Generalized pairwise comparisons for censored data: An overview

Covariate-adjusted generalized pairwise comparisons in small samples

Semiparametric probabilistic index models allow for the comparison of two groups of observations, whilst adjusting for covariates, thereby fitting nicely within the framework of generalized pairwise comparisons (GPC). As with most regression approaches in this setting, the limited amount of data results in invalid inference as the asymptotic normality assumption is not met. In addition, separation issues might arise when considering small samples. In this article, we show that the parameters of the probabilistic index model can be estimated using generalized estimating equations, for which adjustments exist that lead to estimators of the sandwich variance-covariance matrix with improved finite sample properties and that can deal with bias due to separation. In this way, appropriate inference can be performed as is shown through extensive simulation studies. The known relationships between the probabilistic index and other GPC statistics allow to also provide valid inference for example, the net treatment benefit or the success odds.

Restricted Net Treatment Benefit in oncology

OBJECTIVES

The restricted Net Treatment Benefit (rNTB) is a clinically meaningful and tractable estimand of the overall treatment effect assessed in randomized trials when at least one survival endpoint with time restriction is used. Its interpretation does not rely on parametric assumptions such as proportional hazards, can be estimated without bias even in the presence of independent right-censoring, and can include a prespecified threshold of minimal clinically relevant difference. To demonstrate that the rNTB, corresponding to the NTB during a predefined time interval, is a meaningful and adaptable measure of treatment effect in clinical trials.

METHODS

In this simulation study, we tested the impact on the rNTB value, estimation, and power of several factors including the presence of a delayed treatment effect, minimal clinically relevant difference threshold value, restriction time value, and the inclusion of both efficacy and toxicity in the rNTB definition. The impact of right censoring on rNTB was assessed in terms of bias. rNTB-derived statistical tests and log rank (LR) tests were compared in terms of power.

RESULTS

RNTB estimates are unbiased even in case of right-censoring. rNTB may be used to estimate the benefit/risk ratio of a new treatment, for example, taking into account both survival and toxicity and include several prioritized outcomes. The estimated rNTB is much easier to interpret in this context compared to NTB in the presence of censoring since the latter is intrinsically dependent on the follow-up duration. Including toxicity increases the test power when the experimental treatment is less toxic. rNTB-derived test power increases when the experimental treatment is associated with longer survival and lower toxicity and might increase in the presence of a cure rate or a delayed treatment effect. Case applications on the PRODIGE, Checkmate-066, and Checkmate-067 trials are provided.

CONCLUSIONS

RNTB is an interesting alternative to describe and test the treatment's effect in a clear and understandable way in case of restriction, particularly in scenarios with nonproportional hazards or when trying to balance benefit and safety. It can be tuned to take into consideration short- or long-term survival differences and one or more prioritized outcomes.

Istore: a project on innovative statistical methodologies to improve rare diseases clinical trials in limited populations

BACKGROUND

The conduct of rare disease clinical trials is still hampered by methodological problems. The number of patients suffering from a rare condition is variable, but may be very small and unfortunately statistical problems for small and finite populations have received less consideration. This paper describes the outline of the iSTORE project, its ambitions, and its methodological approaches.

METHODS

In very small populations, methodological challenges exacerbate. iSTORE's ambition is to develop a comprehensive perspective on natural history course modelling through multiple endpoint methodologies, subgroup similarity identification, and improving level of evidence.

RESULTS

The methodological approaches cover methods for sound scientific modeling of natural history course data, showing similarity between subgroups, defining, and analyzing multiple endpoints and quantifying the level of evidence in multiple endpoint trials that are often hampered by bias.

CONCLUSION

Through its expected results, iSTORE will contribute to the rare diseases research field by providing an approach to better inform about and thus being able to plan a clinical trial. The methodological derivations can be synchronized and transferability will be outlined.

Factorial survival analysis for treatment effects under dependent censoring

Factorial analyses offer a powerful nonparametric means to detect main or interaction effects among multiple treatments. For survival outcomes, for example, from clinical trials, such techniques can be adopted for comparing reasonable quantifications of treatment effects. The key difficulty to solve in survival analysis concerns the proper handling of censoring. So far, all existing factorial analyses for survival data have been developed under the independent censoring assumption, which is too strong for many applications. As a solution, the central aim of this article is to develop new methods for factorial survival analyses under quite general dependent censoring regimes. This will be accomplished by combining existing nonparametric methods for factorial survival analyses with techniques developed for survival copula models. As a result, we will present an appealing F-test that exhibits sound performance in our simulation study. The new methods are illustrated in a real data analysis. We implement the proposed method in an R function surv.factorial(.) in the R package compound.Cox.

The net benefit for time-to-event outcome in oncology clinical trials with treatment switching

BACKGROUND

The net benefit is an effect measure for any type of endpoint, including the time-to-event outcome, and can provide intuitive and clinically meaningful interpretation. It is defined as the probability of a randomly selected subject from the experimental arm surviving by at least a clinically relevant time longer than a randomly selected subject from the control arm. In oncology clinical trials, an intercurrent event such as treatment switching is common, which potentially causes informative censoring; nevertheless, conventional methods for the net benefit are not able to deal with it. In this study, we proposed a new estimator using the inverse probability of censoring weighting (IPCW) method and illustrated an oncology clinical trial with treatment switching (the SHIVA study) to apply the proposed method under the estimand framework.

METHODS

The net benefit can be estimated using the survival functions of each treatment group. The proposed estimator was based on the survival functions estimated by the inverse probability of the censoring weighting method that can handle covariate-dependent censoring. The simulation study was undertaken to evaluate the operating characteristics of the proposed estimator under several scenarios; we varied the shapes of the survival curves, treatment effect, covariates effect on censoring, proportion of the censoring, threshold of the net benefit, and sample size. We also applied conventional methods (the scoring rules by Péron or Gehan) and the proposed method to the SHIVA study.

RESULTS

Our simulation study showed that the proposed estimator provided less biased results under the covariate-dependent censoring than existing estimators. When applying the proposed method to the SHIVA study, we were able to estimate the net benefit by incorporating the information of the covariates with different estimand strategies to address the intercurrent event of the treatment switching. However, the estimates of the proposed method and those of the aforementioned conventional methods were similar under the hypothetical strategy.

CONCLUSIONS

We proposed a new estimator of the net benefit that can include covariates to account for the possibly informative censoring. We also provided an illustrative analysis of the proposed method for the oncology clinical trial with treatment switching using the estimand framework. Our proposed new estimator is suitable for handling the intercurrent events that can potentially cause covariate-dependent censoring.

Composite endpoints, including patient reported outcomes, in rare diseases

BACKGROUND

When assessing the efficacy of a treatment in any clinical trial, it is recommended by the International Conference on Harmonisation to select a single meaningful endpoint. However, a single endpoint is often not sufficient to reflect the full clinical benefit of a treatment in multifaceted diseases, which is often the case in rare diseases. Therefore, the use of a combination of several clinically meaningful outcomes is preferred. Many methodologies that allow for combining outcomes in a so-called composite endpoint are however limited in a number of ways, not in the least in the number and type of outcomes that can be combined and in the poor small-sample properties. Moreover, patient reported outcomes, such as quality of life, often cannot be integrated in a composite analysis, in spite of their intrinsic value.

RESULTS

Recently, a class of non-parametric generalized pairwise comparisons tests have been proposed, which members do allow for any number and type of outcomes, including patient reported outcomes. The class enjoys good small-sample properties. Moreover, this very flexible class of methods allows for prioritizing the outcomes by clinical severity, allows for matched designs and for adding a threshold of clinical relevance. Our aim is to introduce the generalized pairwise comparison ideas and concepts for rare disease clinical trial analysis, and demonstrate their benefit in a post-hoc analysis of a small-sample trial in epidermolysis bullosa. More precisely, we will include a patient relevant outcome (Quality of life), in a composite endpoint. This publication is part of the European Joint Programme on Rare Diseases (EJP RD) series on innovative methodologies for rare diseases clinical trials, which is based on the webinars presented within the educational activity of EJP RD. This publication covers the webinar topic on composite endpoints in rare diseases and includes participants' response to a questionnaire on this topic.

CONCLUSIONS

Generalized pairwise comparisons is a promising statistical methodology for evaluating any type of composite endpoints in rare disease trials and may allow a better evaluation of therapy efficacy including patients reported outcomes in addition to outcomes related to the diseases signs and symptoms.