Vertical modelling (VM) offers an alternative approach to competing risks models, particularly when relaxing the proportional assumption or when facing missing causes of failure. It focuses on the joint probability, denoted as P(T, D), of the time to failure T and the cause of failure D, which is decomposed into (P(D|T)) and (P(T)). Both components rely on observable quantities: the total hazard and the relative cause-specific hazard, which can be easily estimated using multinomial regression and Cox proportional hazard models adding for covariates.

This paper introduces a novel approach by incorporating a random component in each part of the model to address unobserved heterogeneity in the presence of clusters. Data from the EMergenze-URgenze database, including Emergency Department (ED) access records from 63 Sicilian EDs in 2019, are used to analyze the risk of hospitalization or discharge during the length of stay once admitted to the hospital in a multi-center setting. The Cumulative Incidence Function (CIF) estimated from the vertical mixed model (VMM) is compared with that of the traditional competing risks frailty model.

The VMM with independent random effects represents the first attempt to extend VM and can be viewed as an alternative to the frailty competing risks model when computational time for estimation methods is prohibitive or when exploring different aspects of the data is desired.

In clinical study reports, the very first analysis typically focuses on patient disposition, providing an overview of how many patients have completed, discontinued, or are ongoing in the trial. This analysis is critical for assessing if the trial can reach its goals and highlighting any potential issues. It is particularly important if the study is still ongoing. A comprehensive disposition analysis can thus be just as important as the patient outcome analysis.

Although disposition tables are typically displayed as simple frequency statistics, they can be enriched through time-to-event analyses or, even better, with time-to-event plots. However, the range of survival analysis plots is limited, and the standard Kaplan-Meier plot, while widely used, is often misapplied when competing risks are involved.

In my presentation, I illustrate that stacked probability plots are an effective alternative, providing a clear visual representation that addresses the issue of competing risks. I further argue that a straightforward stacked proportion plot that illustrates descriptive proportions over time is yet another, more pragmatic alternative; it is both very easy to interpret and also immune to competing risks, making it an ideal choice for conveying patient disposition in ongoing clinical trials.

Illness-death models are used in survival analysis to study transitions between health states, particularly modelling progression from a disease-free state to illness and subsequently from illness to death. These models are frequently applied to clinical data to understand disease progression; however, in clinical practice, the exact timing of disease onset is often unobserved. Instead, this information may be interval-censored or unobserved due to death or censoring, which can bias estimates of disease incidence and regression coefficients. This challenge commonly arises in settings where diseases, like soft tissue sarcoma, can only be diagnosed at scheduled follow-up visits. For example, after initial surgery to remove a tumour, a patient may develop metastases that are only detected at these follow-ups – indicating the metastases developed sometime between the last negative and the first positive screening – resulting in interval-censored data for a binary time-dependent disease marker. Although ignoring interval-censoring introduces bias in estimating disease incidence and regression coefficients, its impact on model performance remains unclear.

This study investigates the effect of ignoring the interval-censored nature of observation times on model discrimination performance, measured in terms of time-specific Area Under the Receiver Operating Characteristic Curve (AUC) in both incident/dynamic and cumulative/dynamic definitions. Four different methods to estimate the illness-death model are compared: (1) the Cox model with disease state as time-dependent binary covariate (ignoring the interval-censored nature of the time-dependent covariate), (2) the piecewise-constant model accounting for interval-censoring estimated using the msm R-package, (3) the Weibull and (4) the M-spline models accounting for interval-censoring estimated using the SmoothHazard R-package. A simulation study is conducted considering several data scenarios simulated from illness-death models with Weibull transition hazards, considering different (i) sample sizes, (ii) types of death censoring, and (ii) follow-up visit intervals for observing the disease marker. Finally, the four methods are applied to a dataset of patients with high-grade soft-tissue sarcoma, and their performances are discussed.

The findings of this study suggest that, in the presence of interval-censored disease times, it is important to account for interval-censoring not only when estimating the parameters of the model but also when evaluating the discrimination performance of the disease.

In pharmacoepidemiologic and surgical research, immortal time bias often arises in observational settings, where the waiting period for treatment is misclassified as treatment benefits (Lévesque, et al., 2010). Cox-based methods that account for time-dependent factors, e.g. time-dependent Cox regression and landmark models, are widely used to address this issue (Gleiss, et al., 2018). However, interventions such as surgery may substantially alter patients’ risk profiles, eroding the common memoryless assumption on a single time scale for underlying hazards (Kragh Andersen, et al., 2021). Further complicating this multistate scenario is the interplay of transitions across prognostic states and their sojourn times. For example, disease progression while waiting for a transplant may render a patient ineligible for treatment—an aspect often inadequately addressed in these models.

In this work, we conducted a phase III simulation study to enable neutral comparison (Heinze, et al., 2024; Morris, et al., 2019) through: (1) defining the estimand for assessing mortality under different transplantation strategies in acute myeloid leukemia patients; (2) generating data from time-continuous Markov and semi-Markov processes that incorporate realistic Weibull and log-logistic distributions with multiple time scales and intrinsic rules for treatment administration; (3) assessing bias and other performance measures for estimates derived from different analytical approaches, including time-dependent Cox regression, landmark models, multistate models, and the g-formula; and (4) reanalyzing aggregated acute myeloid leukemia data from the AMLSG and AMLCG cohorts based on our simulation results.

Gleiss, A., Oberbauer, R. and Heinze, G. An unjustified benefit: immortal time bias in the analysis of time-dependent events. Transpl Int 2018;31(2):125-130.

Heinze, G., et al. Phases of methodological research in biostatistics-Building the evidence base for new methods. Biom J 2024;66(1):e2200222.

Kragh Andersen, P., et al. Analysis of time-to-event for observational studies: Guidance to the use of intensity models. Stat Med 2021;40(1):185-211.

Lévesque, L.E., et al. Problem of immortal time bias in cohort studies: example using statins for preventing progression of diabetes. Bmj 2010;340:b5087.

Morris, T.P., White, I.R. and Crowther, M.J. Using simulation studies to evaluate statistical methods. Stat Med 2019;38(11):2074-2102.