Conference Agenda

In leukemia studies, the endpoint event-free survival (EFS) is defined as time from diagnosis or study entry
until date of primary refractory disease, relapse or death, whichever occurs first. Since 2022 the European
LeukemiaNet (ELN) recommends for patients who are considered treatment failures, i.e. who are evaluable
for response but do not achieve remission by a pre-defined landmark or die before the landmark without
response assessments, to record the event at day 1. A similar recommendation holds for patients who are
alive but non-evaluable, only that they are censored at day 1. This leads to a potentially large drop of the
estimated EFS at day 1. However, the shift of some event times to day 1 has the consequence that the margin
of the drop is underestimated by the Kaplan-Meier estimator if patients are censored before the landmark.
Our aim is to present an unbiased estimate for EFS in which patients who are considered treatment failures
are accounted for in a way that is consistent with the intent of the recommendation. For this, ”Event at day 1”
is defined as one event type and ”Event after day 1” as a competing event and the Aalen-Johansen estimator
is used to estimate the event-specific transition probabilities, which are then combined in one EFS estimate.
In addition, we establish a formal link to cure models by equating the patients who are considered treatment
failures with the ”cured” proportion in cure model terminology and present inference methods.

The Cox regression model is an important method for analysing cohort survival data, with the consistency of its parameter estimator established under certain assumptions, such as the independence of all individuals. In practice, this assumption does not always hold. One such situation involves matched cohort datasets, where individuals are pairwise dependent. Matching is currently debated in studies involving stem cell transplantation, for instance, where randomising treatment is challenging or even infeasible. One approach to accounting for the correlation between matched partners is the stratified Cox model, however, one major drawback is reduced effective sample size. An alternative is the marginal Cox model, which estimates parameters in the same way as the classical Cox model. While this approach and the consistency of its estimator are discussed in the literature, a precise proof of consistency does not appear to be available. Once consistency is established, inference may be performed by resampling the matched pairs. This thesis aims to provide a proof of consistency. In addition to random right-censoring, the proof is extended to cover random left-truncation, censoring due to a competing risk and a combination of these mechanisms. Motivations for the latter come from registries on stem cell transplantation (competing risks) and from studying health policy interventions in calendar time (left-truncation). To assess the performance of the estimator in finite samples, a simulation study is conducted. Another simulation study compares the estimation of the variance of the parameter estimator using two methods: bootstrapping the matched pairs and applying a robust variance estimator that accounts for dependence.

Background. Difference in Restricted Mean Survival Time (DRMST) has emerged as a promising summary measure in non-inferiority trials with time-to-event outcomes, offering potential advantages over the widely used Hazard Ratio (HR). However, there are remaining practical methodological questions to be answered before it can be used in trials that were originally designed using HR. These include the choice of horizon time (τ), and the conversion of non-inferiority margins. The PATCH trial serves as a case study to explore whether DRMST can enhance power in non-inferiority tests under proportional hazards scenarios and how these issues should be addressed.

Methods. Simulations were conducted within the ADEMP framework, using PATCH trial design parameters and data generation mechanisms informed by observed data in the non-metastatic patients (M0) cohort. DRMST with various τ values was compared to HR in terms of power and type I error rates. Flexible parametric survival models estimated both DRMST and HR, and non-inferiority margins were converted under different assumptions about baseline hazard functions.

Results. DRMST consistently demonstrated higher power than HR when non-inferiority margins were correctly matched to baseline hazard distributions. However, mismatched margins led to reduced power or inflated type I error rates. Converting the margin based on the observed survival distribution in the control arm seemed an acceptable compromise, not inflating type I errors substantially. Shorter τ values yielded greater power, and DRMST allowed analyses to be conducted with fewer events, enabling earlier trial conclusions.

Conclusions. DRMST offers a robust alternative to HR in non-inferiority trials, with specific advantages in scenarios with proportional hazards. Careful selection of τ and margin conversion strategies is crucial for maximising power and maintaining statistical validity. Future research should address DRMST's performance in non-proportional hazards settings and refine guidance on its implementation in clinical trial design.

Background: Dementia is a chronic disease characterised by neurodegenerative processes and vascular brain injury. In prospective population-based cohorts, the diagnosis of dementia is usually interval-censored as it is made by a neuropsychologist at follow-up visits so that the exact time of dementia is unknown (1). The actual dementia status at death is also not always known as death may occur in between visits before a diagnosis of dementia can be made. The illness-death model for interval-censored data accounts for the uncertainty on the time of dementia and the probability of having dementia between the last visit without dementia and death (2). In this work, we proposed a new regularised estimation procedure for a high dimensional illness-death model with interval censored data, that performs variable selection.

Methods: We considered a proximal gradient hybrid algorithm maximising the regularised likelihood with elastic-net penalty on the 3 transitions (healthy to dementia, health to death and dementia to death). Our algorithm simultaneously estimates all three transitions' regression parameters while having different penalty parameters on each transition. The performances of our algorithm were evaluated in simulations and compared to the alternative strategy of the standard competing risk approach that neglects interval censoring. The method was applied to the data of a French population-based cohort to identify the most important predictors of dementia risk in the elderly.

Results: The illness-death model accounting for interval-censored data showed a very good ability to select relevant variables, in various scenarios. In comparison, the regularized competing risk model neglecting interval censoring tended to select irrelevant variables for the transition to dementia when associated with death. The proposed model also provided Mean Square Error of the probability of dementia very close to the oracle model that included only the relevant variables, and much smaller than the regularized model neglecting interval censoring. In the application, we identified regional brain volumes in addition to cognitive and socio-demographic markers as predictors of dementia risk.

Conclusion: Our illness-death model extended to elastic-net penalty (available in the penidm R package) offers a promising solution to handle interval censored data.

1. Leffondré et al. Interval-censored time-to-event and competing risk with death: is the illness-death model more accurate than the Cox model? International Journal of Epidemiology 2013; 42:1177–86

2. Joly et al. A penalized likelihood approach for an illness-death model with interval-censored data: application to age-specific incidence of dementia. Biostatistics 2002; 3:433–43

Background: Breast cancer treatment depends on tumour subtypes. In particular, patients with oestrogen receptor-positive (ER+) tumours are treated with hormonal therapy (either tamoxifen or aromatase inhibitors). In Sweden, the standard recommended treatment duration has historically been five years. However, current guidelines now suggest offering an additional five years of endocrine therapy to women at high risk of recurrence. This recommendation is supported by studies indicating that prolonged endocrine therapy may be associated with improved disease-free survival [1]. However, the impact of extended therapy on metastatic progression has not been quantified in a detailed way at the population level. In this article, we use a modelling approach to estimate the time-varying effect of hormonal treatment on the time to metastasis diagnosis. We then use it to compare 5-year and 10-year treatments for different tumour sizes.
Methods: We incorporated the effect of endocrine therapy in a biologically inspired natural history model of breast cancer [2]. Individual tumour growth was modelled as exponential, with an inverse growth rate following a gamma distribution. We model the metastatic seeding with a non-homogenous Poisson process dependent on tumour size. We incorporate the treatment effect as a multiplicative factor of the inverse growth rate, allowing us to quantify its impact on tumour dynamics.
Results: We fitted our model using a likelihood-based approach to a cohort of incident cases of 9716 patients diagnosed with invasive oestrogen receptor-positive breast cancer (ER+) between 2005 and 2020 who never received chemotherapy. 299 metastatic events occurred, with a median time to metastasis of 3.91 years [IQR: 2.36-6.15]. Based on our model estimates, for patients with 15mm and 20mm tumours the gains in 10-year metastasis-free survival, from receiving ten years instead of five years of hormonal treatment are expected to be approximately 1.5 and 3 percentage points, respectively.
Conclusion: Our natural history model quantifies the impact of prolonged hormonal treatment on metastatic events in ER+ breast cancer patients. The results demonstrate a significant reduction in tumour growth rates during treatment, supporting the extension of endocrine therapy to 10 years for patients with large tumours.

[1] Zeng, E., et al. (2022). Determinants and effectiveness of extending the duration of adjuvant hormone therapy beyond 5 years in patients with breast cancer. Cancer Research, 82(19), 3614-3621.

[2] Gasparini, A., & Humphreys, K. (2022). Estimating latent, dynamic processes of breast cancer tumour growth and distant metastatic spread from mammography screening data. Statistical methods in medical research, 31(5), 862-881.