurrent event analysis with terminal events

Efficient estimation of the marginal mean of recurrent events in randomized controlled trials

Recurrent events data are often encountered in biomedical settings, where individuals may also experience a terminal event such as death. A useful estimand to summarize such data is the marginal mean of the cumulative number of recurrent events up to a specific time horizon, allowing also for the possible presence of a terminal event. Recently, it was found that augmented estimators can estimate this quantity efficiently, providing improved inference. Improvement in efficiency by the use of covariate adjustment is increasing in popularity as the methods get further developed, and is supported by regulatory agencies EMA (2015) and FDA (2023). Motivated by these arguments, this article presents novel efficient estimators for clinical data from randomized controlled trials, accounting  for additional information from auxiliary covariates.   Moreover, in randomized studies when both right censoring and competing risks are present, we propose a novel doubly augmented estimator of the marginal mean  , which has two optimal augmentation components due to censoring and randomization. We provide theoretical and asymptotic details for the novel estimators,   also confirmed by simulation studies. Then, we discuss how to improve efficiency, both theoretically by computing the expected amount of variance reduction, and practically by showing the performance of different working regression models that are needed in the augmentation, when they are correctly specified or misspecified. The methods are applied to the   LEADER study, a randomized controlled trial that studied cardiovascular safety of     treatments in type 2 diabetes patients.

Pseudo-observations for bivariate survival data

The pseudo-observations approach has been gaining popularity as a method to estimate covariate effects on censored survival data. It is used regularly to estimate covariate effects on quantities such as survival probabilities, restricted mean life, cumulative incidence, and others. In this work, we propose to generalize the pseudo-observations approach to situations where a bivariate failure-time variable is observed, subject to right censoring. The idea is to first estimate the joint survival function of both failure times and then use it to define the relevant pseudo-observations. Once the pseudo-observations are calculated, they are used as the response in a generalized linear model. We consider 2 common nonparametric estimators of the joint survival function: the estimator of Lin and Ying (1993) and the Dabrowska estimator (Dabrowska, 1988). For both estimators, we show that our bivariate pseudo-observations approach produces regression estimates that are consistent and asymptotically normal. Our proposed method enables estimation of covariate effects on quantities such as the joint survival probability at a fixed bivariate time point or simultaneously at several time points and, consequentially, can estimate covariate-adjusted conditional survival probabilities. We demonstrate the method using simulations and an analysis of 2 real-world datasets.

Estimands and Cumulative Incidence Function Regression in Clinical Trials: Some New Results on Interpretability and Robustness

Regression analyses based on transformations of cumulative incidence functions are often adopted when modeling and testing for treatment effects in clinical trial settings involving competing and semi-competing risks. Common frameworks include the Fine-Gray model and models based on direct binomial regression. Using large sample theory we derive the limiting values of treatment effect estimators based on such models when the data are generated according to multiplicative intensity-based models, and show that the estimand is sensitive to several process features. The rejection rates of hypothesis tests based on cumulative incidence function regression models are also examined for null hypotheses of different types, based on which a robustness property is established. In such settings supportive secondary analyses of treatment effects are essential to ensure a full understanding of the nature of treatment effects. An application to a palliative study of individuals with breast cancer metastatic to bone is provided for illustration.

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.

Adverse events in single-arm clinical trials with non-fatal time-to-event efficacy endpoint: from clinical questions to methods for statistical analysis

BACKGROUND

In any single-arm trial on novel treatments, assessment of toxicity plays an important role as occurrence of adverse events (AEs) is relevant for application in clinical practice. In the presence of a non-fatal time-to-event(s) efficacy endpoint, the analysis should be broadened to consider AEs occurrence in time. The AEs analysis could be tackled with two approaches, depending on the clinical question of interest. Approach 1 focuses on the occurrence of AE as first event. Treatment ability to protect from the efficacy endpoint event(s) has an impact on the chance of observing AEs due to competing risks action. Approach 2 considers how treatment affects the occurrence of AEs in the potential framework where the efficacy endpoint event(s) could not occur.

METHODS

In the first part of the work we review the strategy of analysis for these two approaches. We identify theoretical quantities and estimators consistent with the following features: (a) estimators should address for the presence of right censoring; (b) theoretical quantities and estimators should be functions of time. In the second part of the work we propose the use of alternative methods (regression models, stratified Kaplan-Meier curves, inverse probability of censoring weighting) to relax the assumption of independence between the potential times to AE and to event(s) in the efficacy endpoint for addressing Approach 2.

RESULTS

We show through simulations that the proposed methods overcome the bias due to the dependence between the two potential times and related to the use of standard estimators.

CONCLUSIONS

We demonstrated through simulations that one can handle patients selection in the risk sets due to the competing event, and thus obtain conditional independence between the two potential times, adjusting for all the observed covariates that induce dependence.

Win-loss parameters for right-censored event data, with application to recurrent events

The win ratio has become a popular method for comparing multiple event data between two groups in clinical cohort studies. The win ratio compares the event data in prioritized order, where the first prioritized event is death and a typical example for the second prioritized event is hospitalization. Literature is sparse on inference for win and loss parameters, including the win ratio, for censored event data. Inference for two prioritized censored event times has been developed for independent right-censoring. Many clinical studies include recurrent event data such as hospitalizations. In this article, we suggest inference for win-loss parameters for death and a recurrent event outcome under independent right-censoring. The small sample properties of the proposed method are studied in a simulation study showing that the variance formula is accurate even for small samples. The method is applied on a data set from a randomized clinical trial.