Conference Agenda

Observational data with time-to-event (survival) outcomes in medical research often exhibit a hierarchical (or clustered) structure. For instance, siblings tend to be more similar than randomly selected individuals from the general population, and study subjects may be nested within geographical areas or institutions such as schools and hospitals. Subjects within the same hierarchical unit are likely correlated, and ignoring this multilevel structure can lead to biased and inefficient results.

Multilevel hierarchical mixed-effects survival models are commonly used in such settings: these models account for correlation among study subjects within the same cluster and any potential unobserved heterogeneity. However, such analyses typically focus on fixed effects while marginalizing over the random effects, leading to post-estimation predictions that have either a subject-specific or population-level interpretation. Nevertheless, comparing hierarchical units is crucial in certain situations - such as when benchmarking the performance of medical institutions and providers while accounting for differences in case-mix covariates, when quantifying heterogeneity between clusters, or when comparing trials included in individual patient data (IPD) meta-analysis.

In this work, we propose combining regression standardization with cluster-specific posterior predictions of the random effects to quantify the performance of each hierarchical unit. By fixing the predicted random effects and standardizing over the remaining (observed) covariates, we obtain model-based predictions that retain their usual interpretation as survival probabilities - either at a specific time point or over the entire follow-up period. With multiple hierarchical levels, we can also isolate the effect of a specific level while marginalizing over the others. Contrasts of standardized survival probabilities can then be computed, which retain the natural interpretation as risk ratios or differences.

These standardized predictions quantify how the entire study population would have fared under the performance of each cluster, enabling fair comparisons between hierarchical units. Compared to commonly used approaches for quantifying contextual effects, such as the median hazard ratio, our proposed method yields more interpretable quantities that, under certain assumptions, can also have a causal interpretation.

We illustrate this methodology using data on bladder cancer patients with three levels of nesting: patients within surgeons, and surgeons within centers. Finally, we developed user-friendly software in Stata and R to facilitate the application of this method in practice.

Introduction

There is an abundant literature in statistics, biostatistics and econometrics on the modelling, estimation and inference of regression models for survival data subject to censoring. However, only a few of them consider a potential multimodality of the time-to-event. To the best of our knowledge, there is no model that considers both multimodality and the possible presence of a cure fraction, i.e. the presence of a fraction of subjects who do not experience the event of interest. Our aim is to develop a modelling approach that takes both these aspects into account. This is particularly useful in contexts such as modelling cancer recurrence, where recurrences may occur in several waves, but with a proportion of patients never relapsing.

Methods

In this work, we have built a model that considers both multimodality of the time-to-event and a cure fraction. To achieve this aim, we developed an accelerated failure time model in which the error term is assumed to follow a mixture of Sinh-Cauchy distributions. This approach offers greater robustness by combining the flexibility of mixture models with that of the Sinh-Cauchy distribution. We studied the properties of this distribution and implemented an estimation method using the EM algorithm. A simulation study was carried out to illustrate the performance of the proposed approach.

Results

Simulations have demonstrated the relevance and effectiveness of our approach for modelling multimodal time-to-event data with a proportion of cure. The methodology implemented to estimate the various parameters of the model provides reliable results in terms of bias, variance and MSE. Further investigations are ongoing on the selection of the number of components in the mixture, but preliminary results indicate that large flexibility is already achieved with a limited number of mixture components.

Conclusion

The results obtained show that the proposed model is an interesting alternative to traditional cure models in the presence of multimodality and cure while also providing good results for unimodal data. It therefore constitutes a more flexible and robust approach in the context of multimodal survival data with a proportion of cure. In the following, we intend to apply our methodology to real data.

Introduction: Joint modelling is a powerful statistical framework enabling a simultaneous modelling of longitudinal covariate and time-to-event outcome. Typically, a joint model consist of two subparts, a longitudinal sub-model which is modelled using a linear mixed model and a survival sub-model by Cox-proportional hazard model or parametric survival models. Apart from the interdependence between longitudinal and survival outcomes there may exist some unobserved random heterogeneity which can be modelled using a joint frailty model.

Methods: Here we considered joint models to determine the unobserved heterogeneity among individuals by integrating frailty terms in the survival sub-model. Incorporating frailty in the survival sub-model can allow an additional source of variation at the survival endpoint that cannot be explained by the longitudinal data. So here we developed joint frailty model and compared the results with Joint model, Cox model and Frailty model. The analyses were performed using R Software and illustrated using colorectal cancer data.

Results: Joint frailty model demonstrated improved model fit compared to the conventional Cox and Frailty model. When compared with the joint model, the joint frailty model accounts for frailty among individuals or clusters. The inclusion of frailty in the survival sub-model captured additional unexplained heterogeneity among individuals, leading to more precise hazard estimates. The association between the longitudinal biomarker and survival outcome and the frailty variance was found to be statistically significant, reinforcing the benefit of joint frailty modelling. Additionally, the significance of variance of the frailty term suggested the presence of substantial unobserved heterogeneity among individuals.

Conclusion: The joint frailty model provided a more comprehensive framework for analysing longitudinal and survival data by accounting for both the interdependence between these outcomes and unobserved individual variability. The findings highlight the importance of incorporating frailty terms in joint modelling, particularly in cancer prognostic studies where individual heterogeneity plays a crucial role.

Keywords: Joint model, Cox-Proportional hazard, Frailty, Joint-frailty model, Colorectal Cancer

Background: Randomisation is hardly achievable in controlled clinical trials of childhood leukaemia comparing standard continued chemotherapy with allogeneic stem cell transplantation (SCT). Usually standard chemotherapy will be stopped and SCT performed if a donor search identifies a suitable stem cell donor in existing registries of potential donors.

A fair comparison can be based on the two groups formed by the availability or non-availability of suitable stem cell donors. Donor availability is a temporarily unknown external baseline variable whose actual values will become known either when a suitable stem cell donor is identified from the registry or after the end of an unsuccessful donor search. However, donor search can be prematurely ceased, e.g. due to patients’ death or deterioration of patients’ health. Unfortunately, then donor availability and thus group membership will remain unknown. There is currently no graphical approach available to correctly illustrate survival probabilities over time for the two groups.

Methods: For each patient with prematurely ceased donor search, it is possible to calculate the probabilities that a suitable donor might or might not have been identified after the ceasing of the donor search, respectively. These probabilities are utilized to develop adjusted Kaplan-Meier curves for visual group comparison over time. These curves have a valid survival probability interpretation unlike the commonly applied Simon and Makuch curves where patients are allowed to change groups over time.

Estimated survival probabilities derived from adjusted Kaplan-Meier curves can also be used to assess group differences at selected long-term time points, which is especially interesting in case of non-proportional hazards. A corresponding statistical test is proposed and compared to other test strategies.

Results: Data from an international study of children with newly diagnosed Philadelphia chromosome-positive acute lymphoblastic leukaemia are used to exemplify the satisfactory performance of the new approach. Other methods are only able to estimate survival probabilities at selected time points. Results of the different methods are compared and discussed.

Conclusion: The newly proposed method allows for the first time to show Kaplan-Meier curves, when group membership at baseline is unknown and becomes only partly known over time.

In oncology, clinical trials are a cornerstone of evaluating new treatments. However, traditional designs often face significant challenges in efficiency, particularly when assessing multiple treatment options. The emergence of Multi-Arm Multi-Stage (MAMS) designs, such as the "Drop-the-losers" approach, offers innovative solutions by combining multiple hypotheses within a single trial framework.

This work evaluates the "Drop-the-losers" approach (as published by J. Wason et al. in 2017), focusing on its application in Phase II/III oncology trials. We extend existing methodologies by incorporating binary and survival endpoints, addressing limitations of original design which focused primarily on continuous outcomes. Using simulation studies, the statistical performance of the "Drop-the-losers" design was assessed across various scenarios. Key metrics included Type I error control, statistical power, and biases under varying endpoint distributions. Simulations involved a survival endpoint such as progression-free survival (PFS). Results demonstrated that the "Drop-the-losers" design effectively balances statistical rigor and efficiency. The design strongly controls Type I error while ensuring high power in detecting drug effects. Scenarios with harmful or ineffective treatments highlighted the ethical advantage of eliminating suboptimal options early, minimizing patient exposure to ineffective therapies.

One limitation identified is that long-term survival endpoints may not be mature enough to support early treatment selection analyses. Updating the endpoint of interest over time could align with clinical practices, starting with ORR at the first analysis, transitioning to Benefit-Risk scores or PFS at the second analysis, and concluding with OS at the final analysis. However, such an approach requires careful handling of correlations between drug effects across these endpoints (i.e., surrogacy).

This work provides a comprehensive framework for implementing "Drop-the-losers" design in clinical trials, demonstrating its potential to accelerate treatment evaluation in oncology while upholding ethical and scientific standards. This methodology contributes to the ongoing evolution of designs, underscoring their value in modern clinical research.

Wason, James et al. “A multi-stage drop-the-losers design for multi-arm clinical trials.” Statistical methods in medical research vol. 26,1 (2017): 508-524. doi:10.1177/0962280214550759